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CHAPTER 4 -- THE SOLAR SYSTEM

© John F. Graham, 1995
Photos courtesy NASA

From the Earth there are about 5000 celestial bodies visible to the naked eye on a clear night at the top of some mountain far from city lights. We are well acquainted with the obvious bodies the SUN and the Moon. Ancient humans were perceptive enough to recognize that they could see a lot easier in the presence of the Sun than the Moon and also they were warmed by the Sun while the Moon seemed cold. Because of the warmth of the Sun, humans thought that it was a perfect sphere of celestial fire created by the Gods. The Greeks went one step further and named their god Apollo as the God of the Sun; Apollo brought heat and light to Earth because of his countenance of golden hair, a tunic of golden leopard skin, a chariot of beaten gold pulled by horses with golden manes and flaming eyes, and his armament of a gold bow and gold arrows. Little did the ancients know that their god was a ball of burning gas.

The Sun is a class G star composed of ionized hydrogen and helium gas located 150 million Km (93 million miles) from the Earth. Current calculations give its age at about 5 billion years which is about half its life span. It is a second generation star which means that it formed from the remains of some other star which may have exploded between five and ten billion years ago.

The Sun has a mass of 1.98 x 1030 kilograms about 333,000 times larger than the Earth's mass of 5.98 x 1024 kilograms. The Sun's radius is about 695,000 Km compared to the Earth's radius of 6378 Km. These masses and radii really don't make much sense to the ordinary human brain, so let's put them into terms we can understand. If the Sun were an ordinary eight inch soccer ball, then the Earth would be the size of a peppercorn. If you have enough patience and enough money to buy 333,000 pepper corns to see if they fit into an eight inch soccer ball you'd get an even greater appreciation of how large the Sun is. It is so large that it contains 99.86% of the entire mass of the solar system. If one includes all nine known planets, their moons, the asteroids, the meteorites, the comets, and all the remaining dust in the local area it would be 0.14% of the entire mass of the solar system.

Because the Sun is an enormous gaseous sphere it rotates faster around the equator than it does at the poles, 27 days versus about 35 days. Its surface temperature is about 5770º Kelvin (Kelvin scale equals the Fahrenheit scale per degree with the Kelvin 0º starting at about - 463º Fahrenheit) and its interior temperature is about 16 million degrees Kelvin. Its total radiated energy is equivalent to 100 billion tons of TNT exploding per second or the same as a significant portion of the Earth's entire nuclear arsenal exploding every second. This power is obviously important to us because it supports all life on the Earth. It causes seasonal changes, ocean current flows, and atmospheric circulation. It also is responsible for photosynthesis for plant life from which is derived all food and fossil fuels.

The Sun contains several major sections: the core along with the radiative and the convective layers. Even though the nuclear burning occurs in the core, the heat and light generated from this process take about 10 million years to reach the Sun's surface. Once the photons depart the core they must travel through the radiative layer to the convective zone where the temperatures go from 8 million to 7000ºKelvin. After reaching the Sun's surface also known as the photosphere, the photon travels through the chromosphere and it eventually reaches the corona which extends from the Sun in the form of a solar wind and finally the photon reaches the Earth millions of years after it was formed in the Sun's core.

Beyond the Sun in constant, near circular orbits are the nine known planets and other bodies which make up the matter in the solar system. These are divided into three major categories: the terrestrial planets, the gas giants and the minor planetesimals.

The terrestrial planets include the inner four planets or Mercury, Venus, Earth, and Mars. These bodies are characterized by their solid densities, iron-nickel cores, solid mantles and crusts, and cratered surfaces. Only two of these planets have moons, Earth and Mars.

The gas giants are Jupiter, Saturn, Uranus, and Neptune. These planets are huge gas balls consisting largely of hydrogen, helium, and methane. Each of these are characterized by a solid, rocky inner core surrounded by liquid or metallic hydrogen, and topped by a gaseous hydrogen, helium, and methane mixture. Each of these giant planets has a number of moons of varying sizes and each has a turbulent churning atmosphere. Located in the equatorial plane of all of these giants are rings of ice, small rocks, and dust. The most visible of these are Saturn's gorgeous set of rings which make it the most beautiful body in the solar system.

The minor planetesimals include Pluto and its moon Charon, the asteroids, meteorites, comets, and dust. These are as the name implies minor bodies which never accreted into anything larger than a minor moon of one of the gas giants. Let's look at each of the planets, it's size and distance relative to the Sun, and note some of the major discoveries made during the space age.

Mercury is the closest planet to the Sun. It can only be seen from Earth under the most perfect conditions of viewing and then only at twilight or early dawn. Because it was seen so rarely by the ancient astronomers it was named after the swift messenger of the Roman Gods who had wings on his heels and his helmet. This planet is located about ninety-five million Km (58.5 million miles) from the Sun and moves so fast that one Mercury year is equivalent to 88 Earth days. Scientists have also measured one Mercury day to be about 58.7 Earth days long.

Mercury's diameter is about 4880 Km or about 38% of the Earth's diameter of 12756 Km and it's about 1.4 times larger than the Earth's Moon. If the Sun were an eight inch soccer ball, Mercury would be the size of a small pin hole in a piece of paper. Mercury's mass is 5.6% of the Earth's mass of 5.9742 x 1024 kilograms, but is five times more massive than the Moon. This is because of the density of its core. This means that Mercury's core of iron-nickel is larger than the Earth's Moon. Even though it is almost the size of the Earth's Moon, Mercury has a gravitational acceleration one third of Earth's while the Moon has a value one sixth of Earth's gravity. Additionally, Mercury has no moon.

Surprisingly, Mercury was found to have a magnetic field; this is astonishing because the core is thought to have solidified at least two billion years ago, thus not allowing any convective currents for magnetism to flow through it for the generation of a magnetic field.

Mercury's surface looks very much like the Moon with huge craters from the hundreds of kilometers down to craters smaller than 100 meters. The most distinctive feature on Mercury is the Caloris Basin, a crater with a diameter of 1300 Km which may have been formed from a gigantic impact occurring about the time of Mercury's final formation.

There is no atmosphere on Mercury, although a thin layer of hydrogen, helium, and sodium have been detected close to the planet. The best explanation for this phenomenon is that hydrogen and helium particles from the solar wind have become trapped in Mercury's magnetic field which is rather close to the planet. Similarly, the sodium may have come from the planet itself, the remnants of impacts many years ago which have become trapped in the planet's weak magnetic field.

As recently as the summer of 1994 the radio telescope at Arecibo, Puerto Rico claims to have found possible ice caps on the Mercurian north and south poles. This is really startling since the temperature on Mercury's surface is as high as 430º Celsius ( 806ºFahrenheit) in the direct sunlight and -170º Celsius (-274º Fahrenheit) in the shade.

This planet warrants further study and NASA has a robotic exploration of Mercury in its plans for 2004. Perhaps then we will know whether or not Mercury really has ice caps and get a good view of the planet as a whole system.

If the Earth had a twin it would be Venus. Both planets are nearly the same in diameter (12,110 kilometers for Venus and 12,756 kilometers for Earth), composition, mass, and density. If the Sun were an eight inch soccer ball, Venus would be a peppercorn, just like the Earth. The ancients often pondered the brilliant shimmering star which appeared early in the morning just before sunrise or hung like a brilliant jewel a few hours after sunset. Because of this beauty, Venus was named after the Roman Goddess of love and beauty.

With the invention of the telescope astronomers frequently looked at this bright planet. They discovered that Venus had phases similar to the Moon and showed evidence of a perpetual cloud cover. Imaginations abounded as scientists and science fiction writers alike speculated that the planet was a jungle teeming with plant and animal life known only in our own equatorial jungles. This was soon discarded in the late 1950s when radio astronomers detected an atmosphere of carbon dioxide and temperatures around 900º Fahrenheit. In this atmosphere and at these temperatures, life as it exists on Earth would be unlikely. The first space probes to Venus confirmed that the planet was lifeless and would be a great candidate for one of Dante's circles of Hell in his Divine Comedy.

Venus is located 108.2 million Km ( 66.8 million miles) from the Sun. It rotates once around the Sun in 226.46 Earth days and has a day which is longer than its year, 243 Earth days. The planet rotates extremely slowly on its axis in a retrograde direction; this means that the Sun would rise in the west and set in the east if a person were on a Venus with no clouds. Because of this slow rotation the planet does not have the oblateness of the Earth; Venus is an almost perfect sphere.

Venus has no oceans and it hides behind a perpetual cloud cover 15 Km thick; it is so thick that only 1% of the sunlight which strikes Venus actually arrives at its surface. Containing large amounts of sulfuric acid the clouds start about 45 Km altitude and move from east to west with a speed faster than three times that of a hurricane on Earth or from 500 to 1000 Km per hour. Beneath the clouds these winds subside substantially until they are non-existent on the planet's surface.

Beneath the sulfuric acid clouds the atmosphere appears to contain 96.4% carbon dioxide, 3.4% nitrogen, 0.02% sulfur dioxide, and 0.14% water vapor. The clouds and the carbon dioxide have created an atmosphere so dense that it crushes down on the planet 's surface with a pressure 97 times that on the Earth's surface (14.7 lbs/in2). This pressure is equal to that found in the Earth's oceans at a depth of 3000 feet. The various space probes have noted lightning in the clouds especially in areas over volcanic regions which indicates that there may still be frequent volcanic activity occurring on the planet today.

There is no moon orbiting Venus and even though Venus has a iron-nickel core very much like Earth's there is no magnetic field on this planet; this lack of a magnetic field may be due to the planet's slow rotation. Venus has a tortured surface which is covered by at least 85% volcanic rock from lava flows. This indicates volcanic activity and possible tectonic plate movement. There is also abundant evidence of impact cratering over the entire planet. Additionally, there are mountains on the planet which have been deformed strictly by geologic activity. There is no erosion on the planet due to neither flowing water nor surface wind.

Astronaut James Lovell upon returning from orbiting the Moon on Apollo 8 looked at the Earth and remarked that it hung in space like a beautiful jewel and he wondered if a traveler from elsewhere would realize that there was life on that fragile blue planet. Since we are so intimately familiar with the Earth, most people think that humans have discovered all there is to know about our home and that exploration should concentrate on the other planets of the solar system. Nothing is further from the truth. We have made many discoveries about our planet during the space age. In fact, every time we have discovered something different on another planet of our solar system we have been able to apply that discovery to our way of looking at the Earth and have learned more of how our world works.

The Earth's orbit around the Sun is circular with a radius of 150 million Km (93 million miles). This distance also describes an astronomical unit, a scale used to define distances in the solar system. The Earth travels around the Sun once every 365.25 days at an average speed of 30 Km per second. The Earth rotates once every 24 hours on its axis bringing alternate periods of daylight and darkness to the entire globe.

The Earth is a spheroid with a diameter of 12756 Km (7874 miles), a mass of 5.98 x 1024 kilograms, and a density of 5.5 grams per centimeter cubed. If the Sun were an eight inch soccer ball the Earth would be the size of a peppercorn. The interior of the Earth includes a core of liquid iron-nickel, a mantle and a crust. On the crust are the Earth's land and oceans containing some evidence that the Earth first formed as a solid coherent body about 4.7 billion years ago.

The continents of the Earth drift on structures called tectonic plates. At the boundaries of these plates are a number of volcanoes; earthquakes occur along these boundaries with extreme regularity as the continental plates shift. The formation of the Himalayan Mountains by the movement of the Indian landmass into Asia provides proof of the tectonic plate movement. Each year the mountains seem to grow taller as they are pushed higher by the pressure of India against the Asian Landmass.

The Earth has a strong magnetic field with poles at the north in Canada and the south on the shores of Antarctica. This magnetic field deflects the solar wind particles preventing them from striking the ozone layer which protects the Earth's surface from high electromagnetic energy. The Earth's magnetic field also causes the Van Allen radiation belts, two toroidal regions t he first ranging from 2000 to 5000 Km and the second from 13,000 to 19,000 Km. These strong belts of trapped particles from the solar wind could become a serious hazard to astronauts during time of increased solar activity.

The most abundant chemical on the Earth's surface is water. It is present in liquid state in the oceans, rivers and lakes; in the gaseous state in the atmosphere; and in solid state in the ice caps. It is present in every biological entity on the planet and even combines with some of the rocks to form hydrates. Every living thing on Earth needs water in order to survive.

Significant to life on this planet is the dense atmosphere consisting of 78% nitrogen, 21% oxygen and one percent argon. Water vapor is also present varying from zero to 4% of the atmosphere at given locations. The air pressure for the Earth's surface is about 14.7 pounds per square inch equivalent to 760 millimeters of mercury. The atmosphere is divided into five distinct vertical regions known as the troposphere, the stratosphere, the mesosphere, the ionosphere, and the thermosphere. Most life lives in the troposphere while space begins in the thermosphere.

Earth's atmosphere has been formed and dictated by biological activity taking place at its surface. The most important of these cycles is known as the oxygen/carbon dioxide cycle in which plants take carbon dioxide and water from the air via photosynthesis and transform it into sugar and oxygen. Animals inhale the oxygen and exhale carbon dioxide back to the plant life to repeat the process. Most of this process has occurred by means of microscopic sea algae living in the oceans and has given us our oxygen supply which we use today.

Earth's nearest neighbor, the Moon, is also the most explored terrestrial body other than the Earth. Ancient humans used to speculate what the Moon was and whether or not other beings lived there. With the invention of telescopes and the scientific equipment of the 20th Century, the Moon was determined to be a lifeless planet of various rocks formed into hills, valleys, mountains, and thousands of craters.

The Moon has a diameter of 3476 Km (2146 miles) and its mass is 7.35 x 1022 kilograms. It has an acceleration due to gravity one sixth of Earth's, and compared to an eight inch soccer ball Sun its size would be a pin head. The Moon's average distance from Earth is about 389,000 Km (240,000 miles). Because of this distance the Moon affects the tides on Earth. The Moon travels around the Earth once every 28 days and it rotates once in the same time period. Due to this rotation frequency, we only see on e side of the Moon. During its monthly rotation around the Earth the Moon waxes and wanes in various phases from full Moon to Half Moon to quarter Moon to new Moon and then back again.

The Moon has no magnetic field, but does have geological features called highlands and Mare. The highlands are similar to mountains which have been worn down by billions of years of bombardment by particles. The Mare are dark masses of lava which came from molten seas formed when meteorites slammed deep into the interior of the Moon covering its surface with this molten rock. Over the years, the Mare in turn have also been bombarded by numerous meteorites which leave the signatures of their visit spectacularly. This caused the other significant features on the Moon, craters. There are thousands of these craters covering the surface of the Moon. They range in size from the pinhead strikes of microscopic meteorites to the giant craters such as Tycho and Copernicus.

For over 4 billion years the Moon waited in its orbit around the Earth until 1969 when humans began to explore it. Six human trips to the Moon returned 842 pounds of rock and soil samples to the Earth. These samples showed no life on the Moon, no water in any form and no oxygen. In the first mission after Apollo, the space probe Clementine showed there was a possibility of ice being formed in the craters of the lunar poles. This discovery will be monumental because it could pave the way to a permanent lunar base.

The fourth terrestrial planet from the Sun is Mars. Named for the Roman God of War because of its red coloring, Mars is located 249 million Km (154 million miles) from the Sun. When their telescopes were first trained on Mars, astronomers noted two polar caps, which seemed to grow and shrink as the seasons changed. Later, with more powerful telescopes, an Italian astronomer thought he could see canals on the surface of the planet. An American millionaire, Percival Lowell, was fascinated with the concept that there may be a dying civilization on the planet that was bringing water from the polar caps to the equator to keep the intelligent beings alive. Because of Mars, Lowell built an observatory in his name to explore Mars by telescope from Earth. On July 14, 1965 the Mariner 4 spacecraft passed within 9800 Km of the planet and returned 21 pictures which showed that not only were there no canals, but also there was a landscape which resembled the Moon's.

Mars seems to be a frozen miniature Earth. It spins once on its axis every of 24.6 hours and revolves around the Sun in 687 Earth days. The mass of the planet is 11% of the Earth's mass and compared to an eight inch soccer ball Sun, Mars would be another pinhead. Mars diameter is 6760 Km giving it an average density of 3.86 grams per centimeter cubed. The interior of Mars is similar to Earth's with a large iron-nickel core surrounded by a mantle and a crust. Even though Mars has a metal core and spin s on its axis it surprisingly has no magnetic field. The only readily answer to the absence of the magnetic field is that Mars' inner core has solidified similar to Mercury's and the Moon's. The lack of a magnetic field subjects Mars to the full brunt o f the solar wind.

Although there were no canals found on Mars, craters were discovered in abundance. Concentrated in the southern hemisphere of the planet these were not the sharp craters found on the Moon, but were rather well-rounded which meant that some sort of erosion was taking place by wind that caused planet-wide sandstorms and blowing dust.

While Mars' southern hemisphere has all the craters, its northern hemisphere has some fascinating geologic features. Among the most significant discoveries in the northern hemisphere were the presence of volcanoes. Three large volcanoes lie in a row near the Martian equator, but the largest volcano in the solar system lies 1000 Km away. Olympus Mons is 500 - 600 Km across and towers 23 Km (73,000 feet) above the Martian plains. The entire Martian volcanic region sticks out like a large bulge away from the Martian surface. When Mars was volcanically active from one to two billion years ago, the entire northern hemisphere may have been covered with lava.

Another distinctive feature on the planet is a huge gash in the equatorial region called Valles Marineris. This canyon easily dwarfs the Grand Canyon of the Colorado and has a length of 2700 Km and a width of 200 Km and a depth of 6 Km. This valley could stretch across the United States. Because the canyon's floor is sparsely cratered, Valles Marineris may have been formed fairly recently in geologic time, possibly caused by volcanoes and the halt of tectonic plate activity leaving the planet the dead, inactive world it is today.

As previously stated, Mars has two polar caps which vary seasonally. There is still a great controversy about the composition of these ice caps. Some spacecraft have indicated the caps are made of carbon dioxide while other probes show that the ice caps are water ice mixed with dust blown from the surface. These caps appear to be several Km thick and if melted would cover the planet with an ocean a few meters deep. There is currently a theory that the entire surface of Mars is covered with a permafrost containing 10 times greater amounts of water than in the polar caps. Mars is like a frozen ice ball.

The atmosphere of Mars includes 96% thin carbon dioxide, 3% nitrogen, with trace amounts of argon, oxygen, and water vapor. The atmospheric pressure is 0.8% of Earth's which means that life as we understand it could not exist. The temperatures vary from -10ºC in the Summer to -130ºC in the winter. The Martian sky has a pinkish cast caused by the red oxide dust which is always in the atmosphere. Martian dust storms occur during the summer when Mars is at perihelion (closest to the Sun) and last 100 days. During that time, the sand storm covers the entire planet. The peak wind gusts are 120 km per hour while the average wind speed is substantially lower than this.

Mars has two tiny moons, Phobos and Deimos, which are the size of New York City. Phobos is the closer of the moons at 9300 Km while Deimos is located at 23,500 Km. Both moons travel around the planet in the same direction as the planet rotates. Like Mars they are covered with craters; Phobos is the larger of the two moons.

In the space between Mars and Jupiter located at about 2.8 astronomical units (AU = 150 million km) are a number of chunks of rock orbiting the Sun which never came together to form a planet. These are called asteroids. There are probably about 500,000 pieces of these rocks at that location, the largest being a 1000 km diameter moon-like object called Ceres, the smallest being dust the size of sand grains. In the summer of 1994 the Jupiter-bound spacecraft Galileo discovered an unusual phenomenon; a small asteroid, Ida, was found to have another asteroid in orbit around it. Astronomers named this small orbiting asteroid Dactyl. This discovery disproved the theory that there is a limit to the size of a principal body in a two body orbiting system.

At first, the asteroids were speculated to have come from a planet that was ripped apart by the tidal forces of Jupiter and the Sun, but now the popular theory is that the planet never formed in the first place. If it had been a planet, it would have bee n the smallest in the solar system. The combination of Jupiter's gravity and the Sun's influence probably kept any planet from forming at that point.

The fifth planet from the Sun, Jupiter, is also the largest planet in our solar system. Named for the king of the Roman Gods, Jupiter would be the size of a walnut in an eight inch soccer ball Sun solar system. Jupiter also contains two thirds of the entire mass of all the planets. 318 Earths would equal Jupiter's size.

Jupiter is 5.2 AU from the Sun (778.3 million kilometers), travels around the Sun once in 11.86 Earth years, and has a diameter of 143,200 Km. Jupiter's composition resembles that of a small star. It has an atmosphere largely consisting of hydrogen and helium, an interior pressure 100 million times that of Earth's surface atmospheric pressure and a huge magnetic field which stretches millions of miles into space. This field is so strong and so far-reaching that it pours billions of kilowatts of energy into the Earth's magnetic field every day.

Jupiter has its own ring system composed of three bands that are very dark in visible light. These rings may be the result of impact debris. Sixteen moons orbit Jupiter including the four large moons discovered by Galileo in 1610, Io, Europa, Callisto, and Ganymede.

Jupiter's inner structure consists of a 30,000 km thick mantle made of liquid hydrogen and helium. The liquid hydrogen is in the molecular phase known to us on Earth as H2. In Jupiter's core the temperature becomes 11,000º C and the hydrogen become s "metallic". In spite of the high temperatures this core seems to composed of rock ice.

Jupiter's atmosphere is 81% hydrogen and 19% helium with slight traces of ammonia, methane, water vapor, and several other hydrocarbon compounds. There is a complex layer of clouds in the upper atmosphere which looks like a swirling cauldron. Located in the southern hemisphere along the brightly colored bands is a huge red spot which could hold three planet Earth's easily. This "storm" has been going for over three hundred years since Galileo first noted it with his observations. Rising plumes and spinning eddies suggest there is a strong heat source in the planet's interior. This storm and other clouds travel around the planet from east to west at speeds upward of 540 Km/hour. These clouds rotate as fast as the planet completing one revolution in 9 hours and fifty minutes.

As mentioned previously, Jupiter has a tremendously powerful magnetic field containing 400 million times as much energy as Earth. It is probably produced by convective currents generated through the liquid metallic core. This radiation is so intense that humans could not approach Jupiter without storm shelters or lead-lined protection because of the extensive radiation many times more powerful than the Van Allen belts. At 42,800 km from Jupiter Pioneer 11 received a radiation dose 100 times stronger than that required to kill a human. Even electronic components aboard the spacecraft were damaged. Jupiter would not be a hospitable planet for human exploration into its atmosphere; exploration would have to be confined to its large moons.

The sixth planet from the Sun, Saturn, was the outermost edge of the solar system until the age of the telescope. Named after the Roman God of agriculture this second largest planet is distinguished from all the other planets by its beautiful ring system making Saturn the "jewel of the solar system."

At 10 AU Saturn is twice as far as Jupiter from the Sun and has a orbital period of 29.48 Earth years. It has a diameter of 116,400 Km which doesn't include its nearly one thousand rings. Compared to our eight inch soccer ball Sun, Saturn would be the size of a chestnut.

The planet rotates rapidly around its axis like Jupiter, making a complete turn in 10.2 hours. Like Jupiter, Saturn is composed mainly of hydrogen and helium, but there are significant structural differences which gives Saturn a density of 0.71 g/cm3 which means, if we could find a big enough bathtub, Saturn would float. In spite of Saturn's large size its acceleration due to gravity is only 1.07 times that of Earth giving further credence to its light density.

Saturn's interior is much like Jupiter's with a mantle of liquid hydrogen and helium over a slushy core of metallic hydrogen and helium which in turn surrounds a rocky ice core very similar to Jupiter's. Similar to Jupiter, Saturn has its own internal heat source which emits three times as much heat as it receives from the Sun. Since Saturn is not as dense as Jupiter its heat source is influenced by helium which sinks from the outer atmosphere to the planet's interior.

Saturn's atmosphere is very similar to Jupiter's being composed mainly of hydrogen and helium. Ammonia and methane are also present, but they are in 1/1000 proportions, not enough to be significant. Saturn's upper atmosphere clouds reach speeds up to 40 0 m/sec, the fastest wind speeds in the solar system, nearly four times faster than the winds on Jupiter. These winds may be generated by condensing clouds of water and ammonia crystals. Saturn's atmosphere is far less colorful than Jupiter's, probably because the clouds lie so much deeper into the atmosphere than do the clouds on Jupiter. There is a large storm akin to Jupiter's great red spot, but this storm is only 10,000 km long and rotates at 100 m/sec. Because of Saturn's tornado winds, storms larger than 1000 km cannot form and thus are extremely rare.

Saturn's ring system is the most strikingly beautiful feature about this planet. Galileo saws these rings in 1610, describing them as a set of ears on the planet. In 1655 Huygens reported the ring system for what it was; a thin, flat disk coinciding with the planet's equatorial plane.

Saturn has eight major ring systems: the D system, the C ring, the B ring, the A ring, the F ring, the G ring and the E ring. The Cassini division between the A and B rings was noted to have several light rings in its composition so it forms the eighth ring system. The rings are made of ice and rocks from the size of boulders to dust particles. Nobody knows what scientific process created the ring system. Theories abound from catastrophic tidal wave destruction to cometary remnants and even debris ejected by its moons. The outer rings appear to be shepherded by two moons gravitationally moving the rings into the outer F ring and even braiding and clumping the ring particles.

Saturn has 18 known moons, the largest, strangest and most interesting being Titan. This moon, which is slightly larger than Mercury has a largely nitrogen atmosphere a possible model for Earth's original atmosphere. Large amounts of carbon compounds abound in the atmosphere meaning that these type of materials may have been frozen into the planet's ices as it was created. Astronomers and space probes have not seen the surface of this moon, but the Cassini space probe to be launched near the end of the century is scheduled to send a probe into Titan's atmosphere to discover some of the shrouded planet's secrets.

In 1781 William Herschel noticed the movement of a faint star which had been plotted in 1690. The movement he noticed indicated the star was not a star, but rather a planet. He was persuaded to name the planet after the father of Saturn and grandfather of Jupiter, Uranus. This planet is located at 19.2 AU from the Sun, about twice as far as Saturn; it takes Uranus 84 years to circle the Sun.

Uranus has a diameter of 52,300 km which places it between the huge gas giants and the large terrestrial planets. In our eight inch soccer ball Sun solar system, Uranus would be the size of a coffee bean. The mass of the planet, 8.67 x 1025 kg or about 14.5 Earths, is readily determined by using the five moons which circle it. The planet's density is sufficiently large enough to indicate that its composition is not entirely hydrogen and helium like Saturn and Jupiter, but rather it is a combination of heavier compounds such as water, ammonia, and methane. These compounds give Uranus its pale blue-green color noted through a telescope and as shown by the Voyager 2 flyby in January 1986.

Because there are no surface features or clouds it is difficult to measure Uranus' rotation rate; it was finally determined to be 17 hours 14 minutes. While trying to determine the planet's rotation rate, astronomers discovered that the equator is perpendicular to the ecliptic plane ( the plane created by the Sun's equator); the planet is turned over on its side. This is the only planet with this characteristic; all of the other planets' equators lie approximately parallel to the ecliptic plane. Uranus ' motion leads to extreme seasonal variations at its polar regions; each pole has four seasons. The north pole has 21 years of summer in perpetual sunlight; 21 years of winter in constant darkness; 21 years of spring and 21 years of fall where there is a combination of darkness and light. One would think that this would really affect the planet's temperature, but at its distance from the Sun, Uranus gets an energy input 360 times less than that of Earth. The temperature in the planet's clouds remains at a constant -220ºC.

The wind blows westward on the planet at speeds between 100 and 600 km/hour, but there are no significant markings or cloud as on Jupiter and Saturn; however, like Jupiter and Saturn, Uranus has a ring system. There is a system of 11 dark rings around the planet. These thin rings orbit the planet at a distance of 1.4 to 2.0 Uranian radii and are composed of bits of debris which make this system extremely dark. The rings are located around the equator almost perpendicular to the ecliptic. Uranus has 15 moons the largest of which are from 13 - 15% the size of the Earth's Moon. These moons have mostly frozen water, craters and fractures with strange designs, not seen anywhere else in the solar system. The moons are in the same plane as Uranus' equator.

One strange phenomenon on Uranus is the fact that its magnetic poles are displaced 60º from the geographic poles. If one were to look at the magnetic field without looking at the planet's normal rotation, he/she would think that Uranus was like the other planets. This magnetic field has a similar strength to that of Earth's.

In 1846 the German astronomer Johann Galle discovered Neptune. Because of the irregularities in Uranus' orbit, mathematical astronomers predicted that there was another planet beyond Uranus and so Neptune was discovered. Neptune is in almost a perfect circular orbit about 30.1 AU from the Sun. It takes Neptune 158.5 Earth years to orbit once about the Sun. Neptune's mass( 1.03 x 1026 kg) is almost the same as Uranus' which means in our eight inch soccer ball Sun solar system, Neptune is also the size of a coffee bean. Neptune rotates once in 16 hours and three minutes and has an average temperature of -355ºF.

Like the other gas giants, Neptune has a ring system consisting of four rings; two main or bright rings and two dark or diffuse rings. Scientists are not sure whether Neptune's ring system is in the process of formation or if it is being worn away.

Eight moons circle Neptune including Triton and Nereid. Six newly discovered moons have highly irregular shapes with no signs of geologic evolution. Triton is the only moon in the solar system which travels in the opposite direction to its planet's rotation. This has led to a theory that Triton was captured rather than accreted when the planet was formed. Triton is the coldest body in the solar system with average temperatures of -400ºF. On Triton there appear to be three types of volcanic activity: 20 miles wide fault line filled with viscous icy material, multiple flooding phases in broad calderas with ice-like lava, and nitrogen vents which may be the result of explosive discharges of liquid nitrogen ice from the moon's interior.

Another discovery on Neptune was a magnetic field which is tilted 50º from the planet's rotation axis. This is very similar to Uranus' both in strength as well as location. Scientists do not know why.

Neptune's atmosphere is very dynamic with a great dark spot the same size as Earth located in the southern hemisphere. This spot is similar to Jupiter's great red spot in that both are located in the same area of the planet and both are proportionally the same size compared to the size of their respective planets. There is also a smaller dark spot located further south which could be the upwelling of interior atmospheric gases. The atmospheric dynamics is very surprising since the amount of sunlight which the planet receives and its own internal heating is about 5% of that of Jupiter. There was also a small bright feature rotating rapidly around the planet in a high-speed wind jet located between the large and small spots. This little storm was nicknamed "Scooter" by the imaging team at the Jet Propulsion Laboratory where these discoveries took place. Other very high clouds are observed throughout the surface of the planet. Neptune was the last planet explored up to this time by Voyager 2 the spacecraft from Earth.

In 1995 the Hubble Space Telescope discovered another storm on Neptune's northern hemisphere. This is the first time such a phenomenon was seen on the gas giants. Saturn had several storms around its equator, but nothing in the northern hemisphere.

In 1930 astronomer Clyde Tombaugh was looking at a number of photographic plates when he happened to notice a slight motion on plates taken during successive nights. This new planet was named Pluto for the Roman God of the underworld. Pluto is unique in that it is the coldest, the smallest and the farthest planet from the Sun. Located at 6 billion kilometers from the Sun, 40 AU, Pluto has a diameter smaller than the Moon's, 2400 kilometers. Made largely of rock and ice, the planet has an atmosphere one millionth of Earth's and it is covered with exotic snows of methane, nitrogen, and carbon monoxide.

Pluto's orbit is very elliptical sometimes putting the planet inside Neptune's orbit. It also is inclined 17º above the ecliptic plane which means it behaves more like a comet or an asteroid rather than a planet. Many scientists would like to reclassify Pluto as a planetesimal because of its small size and strange orbit.

In 1978 astronomers discovered that Pluto had a moon half the size of the planet. The moon was named Charon which makes the Pluto-Charon duo a nearly binary planet system. Charon is covered by dirty water ice and doesn't reflect as much light as Pluto. Due to a series of mutual eclipses in the 1980s astronomers were able to map the surfaces of both Pluto and Charon. Pluto appears to have polar ice caps and dark spots around its equator.

Because of its present position from the Sun, Pluto's atmosphere is prominent, but as the planet travels farther from the Sun its atmosphere will collapse in a huge planetary snowstorm and will remain collapsed until it is again closer to the Sun. Before this collapse scientists would like to send a probe to the strange, cold, planet. NASA has proposed the fast flyby of Pluto before 2008 when its atmosphere is supposed to collapse, but this effort is pending funding.

Beyond Pluto out as far as 100,000 AU lie the Oort clouds - breeding ground for comets - the primordial snowballs. Comets frequently visit the inner solar system and are though to be one of the origins of water on Earth and possibly the other terrestrial planets. Life may have had its start from one impacting comet while dinosaurs may have perished from another.

A comet consists of a nucleus, a coma, and a tail. A comet's nucleus is basically a "dirty snowball" made of water ice, rock, dust and other frozen gases. As the nucleus approaches closer to the Sun it heats up and the coma is formed. The coma is the visible gas which surrounds the comet and becomes similar to an atmosphere. A much larger hydrogen cloud also forms around the entire comet. A dust tail is formed by the pressure of photons from the Sun pushing dust particles from the coma into the opposite direction of the traveling sunlight. This smooth, curved tail of dust particles reflects sunlight. Plasma tails also form because of the solar wind particles interacting with molecules and atoms from the coma. This tail is quite irregular and may or may not appear on a comet. Some comets may have both tails, most have one or the other.

After the comet's trajectory starts to take it away from the Sun, the comet begins to cool and the tails, the hydrogen cloud, and the coma scatter into space leaving only the nucleus. If the comet has an elliptical orbit it will again approach the Sun an d make a new coma, cloud, and tail. Each time a comet approaches a planet, the nucleus' orbit may be changed. In 1993 Eugene and Carolyn Shoemaker along with David Levy found a comet torn apart by Jupiter's gravitational tidal forces. In 1994 comet Shoemaker-Levy's 21 pieces slammed into Jupiter in a cosmic retribution for Jupiter's ripping it apart. In the summer of 1995 the Hubble Space Telescope still records the remnants from this cataclysmic collision.

These are basically the major bodies in the solar system. Is this solar system typical around all stars? We don't know. The distances between stars almost prohibit the discovery of planetary systems. Returning to our eight inch soccer ball Sun solar system, the distance from the Sun to the Earth would be about 26 meters. The distance from the Sun to Pluto would be about 1000 meters. The distance to the Oort clouds would be about 1600 Km, one light year, and the distance to the nearest star, Proxima Centauri would be 6500 Km or a little more than four light years away, a light year being about six trillion miles. These distances are indeed prohibitive at this time for exploration, but as one first begins to walk we must explore a step at a time. But before a person takes his/her first steps he/she must become familiar with the equipment required to do the job: the feet. So, too, the space explorer has to begin with the very basics before starting the journey into space. These basic space facts are extremely important for the beginning of space travel. They are a knowledge of orbital mechanics and rocket science.

Photos courtesy NASA


CHAPTER 5 -- Orbital Mechanics

© John F. Graham, 1995
Photos courtesy NASA

When Sputnik was placed into orbit in 1957 it reawakened an entire physical and mathematical science which had gone as far as it could go without space travel, Celestial Mechanics. Celestial Mechanics is the study of the motion of natural bodies in relation to a principal body. In the our case this is the study of the Earth and the other planets in motion around the Sun.

With the advent of the space age in 1957 a new practical subset of Celestial Mechanics was born, Orbital Mechanics. Orbital mechanics is the study of the motion of human made objects as they travel around a principal body, in the majority of flights the Earth. In the next chapters of the book we will discuss the travel of astronauts and cosmonauts into near Earth space and journeys to the Moon. What forces allowed these intrepid adventurers to travel in the vacuum and microgravity of space? The answer to this question lies in the study of orbital mechanics.

To gain an elementary understanding of orbital mechanics one must first understand the definition of an orbit. An orbit is the curved path a body follows when the only force acting upon it is gravity. There are several key words in this definition which one must grasp. The first is force, the second is gravity, the third is the meaning of body, and the fourth is a curved path.

A force is an action which can change the motion or momentum of a body. Four natural forces are currently in vogue. The strong nuclear force and its close relative the weak nuclear force bind an atom's nucleus together. The third force is the electromagnetic force which dictates electrical charges of electrons and protons. These three forces all concern extremely small bodies on the scale of atoms and molecules. The fourth force is gravity, an attraction force between large bodies.

Gravity is a property of all matter. Matter is that of which everything is composed. People have matter, trees have matter, and the Sun contains matter. Matter makes up a body in the definition of an orbit. The amount of matter an object contains is called the body's mass. The more mass a body contains, the stronger is its gravitational field or attraction capabilities. One can actually measure the gravitational force between two bodies such as two people, two automobiles, or two buildings such as New York's World Trade Center's Twin Towers. One can also measure this gravitational field between the Earth and the Moon, the Earth and the Sun, and the Earth and a human made spacecraft.

An orbit is always the curved path around an object; this object is also known as the central attracting body. The central attracting body for an orbiting spacecraft is the Earth, the Moon, the Sun, or any other major massive body. A body's gravitational field extends outward in all directions. This field is strongest close to the body and gets progressively weaker as the distance away from the body increases until this reaches infinity. In the real world, a spacecraft can escape the influence of one primary body by reaching its radial sphere of influence only to fall under the influence of a more massive body. For example, a spacecraft can escape the earth's influence at about one million kilometers, but the craft will at that point have the Sun as its central attracting body.

The strength of the gravitational field depends only on the mass of an object not its volume. If one could compress the Earth into the size of a grapefruit, it would still have the same gravitational field as in its present size because the amount of matter remains the same.

One can easily demonstrate an orbit by throwing a baseball or shooting a gun. Once the ball leaves the hand or the bullet leaves the gun these objects are primarily under the influence of the Earth's gravitational field. They are also being acted upon by the drag associated with the Earth's atmosphere, but the primary force is gravity. The person throwing the ball or shooting the gun only sees a small part of the orbit. If the mass of the Earth were not in the baseball's or bullet's path it would circle around the center of Earth's mass and return to the thrower or the shooter. This small segment of the orbit that occurs when the ball or the bullet strike the ground is called a trajectory.

There are four curved paths or trajectories which an orbit follows: a circle, an ellipse, a parabola, and a hyperbola. These orbits are basically categorized into two groups: the escape group containing the parabola and hyperbola; and the captive group containing the circle and the ellipse. Spacecraft such as the Voyager 2 fly escape orbits while the space shuttle flies a captive orbit.

The path of an orbit lies in a plane defined as a two dimensional flat surface. This plane of an orbit must pass through the center of mass of the primary or central attracting body. For most satellites this is defined as the center of the Earth. Because the Earth is not a perfect sphere, with its mass evenly distributed, a spacecraft has a very difficult if not impossible task of flying a circular orbit. Even though a number of these orbits are very close to being circular, they are still in imperfect circles called ellipses. The plane of the elliptical orbit like the circular orbit still passes through the Earth's center of mass.

An ellipse is a squashed circle. Instead of having a central point like the center of a circle, the ellipse has two central points called foci. If the foci get extremely close together the ellipse becomes circular; as the foci gets further apart, the ellipse begins to resemble an egg and then a football. In orbital mechanics, the center of the central attracting body is always at one focus and the other focus is vacant.

The longest dimension of the ellipse is a straight line that passes through both foci. This line is called the major axis, a very important dimension in orbital mechanics because the major axis determines the size of an elliptical orbit. The line perpendicular to the major axis and that bisects it is called the minor axis. The minor axis as the name suggests has a minor role in orbital calculations.

The distance between the foci has no particular name. but it is very important in determining the parameter determining the shape of the elliptical orbit. This parameter is called the eccentricity. The eccentricity measures the deviation of an ellipse from a circle. It is found by dividing the distance between the foci by the length of the major axis. If the orbit is very close to circular, the distance between the foci is zero. Zero divided by any length is zero; therefore, the eccentricity of a circle is zero. When the distance of the foci equals the major axis the curve becomes a parabola and when the distance between the foci is greater than the major axis the curve becomes a hyperbola. An easy method of determining an orbit's shape is to investigate its eccentricity. If the eccentricity is equal to zero the curve is a circle; if the eccentricity is between zero and one the curve is an ellipse; if the eccentricity equals one the curve is a parabola; and, if the eccentricity is greater than one the curve is a hyperbola.

Johannes Kepler (1571-1630) first discovered three laws which determined how bodies orbit other bodies. The first law states that a planet travels around the Sun in an elliptical orbit with the Sun at one focus; this is also known as the law of ellipses. Kepler's second law states that a body sweeps out equal areas in equal times; also called the law of areas. Kepler's third law states that the square of a period of revolution is proportional to the cube of the orbit's semi-major axis which is half a major axis. Kepler determined these laws after studying accurate observations of the orbit of Mars for almost ten years.

Kepler told us how orbital motion acts, but he didn't say why. This was determined by Sir Isaac Newton (1642-1727) and his four laws. Newton's first law states that an object at rest remains at rest or an object in motion remains in motion unless it is acted upon by some outside force; this is also known as the law of inertia. Newton's second law states a force placed upon a body is directly proportional to the product of the mass of the body and its change in motion or momentum. This is called the law of acceleration. Newton's third law states that for every action there occurs an equal and opposite reaction or the law of reaction. These three laws are called Newton's Laws of Motion and determine mechanically how a spacecraft's motion begins and changes. Newton's fourth law pertaining to orbital mechanics is one of the most important because it relates how the force of gravity works. The force of gravity is directly proportion to the product of the masses of two bodies and is indirectly proportional to the square of the distance between them. Simply stated, the more massive or closer a body the greater its force of gravity.

Newton illustrated the use of his laws when he pictured a cannon mounted parallel to the Earth's surface on top of a mountain above the atmosphere. The cannon balls are fired from the cannon with increasingly larger charges. The cannonballs fall to Earth with a larger and larger trajectory until just enough powder is added to put the ball into a circular orbit. If more powder is placed into the cannon the cannonball goes into an elliptical orbit and more powder increases the orbit's eccentricity which elongates the ellipse. Finally, enough powder is used to blow the cannonball away from Earth into an escape orbit and the orbit becomes a parabola. If any more powder is used the orbit becomes hyperbolic. Thus Newton was able to combine his laws of motion and gravity with Kepler's Laws of orbits to give us today's orbital mechanics.

Only one speed will produce a circular orbit at a given altitude. This is called the local circular speed. If the altitude is raised the local circular speed will decrease. This speed gets progressively lower the greater the distance from Earth because it is based upon the Earth's gravitational field strength.

Another parameter which is measured in an orbit is its period or the time it takes a spacecraft to complete one revolution. The period is directly relate to the major axis. If the major axis' size increases meaning that the satellite's altitude is higher, the period or time to complete one orbit increases. If a satellite in a circular orbit around the equator has a period equal to about twenty four hours it is said to be in a geosynchronous orbit because the orbital speed is synchronized with the Earth's rotation. A satellite in such an orbit would appear to remain stationary in the sky. Communications and weather satellites use such orbits.

In an elliptical orbit around the Earth our home planet is at the position known as the primary focus. The point on this orbit where the satellite is closest to the Earth is called the perigee and the point where the satellite is farthest is called the apogee. The line connecting the apogee and the perigee through the middle of the Earth is the major axis of the ellipse. Another name for the major axis is the line of apsides.

After a rocket's engines are shut down and it has placed a satellite into orbit, a process known as orbital insertion, the spacecraft coasts around the orbit influenced only by gravity. As the satellite goes from perigee to apogee it is gaining altitude and as it goes from apogee to perigee it is losing altitude. The mathematical portions of the orbit are determined from the center of the Earth, not its surface.

A roller coaster is the best example to compare the satellite's motion in orbit. A roller coaster is pulled to the top of the initial hill by a chain powered by a motor; this is comparable to a rocket lifting a satellite from the Earth's surface. Once a roller coaster has reached the top of the first hill there is no more power for the rest of its trip. Likewise, because the rocket's fuel has been depleted placing the satellite into orbit, there is no more rocket power to change a satellite's velocity and its orbit.

To achieve orbit the rocket must carry the satellite to at least 80 miles above the Earth's surface and give the satellite enough horizontal velocity, 17,000 miles per hour or 7.7 Km per second, to sustain its orbit. At first the rocket rises vertically to escape the majority of the Earth's atmosphere and then it pitches over to travel more and more horizontally to gain horizontal velocity. By the time a rocket reaches orbital velocity it is traveling parallel to the Earth's surface. The rocket continues to accelerate horizontally until it reaches its correct velocity. At this time the rocket engines are shut down and the spacecraft begins to coast. This point of the flight is called main engine cutoff or MECO. The point at which MECO occurs is the orbital insertion point.

At the insertion point the engineers can arrange to have the spacecraft either climbing, going toward apogee, or descending, traveling toward perigee, or remaining horizontal. This angle of climb of descent is called the flight path angle. If the spacecraft is horizontal with a flight path angle of zero degrees and its orbital insertion speed exactly equals the local circular speed, the spacecraft will remain in a near circular orbit. The orbit's size, major axis, and the orbit's shape, eccentricity, are determined by two factors at orbital insertion: the spacecraft speed and its flight path angle.

Using the roller coaster analogy, assume that the spacecraft arrived at apogee when MECO is performed. At this point our roller coaster has completed its initial climb via engine power and is at the very top of a high platform. This is the point where the roller coaster begins its first plunge. Likewise, the spacecraft will immediately begin to lose altitude as it descends toward perigee. Just like the roller coaster gets faster as it goes downhill, the spacecraft's speed will increase as it loses altitude and approaches perigee.

When the spacecraft passes perigee and begins to ascend to apogee, it will slow down as it gains altitude just like the roller coaster does as it approaches the next hill. For the satellite this speed up downhill and the slowdown uphill will continue as long as the spacecraft stays in its elliptical orbit.

This speed and altitude change is best stated in terms of the law of the Conservation of Energy. This law states that energy can be neither created no destroyed; it can be changed from one form into another. There are three kinds of energy associated with satellite flight. There is kinetic energy, the energy of motion, potential energy, the energy of position, and total energy, the sum of kinetic and potential energy.

Kinetic energy is based upon the mass and velocity squared of an object. The greater the velocity of an object; the greater is its kinetic energy. Potential energy is based upon the mass of an object, the acceleration due to gravity of the principal attracting body, and the height or altitude the object is above the attracting body. The higher the object is above the attracting body the greater is the object's potential energy. The total energy, the sum of potential and kinetic energy always remains constant.

As a satellite moves from apogee to perigee it loses altitude, therefore decreasing potential energy, and increases velocity, thereby increasing kinetic energy. The opposite happens when the spacecraft moves from perigee to apogee. The increase in one kind of energy is exactly balanced by the loss of the other kind of energy and the total energy remains constant. After MECO occurs there is no other energy imparted to the spacecraft and the total energy of the satellite will remain constant.

A circular orbit has no varying of kinetic energy because the velocity is always the local circular speed and there is also no varying of potential energy because the distance of the satellite from the center of the Earth remains the same.

Parabolic and hyperbolic orbits also obey the Law of Energy Conservation. As a spacecraft continues on its way from Earth, its distance or potential energy, keeps increasing while its velocity or kinetic energy, slows until the satellite reaches infinity.

A study of the flight path angle is necessary to see how a spaceflight relates practically to the law of Energy Conservation. The flight path angle is the climb or descent angle of the satellite at various positions on its orbit. To accurately describe the flightpath angle a coordinate system is needed. Drawing a line from the center of the Earth through the center of the spacecraft creates the satellite's local vertical. A line drawn perpendicular to the local vertical through the middle of the spacecraft is called the local horizontal. This coordinate system is called the LVLH (Local Vertical/Local Horizontal) and moves around the orbit with the spacecraft.

The spacecraft's velocity is a vector tangent to the satellite's path with a magnitude equal to the spacecraft's speed. The angle between the local horizontal and the velocity vector is the flight path angle. When the velocity vector is above the LH the flight path angle has a positive value and when the velocity vector is below LH the flight path angle has a negative value. Just like kinetic energy and potential energy the flight path angle changes as it moves around an elliptical orbit.

At perigee, the velocity vector is exactly parallel to the LH and the flight path angle is zero. As the spacecraft and the LVLH system move toward apogee, the flight path angle increases to a maximum positive value and then decreases to zero when the spacecraft reaches apogee. After apogee the flight path angle becomes negative and decreases to a minimum value and then increases until it is again zero at the orbit's perigee point.

To summarize, when the flight path angle is positive the spacecraft is gaining altitude and decreasing its velocity and when the flight path angle is negative the spacecraft is losing altitude and increasing its velocity. The flight path angle is zero at apogee and perigee.

The flight path angle on a circular orbit is always zero because the LH is always parallel to the satellite's velocity vector. The flight path angles on a parabola and a hyperbola are always positive because the spacecraft's altitude is always increasing away from the Earth.

If we know the flight path angle of a spacecraft on an elliptical orbit we know the following facts:

        (1)  Given a positive flight path angle, the satellite is
                (a)  Moving toward apogee
                (b)  Losing speed

        (2)  Given a negative flight path angle, the satellite is
                (a)  Moving toward perigee
                (b)  Gaining speed

The orbit's size and the shape are determined by the velocity and the flight path angle of the spacecraft at MECO. If the spacecraft has a zero flight path angle and a local circular speed it will be in a circular orbit. If the spacecraft has a zero flight path angle and insertion occurs at a greater than circular speed the spacecraft will be in an elliptical orbit at perigee. If the spacecraft is at a zero flight path angle and orbital insertion occurs at a less than circular speed the spacecraft will be in an elliptical orbit at apogee. The insertion speed will also determine the altitude on the opposite end of the orbit. High speed at insertion equals high speed at a position opposite the point of insertion and low speed equals low altitude at the position opposite the point of insertion.

What happens if the spacecraft arrives at MECO at exactly local circular speed, but with a positive flight path angle? The satellite will be moving toward apogee on an elliptical orbit and be slowing down. If the satellite has exactly local circular speed and a negative flight path angle it will be moving toward perigee in an elliptical orbit and speeding up. For both of these cases the orbital insertion point coincides with the respective ends of the minor axes.

A satellite will be of no benefit to its users unless its position is known in order to receive the spacecraft's information. To do this there are six items known as orbital elements used by satellite trackers to determine a spacecraft's orbit. These elements determine the size of an orbit, its shape, the orientation of the orbit, and a time reference frame.

The size of the orbit is determined by the semi-major axis or half of the major axis. This value is denoted as a. The eccentricity determines the orbit's shape; it is designated by e.

An orbit's orientation is determined by measuring three angles. To find these angles one has to note two planes which are flat two dimensional surfaces. The first plane we've already discussed; it's called the orbital plane. The orbital plane goes through the middle of the Earth and contains the satellite's orbit. The second plane is the Earth's equatorial plane; it is a flat two dimensional surface going through the middle of the Earth and contains the Earth's equator.

The first orientation element is called the inclination; it is designated by i. The inclination is the angle between the orbital plane and the equatorial plane. An orbit's inclination depends upon the spacecraft's launch site and the direction in which its rocket is launched. Once in orbit, a satellite's inclination determines how far its ground track will travel north and south of the equator.

The second orientation element is called the right ascension of the ascending node. As a satellite travels in an orbit around the Earth, the points where the orbit crosses the equator are called nodes. The point at which the spacecraft crosses the equator going from south to north is called the ascending node. The opposite point is called the descending node. The line of nodes connects these two points through the center of the Earth. Right ascension is determined by a line drawn from the Sun through the Earth to the constellation Aries at the Vernal Equinox or the first day of Spring. This line is known as the First Point of Aries and is a permanent reference point which never changes. It creates a coordinate system located in the Earth's equatorial plane with the third axis going from the center of the Earth through the north pole. The angle measured from the first point of Aries to the ascending node in the equatorial plane is called the right ascension of the ascending node and is designated by 1/2.

The third orientation element is called the argument of perigee. This angle is measured from the ascending node in the orbital plane to the perigee point. This element is designated by w (little omega).

The final orbital element is the time that the spacecraft passes the perigee point of the orbit. If all six of these elements are known then the ground stations can track these satellites and assist them in their missions.

Very often a satellite's mission dictates that it move from one orbit to another. In order to do this the satellite must have some method to apply energy to the spacecraft to accomplish this change. Most spacecraft have a variety of maneuvering thrusters or engines. The space shuttle orbiter has two orbital maneuvering engines (OMS) located in the rear of the spacecraft that fire only along the spacecraft's longitudinal axis. It also contains three reaction control systems (RCS) consisting of a number of small thrusters which can fire along all three axes of the spacecraft's roll, pitch, and yaw. If any of these engines are fired, the spacecraft experiences more kinetic energy which will alter the satellite's orbit. In fact, this applied thrust will change every point along the spacecraft's orbit except the point at which the thrust occurs. This orbital change will occur only if the thrust is unbalanced, in other words, it causes the spacecraft to move in a single direction and is not countered by an opposing thruster to cause rotation around an axis.

Delta V,V, is the term used to described the application of an unbalanced thrust that changes the speed or direction of a spacecraft. These maneuvering thrusts are classified into four different categories: posigrade, retrograde, radial and out-of-plane.

Posigrade thrust is any force that increases the velocity of the spacecraft. As you recall if a satellite is in a near-circular orbit it is coasting at a constant velocity, a nearly constant altitude, and its flight path angle is zero. If thrusters are fired to increase the satellite's speed, the spacecraft is now moving at greater than local circular speed and it can no longer be in a circular orbit, but rather an elliptical one. This thruster firing is the same as accomplishing an orbital insertion at zero flight path angle with speed greater than local circular speed. The spacecraft will be at perigee on its way toward apogee half an orbit away. Therefore, the larger the ÆV, the higher is the apogee. A posigrade thrust will raise every point on the orbit except the thrust point. This action will also lengthen the major axis which also lengthens the orbit's period. Posigrade thrust will always increase an orbit's period.

Retrograde thrust is any force that decreases the velocity of a spacecraft. Once again, if a satellite is in a circular orbit it has a constant altitude, constant velocity, and zero flight path angle. If the thrusters are fired to slow the spacecraft's speed, the results are the same as orbital insertion at a zero flight path angle with lower than local circular speed. The thrust point coincides with the new orbit's apogee and perigee is half an orbit away. The greater the V, the lower the perigee. The retrograde thrust lowers every point on the orbit except the thrust point; it also shortens the major axis which means the orbit's period decreases. Retrograde thrust always decreases an orbit's period.

Posigrade and retrograde thrusts are the most common types used in spacecraft maneuvers. These thrusts are used frequently over the course of space missions to rendezvous with another spacecraft for purposes of inspection, retrieval, or repair. They were used almost exclusively during the Hubble Space Telescope repair and in the rendezvous and docking of the space shuttle mission STS-71 with the Russian Space Station Mir.

A rendezvous, such as the space shuttle with the Hubble Space Telescope (HST), begins with the shuttle in a lower orbit. To raise the shuttle to the HST orbit two thrusts are required. If fuel is abundant, this maneuver is done by two large thrusts in a high energy transfer. These thrusts must change both the speed and direction of the shuttle and require copious amounts of energy which equates directly to fuel. Fuel is at a premium on the shuttle and every effort is made to conserve it. The high energy transfer is accomplished if time is critical and fuel is no object.

A most fuel efficient method of orbital transfer used by the space shuttle is called the Hohmann Transfer, named for the German engineer who developed it in 1925. This transfer uses two posigrade thrusts. The first V is designed to lengthen the spacecraft's major axis until the orbit's apogee exactly coincides with the target's orbit. The second V is performed upon reaching the new apogee point. This posigrade V is used to increase the spacecraft's velocity up to the local circular speed. This procedure is called orbital circularization. During a rendezvous an obvious problem is to time both V's so that the shuttle arrives at the orbital circularization point the same time as the HST.

Similarly, the shuttle can be transferred to a lower orbit using a retrograde V in a Hohmann Transfer orbit. This is how the shuttle returns home. It executes a retrograde V which shortens its major axis. The perigee point on this orbit correspond to a position at 10 kilometers above the Earth. The increased kinetic energy from the increased velocity created by the spacecraft going from apogee to perigee is dissipated by the shuttle's drag increasing as it encounters the Earth's atmosphere. Much of this drag converts the kinetic energy into heat energy which is absorbed by the shuttle's thermal protection system (heat tiles). The shuttle further reduces the kinetic energy by performing four large S-turns or roll reversals which bleed off air speed thus reducing kinetic energy.

Another very important Hohmann Transfer is used to place satellites from the shuttle into geosynchronous orbit (GEO). Following launch from Kennedy Space Center, MECO occurs at 62 miles above the Earth at a speed greater than the local circular speed. The shuttle coasts out to its designated orbit of about 185 miles and upon reaching that point accomplishes a V also known as an OMS-2 burn circularizes the shuttle's orbit. The shuttle's payload bay doors are opened and the satellite is deployed into the shuttle's orbit. Each satellite going to GEO has two rockets on board to accomplish the required Vs. After traveling for half an orbit, the satellite's first solid rocket fires to accomplish a posigrade V. This solid rocket motor, called a perigee kick motor (PKM), increases the satellite's orbit until its apogee coincides with the GEO altitude of 22,300 miles or 35,862 kilometers. The satellite discards its PKM and coasts to its new apogee position. After arriving at apogee the spacecraft's second solid rocket motor, the apogee kick motor (AKM), fires a posigrade V to increase the satellite's speed to local circular velocity. The AKM usually stays with the new GEO spacecraft after it has completed its V. GEO satellite deployments must be timed with the Earth's rotation to arrive at GEO altitude over the desired geographic location to take up its station.

A Hohmann transfer is also used to send spacecraft to other planets. A V must be performed to boost the spacecraft from Earth orbit using the Sun as the new primary body to arrive at the target planet at the spacecraft's aphelion point (Point in orbit farthest from the Sun which corresponds to apogee, the farthest point in orbit from the Earth). An orbit with the Sun as the primary attracting body is called heliocentric. Posigrade thrusts would be required to send spacecraft out to planets farther from the Sun than the Earth. These planets are called superior planet orbits. They include the orbits of Mars, the asteroids, Jupiter, Saturn, Uranus, Neptune, and Pluto. Retrograde thrusts, opposed to the Earth's orbit around the Sun. would be required to reach the inferior planet orbits of Venus and Mercury.

Beside posigrade and retrograde thrusts there is also the capability to perform radial thrusts. Since a radial thrust is one which is directed toward or away from the central attracting body of the orbit there are two types of radial Vs, an inward and an outward.

The space shuttle accomplishes an inward radial thrust maneuver by pointing its nose directly at the center of the Earth and firing its OMS engines. Since this V is perpendicular to the spacecraft's velocity vector, it does not change the vehicle's speed, only its direction. By performing the V in this direction, the spacecraft's flight path angle is negative which means it's moving toward perigee and increasing speed. Normally the spacecraft will reach the perigee point within 90º of a inward radial thrust V.

The space shuttle performs a radially outward thrust by pointing its OMS engines directly at the Earth and firing them. This V produces a positive flight path angle which means that the spacecraft is now slowing down and will reach the apogee point of its new orbit within 90º.

Since the speed of the spacecraft has not changed and the size of the orbit's major axis has not changed because it is equal to the diameter of the old circular orbit, the orbit's period remains the same. This is critical when the shuttle is performing the final stages of a rendezvous when the shuttle has to align its major axis with the target satellite's. Radial Vs are also mandatory for the spacecraft's final approach to its docking target. Radial thrusts were used continuously when the STS-71 docked with the Mir from 270 feet through docking on June 29, 1995.

The inclination of an orbit is the angle at which the orbital plane crosses the equatorial plane. A satellite orbit over the equator has an inclination of 0º while that over the poles has one of 90º. Out-of-plane thrusts are designed to change the orbital plane by changing the orbit's inclination. This is accomplished by firing a rocket engine or thruster in a direction which is perpendicular to the orbital plane. The details of this change vary depending upon where the V takes place. If the shuttle's nose is pointed toward the north, perpendicular to the orbital plane, the resulting V will increase the orbital inclination. If the shuttle's nose is pointed south, perpendicular to the orbital plane, the resulting V will decrease the orbital inclination. In order to keep the orbital parameters from changing, these out-of-plane Vs are performed at an orbital node. If such a V is not performed at the node points, the line of nodes will rotate thus changing all of the orbit orientation elements. Out-of-plane Vs are used to match the shuttle's orbit with that of its target. Additionally, an out-of-plane change is required for spacecraft being transferred to GEO because most of the initial shuttle inclinations are 28.5º and it needs to change to 0º to be at the correct position on the equator. If a GEO satellite has any inclination its ground track will resemble that of a figure eight.

This has been a very minor presentation of a very complicated subject. There are a number of outstanding textbooks explaining the very complicated items discussed in a very understandable manner. Two of the best are Adventures in Celestial Mechanics by Dr. Victor G. Szebhely, from the University of Texas, and Spacecraft Mission Design by Charles D. Brown, from the American Institute of Aeronautics and Astronautics in Washington, D.C.


CHAPTER 6 -- Rockets and Rocket Science

© John F. Graham, 1995
Photos courtesy NASA

In order for a satellite to go into orbit it must accomplish two major tasks. First, the satellite must rise above the atmosphere which surrounds the Earth's surface. The atmosphere contains enough particles which slow the spacecraft preventing it from orbiting the planet. A propulsion device must strain against gravity to rise above the atmosphere. Second, the satellite must also be provided with enough horizontal velocity above the atmosphere to at least equal the local circular speed upon orbital injection otherwise it will reenter the atmosphere and burn due to friction. Both of these jobs are done by rockets.

A simple rocket is usually a tall cylinder containing propellant. Propellant always contains two items: fuel and oxidizer. Fuel is the item which burns to provide rocket thrust. In a simple liquid rocket it is stored in its own separate fuel supply tank. To support fuel combustion the rocket also contains a source of oxygen needed after the spacecraft passes above the atmosphere and cannot collect oxygen in any form. This oxygen is in the form of an oxidizer to aid in combustion; it is stored in a container which resembles the fuel supply tank.

The contents from fuel tank and the oxidizer tank flow from their respective tanks via plumbing; valves, pipes and pumps; into an area called the combustion chamber where the oxidizer joins with the fuel to burn. This combustion causes pressure to build up within the chamber's walls; the resultant pressure, called exhaust gas, is forced through a bell-shaped nozzle at the rocket's base. The nozzle is tapered in the middle in an area called the throat to allow the exhaust gas to build up even more pressure and to increase its flow rate out into the wider portion of the nozzle. The gas goes into the wide nozzle portion very fast and produces a force called thrust.

If the thrust is greater than the rocket's weight, the craft will lift off. This principle is called the thrust-to-weight ratio which must be greater than one or the vehicle will not lift off its pad. This thrust not only overcomes the payload's mass, but also its gravitational attraction to Earth. Any additional thrust above the thrust-to-weight ratio of one causes the rocket to accelerate. The greater excess thrust means greater rocket acceleration in a unit known as g's or numbers of times the norm al acceleration due to gravity at 9.8 meters/second2. In other words, one g equals 9.8 m/s2 , two g's equal an acceleration of 19.6 m/s2, three g's equal 29.4 m/s2, etc. Weight is also measured in g's because a natural part of weight is the acceleration due to gravity. Therefore at one g a 100 pound woman weighs 100 pounds; at 2 g's she weighs 200 pounds; 3 g's she weighs 300 pounds; etc. As more fuel and oxidizer are used the rocket's weight (mass) decreases and its thrust to weight ratio increases. To maintain the same thrust with a mass reduction, the spacecraft's acceleration must increase in order to obey Newton's second law, F = ma.

The first rockets needed wings to guide or steer them into space. Engineers soon found that these wings could be ripped off the rocket's body as it approached the sound barrier. The wings were then downsized into small little winglets called guide vanes . These guide vanes steered the rocket on to its appropriate trajectory to gain altitude and to increase the vehicle's horizontal velocity. As rockets matured, the engineers found that steering could be accomplished more efficiently by including small jets instead of vanes around the base of the craft. The original Atlas rocket employed this capability. As the engineers grew cleverer they found that the same steering could be done by moving the spacecraft engines and diverting the thrust into a different direction. This was called gimbaling and is used exclusively to launch today's modern rockets.

At the top of the rocket is its business end, a hollow cone containing the spacecraft's payload. The upper stage is shaped like a cone to minimize the rocket's cross section which has to penetrate the atmosphere. This reduces the amount of energy required to push the rocket through the atmosphere into space. The nose cone protects the payload against aerodynamic wind blast which is very prevalent when a vehicle speeds through the Earth's atmosphere.

As previously stated, rocket fuel is also called propellant. Propellant includes not only a fuel which is actually burned, but also an oxidizer which supplies oxygen for the combustion process. Propellant efficiencies are measured by a term called specific impulse, Isp. This measurement determines how much thrust a propellant produces; it is a similar gauge rating such as octane is for gasoline. Isp is measured in seconds; it is the amount of time one pound of propellant produces one pound of thrust. There are two classes of propellant mixtures: liquid and solid.

Liquid propellants develop the most efficient thrusts for rocket power. There are many liquid propellant combinations which are used for rocket flight such as kerosene/liquid oxygen (LOX), alcohol/LOX, gasoline/LOX, and liquid hydrogen (LH2)/LOX. Such a propellant with the highest Isp is LH2/LOX with a 400 second rating for operation in the atmosphere and a 453 second rating in a vacuum. Another liquid fuel with a medium efficiency is Aerozine 50 (kerosene) with Nitro Tetroxide (N2O4) for an oxidizer. This propellant has an Isp of 254 seconds at sea level and a 302 second rating in a vacuum. These highly efficient fuels and oxidizers still need an ignition spark to start the combustion process.

A special liquid propellant which does not need ignition to start combustion is a fuel which ignites spontaneously when it comes into contact with its oxidizer. This type of fuel is called hypergolic. A typical hypergolic propellant combination is hydrazine (N2H4) and nitrogen tetroxide (N2O4). Most spacecraft use a monopropellant for operation; the most popular of these fuels is hydrazine which is easily stored and used on orbit for many years.

There are two important advantages of using a liquid fuel. The first is the capability to throttle the thrust. A liquid engine can start, stop, restart, or be reduced in thrust as the rocket flies. The second big advantage of liquid fuel is its increased efficiency, Isp. LH2 has a typical Isp of about 496 seconds whereas the solid fuel has a typical Isp of about 250 seconds.

The disadvantages of using liquid fuel are included in three areas. The first is the cryogenic nature of the fuel meaning it is difficult to store because of the required cold temperatures. A second disadvantage is the handling of this fuel by workers and the special precautions such as wearing heavy, insulated gloves and eye protection must be taken. A third disadvantage is that liquid fuel rocket engines are extremely complex with many moving parts including pumps, valves, lines, and chambers. Every one of these parts must work perfectly or the engine fails.

Solid propellant consists of a flammable putty or rubber which contains both the fuel and the oxidizer within this mixture. For example, the mixture in the space shuttle's solid rocket booster is a typical solid rocket fuel. The ingredients include 16% atomized aluminum powder as the fuel, 70% ammonium per chlorate as the oxidizer, a 12% polybutadiene acrylic acid acrylonitril as a binding agent, 2% epoxy for curing and extremely small traces of iron oxide to control the burn rates during flight.

The solid rocket fuel fills the inside of the rocket from its top to the bottom. In the middle of the rocket is a shaped clearing that provides combustion area and allows the mixture to burn evenly. This shape may be a circle or a star depending upon the type of thrust desired for launch. The rocket's ignition commences by shooting flames down its entire length to initiate the combustion evenly throughout the grain, another term for solid rocket propellant. As the fuel burns and its waste parts are ejected out the nozzle the propellant area grows. As the propellant area grows there is more propellant to burn which means that the rocket's thrust increases.

The advantages of the solid rocket boosters include easy handling. Once the propellant is manufactured and shipped, the technicians need no extensive protective clothing or procedures. The solid rocket fuel can be stored indefinitely in its solid state with only random inspections to insure that its seals are still functioning. In a solid rocket motor there are no moving parts which can fail just by mechanical movement. Despite of the numerous advantages of solid rocket propellant there are a number of disadvantages as well.

The biggest disadvantage of a solid rocket booster is that once it starts it is not going to be stopped. Therefore, it has no control functions such as throttles to control the burn. If thrust is to be either reduced or increased it must be done in the design of the grain. For example, the space shuttle SRBs are designed so that the burn reduces during transonic region passage also known as the maximum dynamic pressure. A second disadvantage is the low Isp rating. Solid propellant is just not efficient because it burns so quickly. A third disadvantage is that the rocket emits solid particles not only polluting the atmosphere, but once the vehicle gets into space, these particles also become solid debris, a hazard for satellites and other launchers.

Which type of rocket propellant does one choose? It depends on the mission and the type of energy required for it. If the engineer needs fast and responsive energy, a solid would probably work best, but if the scientist needs a slow, but steady launch capability then perhaps a liquid would be better. The choice depends upon the mission.

There are also two types of rockets based upon their recovery: expendable rockets and reusable rockets.

The only reusable rocket currently in the world's inventory is the space shuttle. This system is really only a partially reusable rocket because the orbiter, the space shuttle main engines and the solid rocket boosters return to be used again, but the shuttle's largest component, the external tank, is thrown away after use by letting it crash into either the Indian or Pacific Oceans.

Expendable launch vehicles abound around the world. The Russians use the Soyuz, the Zenit, the Proton and the Energia. The European Space Agency launches several variations of its highly successful Ariane. The Chinese have been highly successful in developing their series of "Long March Launchers" based upon their ICBM technology. The Japanese have launched their newest vehicle the H-II with hopes of capturing much of the world's lucrative satellite communications market. The Indians, the Israelis, and the Swedes have also developed launchers for satellites. The United States has several expendable launchers the most important of which are the Atlas, the Delta, the Titan, and the Pegasus.

The Delta class rocket launches small to medium weight payloads with a maximum mass of 8420 pounds. The Delta consists of a liquid propellant first and second stage, a solid propellant third stage, and nine small solid strap-on rockets attached to the first stage. These rockets have been noted for their reliability and dependability since the first flight in 1960. McDonnell Douglas Space Company manufactures the Delta and offers it for commercial use.

The Atlas class rocket offers the experience of a rocket which has evolved since its first use in the late 1950s. The Atlas II, the latest evolution of this rocket, can launch a medium size payload with a launch weight of 14100 pounds into Low Earth Orbit (LEO). Atlas II consists of two stages. The first stage uses three liquid propellant engines that thrust at lift off. Two of these engines drop off after three minutes of flight. The second stage is the Centaur which employs two liquid propellant engines. The Atlas, formerly made by General Dynamics Corporation, is now manufactured by Martin Marietta.

The Titan-4 flies heavy payloads with weights of 39,000 pounds These rockets again date back to the early 1960s and served as ICBMs. The Titan-4 uses liquid propellant first and second stages with two large solid rocket boosters for first stage thrust augmentation. The Titan-4 uses the Centaur for its third stage to place a payload into orbit with its highly efficient cryogenic propellant. This Titan IV can place heavy payloads such as 35,000 pounds into LEO and 10,000 pounds into geosynchronous orbit (GEO). Martin Marietta manufactures the Titan-4 for commercial use as well. For heavier payloads the US must rely on the space shuttle.

The Pegasus is the first orbital system designed for aircraft deployment since the 1960s. Manufactured by Orbital Sciences Corporation, it was first launched on April 5, 1990 from the right wing of a B-52; its principal application is to place small payloads into LEO. Its three stages can place a 400 pound small satellite into orbit. This is a brand new spacecraft which didn't have to rely upon old ICBM designs. It is normally a three stage solid rocket configuration but can carry a fourth stage of hydrazine propellant. In 1994 a Lockheed L-1011, specifically designed for the Pegasus rocket, launched its first satellite. The projected capability for this rocket is to be one launch per month for the next three years. Recently, the Pegasus has undergone a number of failures in its Pegasus XL model. Investigations by the U.S. Air Force, NASA, and Orbital Sciences are underway to determine why the craft has malfunctioned.

Rockets did not just appear for modern humanity to start using; they are the result of years and years of evolution. The rocket had its true start about 3000 years ago in the deserts of China. Let's look at the history of piloted and robotic space exploration.