## Gravity & Orbital Motion

### Gravitation

Gravitation & Mechanics - animations

Law of Universal Gravitation
Inverse Square Relationship

### Gravity Gradients & Tidal Forces

Gravity's strength is inversely proportional to the square of the objects' distance from each other. For an object in orbit about a planet, the parts of the object closer to the planet feel a slightly stronger gravitational attraction than do parts on the other side of the object. This is known as gravity gradient. It causes a slight torque to be applied to any orbiting mass which has asymmetric mass distribution (for example, is not spherical), until it assumes a stable attitude with the more massive parts pointing toward the planet. An object whose mass is distributed like a bowling pin would end up in an attitude with its more massive end pointing toward the planet, if all other forces were equal.

Consider the case of a fairly massive body such as our Moon in Earth orbit. The gravity gradient effect has caused the Moon, whose mass is unevenly distributed, to assume a stable rotational rate which keeps one face towards Earth at all times, like the bowling pin described above.

The Moon's gravitation acts upon the Earth's oceans and atmosphere, causing two bulges to form. The bulge on the side of Earth that faces the moon is caused by the proximity of the moon and its relatively stronger gravitational pull on that side. The bulge on the opposite side of Earth results from that side being attracted toward the moon less strongly than is the central part of Earth. Earth's atmosphere and crust are also affected to a smaller degree. Other factors, including Earth's rotation and surface roughness, complicate the tidal effect. On planets or satellites without oceans, the same forces apply, causing slight deformations in the body. This mechanical stress can translate into heat, as in the case of Jupiter's volcanic moon Io.

#### For Further Study

Select the "Links" section below for additional references, including mathematical tutorials and example problems.

All objects with mass attract each other

 Gravitation is the mutual attraction of all masses in the universe. While its effect decreases in proportion to distance squared, it nonetheless applies, to some extent, regardless of the sizes of the masses or their distance apart. The concepts associated with planetary motions developed by Johannes Kepler (1571-1630) describe the positions and motions of objects in our solar system. Isaac Newton (1643-1727) later explained why Kepler's laws worked, by showing they depend on gravitation. Albert Einstein (1879-1955) posed an explanation of how gravitation works in his general theory of relativity. In any solar system, planetary motions are orbits gravitationally bound to a star. Since orbits are ellipses, a review of ellipses follows

### Newton's 1st Law

Linear vs Circular Motion

Relative Motion

### Newton's Principles of Mechanics

Sir Isaac Newton realized that the force that makes apples fall to the ground is the same force that makes the planets "fall" around the sun. Newton had been asked to address the question of why planets move as they do. He established that a force of attraction toward the sun becomes weaker in proportion to the square of the distance from the sun.

Newton postulated that the shape of an orbit should be an ellipse. Circular orbits are merely a special case of an ellipse where the foci are coincident. Newton described his work in the Mathematical Principles of Natural Philosophy (often called simply the Principia), which he published in 1685. Newton gave his laws of motion as follows:

1. Every body continues in a state of rest, or of uniform motion in a straight line, unless it is compelled to change that state by forces impressed upon it.

2. The change of motion (linear momentum) is proportional to the force impressed and is made in the direction of the straight line in which that force is impressed.

3. To every action there is always an equal and opposite reaction; or, the mutual actions of two bodies upon each other are always equal, and act in opposite directions.

(Notice that Newton's laws describe the behavior of inertia, they do not explain what the nature of inertia is. This is still a valid question, as is the nature of mass.)

There are three ways to modify the momentum of a body. The mass can be changed, the velocity can be changed (acceleration), or both.

### Acceleration

Force (F) equals change in velocity (acceleration, A) times mass (M):

#### F = MA

Acceleration may be produced by applying a force to a mass (such as a spacecraft). If applied in the same direction as an object's velocity, the object's velocity increases in relation to an unaccelerated observer. If acceleration is produced by applying a force in the opposite direction from the object's original velocity, it will slow down relative to an unaccelerated observer. If the acceleration is produced by a force at some other angle to the velocity, the object will be deflected. These cases are illustrated below.

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The world standard of mass is the kilogram, whose definition is based on the mass of a metal cylinder kept in France. Previously, the standard was based upon the mass of one cubic centimeter of water being one gram, which is approximately correct. The standard unit of force is the newton, which is the force required to accelerate a 1-kg mass 1 m/sec2 (one meter per second per second). A newton is equal to the force from the weight of about 100 g of water in Earth's gravity. That's about half a cup. A dyne is the force required to accelerate a 1-g mass 1 cm/s2.

### Circular Motion

Rotate

Revolve

Period/Rotation Speed

Tangential Velocity

### Acceleration in Orbit

Newton's first law describes how, once in motion, planets remain in motion. What it does not do is explain how the planets are observed to move in nearly circular orbits rather than straight lines. Enter the second law. To move in a curved path, a planet must have an acceleration toward the center of the circle. This is called centripetal acceleration and is supplied by the mutual gravitational attraction between the sun and the planet.

### Rotational Mechanics

Centripetal Acceleration

Centrifugal Force

### Rotation and Revolution

"Rotation" refers to an object's spinning motion about its own axis. "Revolution" refers the object's orbital motion around another object. For example, Earth rotates on its own axis, producing the 24-hour day. Earth revolves about the Sun, producing the 365-day year. A satellite revolves around a planet.

### Earth's Rotation

The Earth rotates on its axis relative to the sun every 24.0 hours mean solar time, with an inclination of 23.45 degrees from the plane of its orbit around the sun. Mean solar time represents an average of the variations caused by Earth's non-circular orbit. Its rotation relative to "fixed" stars (sidereal time) is 3 minutes 56.55 seconds shorter than the mean solar day, the equivalent of one solar day per year.

Kepler

### Kepler's Laws

Johannes Kepler's laws, as expressed by Newton, are:

1. If two bodies interact gravitationally, each will describe an orbit that is a conic section about the common mass of the pair. If the bodies are permanently associated, their orbits will be ellipses. If they are not permanently associated with each other, their orbits will be hyperbolas (open curves).

2. If two bodies revolve around each other under the influence of a central force (whether or not in a closed elliptical orbit), a line joining them sweeps out equal areas in the orbital plane in equal intervals of time.

3. If two bodies revolve mutually about each other, the sum of their masses times the square of their period of mutual revolution is in proportion to the cube of the semi-major axis of the relative orbit of one about the other.

The major application of Kepler's first law is to precisely describe the geometric shape of an orbit: an ellipse, unless perturbed by other objects. Kepler's first law also informs us that if a comet, or other object, is observed to have a hyperbolic path, it will visit the sun only once, unless its encounter with a planet alters its trajectory again.

Kepler's second law addresses the velocity of an object in orbit. Conforming to this law, a comet with a highly elliptical orbit has a velocity at closest approach to the sun that is many times its velocity when farthest from the sun. Even so, the area of the orbital plane swept is still constant for any given period of time.

CLICK IMAGE TO START / STOP ANIMATION

Kepler's third law describes the relationship between the masses of two objects mutually revolving around each other and the determination of orbital parameters. Consider a small star in orbit about a more massive one. Both stars actually revolve about a common center of mass, which is called the barycenter. This is true no matter what the size or mass of each of the objects involved. Measuring a star's motion about its barycenter with a massive planet is one method that has been used to discover planetary systems associated with distant stars.

Obviously, these statements apply to a two-dimensional picture of planetary motion, which is all that is needed for describing orbits. A three-dimensional picture of motion would include the path of the sun through space.

Circular

Elliptical

### Orbiting a Real Planet

Isaac Newton's cannonball is really a pretty good analogy. It makes it clear that to get a spacecraft into orbit, you need to raise it up and accelerate it until it is going so fast that as it falls, it falls completely around the planet.

In practical terms, you don't generally want to be less than about 150 kilometers above surface of Earth. At that altitude, the atmosphere is so thin that it doesn't present much frictional drag to slow you down. You need your rocket to speed the spacecraft to the neighborhood of 30,000 km/hr (about 19,000 mph). Once you've done that, your spacecraft will continue falling around Earth. No more propulsion is necessary, except for occasional minor adjustments. It can remain in orbit for months or years before the presence of the thin upper atmosphere causes the orbit to degrade. These same mechanical concepts (but different numbers for altitude and speed) apply whether you're talking about orbiting Earth, Venus, Mars, the Moon, the sun, or anything.

### A Periapsis by Any Other Name...

Periapsis and apoapsis are generic terms. The prefixes "peri-" and "ap-" are commonly applied to the Greek or Roman names of the bodies which are being orbited. For example, look for perigee and apogee at Earth, perijove and apojove at Jupiter, periselene and apselene or perilune and apolune in lunar orbit, perichron and apochron if you're orbiting Saturn, and perihelion and aphelion if you're orbiting the sun, and so on.

### Freefall

If you ride along with an orbiting spacecraft, you feel as if you are falling, as in fact you are. The condition is properly called free fall. You find yourself falling at the same rate as the spacecraft, which would appear to be floating there (falling) beside you, or around you if you're aboard the International Space Station. You'd just never hit the ground.

Notice that an orbiting spacecraft has not escaped Earth's gravity, which is very much present -- it is giving the mass the centripetal acceleration it needs to stay in orbit. It just happens to be balanced out by the speed that the rocket provided when it placed the spacecraft in orbit. Yes, gravity is a little weaker on orbit, simply because you're farther from Earth's center, but it's mostly there. So terms like "weightless" and "micro gravity" have to be taken with a grain of salt... gravity is still dominant, but some of its familiar effects are not apparent on orbit.

#### For Further Study

Select the "Links" section below for additional references, including mathematical tutorials and example problems.

### Ellipses

An ellipse is a closed plane curve generated in such a way that the sum of its distances from two fixed points (called the foci) is constant. In the illustration below, the sum of Distance A + Distance B is constant for any point on the curve.

#### Ellipse Foci

An ellipse results from the intersection of a circular cone and a plane cutting completely through the cone. The maximum diameter is called the major axis. It determines the size of an ellipse. Half the maximum diameter, the distance from the center of the ellipse to one end, is called the semi-major axis.

The shape of an ellipse is determined by how close together the foci are in relation to the major axis. Eccentricity is the distance between the foci divided by the major axis. If the foci coincide, the ellipse is a circle. Therefore, a circle is an ellipse with an eccentricity of zero.

Orbital Speed

Conservation of Orbital Energy

### How Orbits Work

 CLICK IMAGE TO START / STOP ANIMATION

These drawings simplify the physics of orbital mechanics, making it easy to grasp some of the basic concepts. We see Earth with a ridiculously tall mountain rising from it. The mountain, as Isaac Newton first described, has a cannon at its summit.

1.   When the cannon is fired, the cannonball follows its ballistic arc, falling as a result of Earth's gravity, and of course it hits Earth some distance away from the mountain.

2.  If we pack more gunpowder into the cannon, the next time it's fired, the cannonball goes faster and farther away from the mountain, meanwhile falling to Earth at the same rate as it did before. The result is that it has gone halfway around the cartoon planet before it hits the ground. (You might enjoy the more elaborate animation at Space Place.)

 CLICK IMAGE TO START / STOP ANIMATION In order to make their point these cartoons ignore lots of facts, of course, such as the impossibility of there being such a high mountain on Earth, the drag exerted by the Earth's atmosphere on the cannonball, and the energy a cannon can impart to a projectile... not to mention how hard it would be for climbers to carry everything up such a high mountain! Nevertheless the orbital mechanics they illustrate (in the absence of details like atmosphere) are valid.

3.   Packing still MORE gunpowder into the capable cannon, the cannonball goes much faster, and so much farther that it just never has a chance to touch down. All the while it would be falling to Earth at the same rate as it did in the previous cartoons. This time it falls completely around Earth! We can say it has achieved orbit.

 APOAPSIS PERIAPSIS CLICK IMAGE TO START / STOP ANIMATION

That cannonball would skim past the south pole, and climb right back up to the same altitude from which it was fired, just like the cartoon shows. Its orbit is an ellipse.

This is basically how a spacecraft achieves orbit. It gets an initial boost from a rocket, and then simply falls for the rest of its orbital life. Modern spacecraft are more capable than cannonballs, and they have rocket thrusters that permit the occasional adjustment in orbit, as described below. Apart from any such rocket engine burns, they're just falling. Launched in 1958 and long silent, the Vanguard-1 Satellite is still falling around Earth.

In the third cartoon, you'll see that part of the orbit comes closer to Earth's surface that the rest of it does. This is called the periapsis of the orbit. The mountain represents the highest point in the orbit. That's called the apoapsis. The altitude affects the time an orbit takes, called the orbit period. The period of the space shuttle's orbit, at say 200 kilometers, is about 90 minutes. Vanguard-1, by the way, has an orbital period of 134.2 minutes, with its periapsis altitude of 654 km, and apoapsis altitude of 3969 km.

## Astronomical Dimensions

### Units of Measure

the AU - Astronomical Unit

Light Years, Parsecs, Eons

Relative to Things Familiar

### How Many?

Galaxies

Stars

Solar Systems/Planets

### How Big?

The Universe

Galaxies

The Milky Way

Our Sun

Earth & the Other Planets

Asteroids

Comets

### How far?

to the Sun

to the Moon

to the Other Planets

to the Nearest Star

to the Nearest Solar System

to the Center of the Milky Way

to the Nearest Galaxy

### How Old?

the Universe

the Stars

Our Sun

Our Solar Sytem

The Earth, Moon, and Planets

## Chemical Composition

### of the Universe

Galaxies

Stars

Interstellar Space

Dark Matter

### of Our Solar System

Sol - the Sun

Terra - the Earth

Luna - the Moon

the Planets

Asteroids

Comets

## Sources of Light & Energy

### Temperature

Heat

Heat Transfer in Space

Visible

Infrared

## Formation, Evolution, & Age

### of the Universe

Before

Big Bang

Universal Expansion

The Center

The End

Nebulae

### Our Solar System

the Sun

The Earth & Moon

The Planets

Asteroids

Comets

 The structure and composition of the universe can be learned from studying stars and galaxies and their evolution. As a basis for understanding this concept: a. Students know galaxies are clusters of billions of stars and may have different shapes. b. Students know that the Sun is one of many stars in the Milky Way galaxy and that stars may differ in size, temperature, and color. c. Students know how to use astronomical units and light years as measures of distances between the Sun, stars, and Earth. d. Students know that stars are the source of light for all bright objects in outer space and that the Moon and planets shine by reflected sunlight, not by their own light. e. Students know the appearance, general composition, relative position and size, and motion of objects in the solar system, including planets, planetary satellites, comets, and asteroids originally thought to be stars are now known to be distant galaxies.

4.a. Galaxies them-selves appear to form clusters that are separated by vast expanses of empty space. As galaxies are discovered they are classified by their differing sizes and shapes. The most common shapes are spiral, elliptical, and irregular. Beautiful, full-color photo-graphs of astronomical objects are available on the Internet, in library books, and in popular and professional journals. It may also interest students to know that astronomers have inferred the existence of planets orbiting some stars.

4.b The Sun is a star located on the rim of a typical spiral galaxy called the Milky Way and orbits the galactic center. In similar spiral galaxies this galactic center appears as a bulge of stars in the heart of the disk. The bright band of stars cutting across the night sky is the edge of the Milky Way as seen from the perspective of Earth, which lies within the disk of the galaxy. Stars vary greatly in size, temperature, and color. For the most part those variations are related to the stars’ life cycles. Light from the Sun and other stars indicates that the Sun is a fairly typical star. It has a mass of about 2 × 1030 kg and an energy output, or luminosity, of about 4 × 1026 joules/sec. The surface temperature of the Sun is approximately 5,500 degrees Celsius, and the radius of the Sun is about 700 million meters. The surface temperature determines the yellow color of the light shining from the Sun. Red stars have cooler surface temperatures, and blue stars have hotter surface temperatures. To connect the surface temperature to the color of the Sun or of other stars, teachers should obtain a “black-body” temperature spectrum chart, which is typically found in high school and college textbooks.

4.c Distances between astronomical objects are enormous. Measurement units such as centimeters, meters, and kilometers used in the laboratory or on field trips are not useful for expressing those distances. Consequently, astronomers use other units to describe large distances. The astronomical unit (AU) is defined to be equal to the average distance from Earth to the Sun: 1 AU = 1.496 × 1011 meters. Distances between planets of the solar system are usually expressed in AU. For distances between stars and galaxies, even that large unit of length is not sufficient. Interstellar and intergalactic distances are expressed in terms of how far light travels in one year, the light year (ly): 1 ly = 9.462 × 1015 meters, or approximately 6 trillion miles. The most distant objects observed in the universe are estimated to be 10 to 15 billion light years from the solar system. Teachers need to help students become familiar with AUs by expressing the distance from the Sun to the planets in AUs instead of meters or miles. A good way to become familiar with the relative distances of the planets from the Sun is to lay out the solar system to scale on a length of cash register tape.

4.d The energy from the Sun and other stars, seen as visible light, is caused by nuclear fusion reactions that occur deep inside the stars’ cores. By carefully analyzing the spectrum of light from stars, scientists know that most stars are composed primarily of hydrogen, a smaller amount of helium, and much smaller amounts of all the other chemical elements. Most stars are born from the gravitational compression and heating of hydrogen gas. A fusion reaction results when hydrogen nuclei combine to form helium nuclei. This event releases energy and establishes a balance between the inward pull of gravity and the outward pressure of the fusion reaction products.

Ancient peoples observed that some objects in the night sky wandered about while other objects maintained fixed positions in relation to one another (i.e., the constellations). Those “wanderers” are the planets. Through careful observations of the planets’ movements, scientists found that planets travel in nearly circular (slightly elliptical) orbits about the Sun.

Planets (and the Moon) do not generate the light that makes them visible, a fact that is demonstrated during eclipses of the Moon or by observation of the phases of the Moon and planets when a portion is shaded from the direct light of the Sun.

## Various types of exploratory missions have yielded much information about the reflectivity, structure, and composition of the Moon and the planets. Those missions have included spacecraft flying by and orbiting those bodies, the soft landing of spacecraft fitted with instruments, and, of course, the visits of astronauts to the Moon

### Teachers should look for field trip opportunities for students to observe the night sky from an astronomical observatory or with the aid of a local astronomical society. A visit to a planetarium would be another way of observing the sky. If feasible, teachers should have students observe the motion of Jupiter’s inner moons as well as the phases of Venus. Using resources in the library-media center, students can research related topics of interest.

Solar System

The solar system has been a topic of study from the beginning of history. For nearly all that time, people have had to rely on long-range and indirect measurements of its objects. For all of human history and pre-history, observations were based on visible light. Then in the 20th century people discovered how to use additional parts of the spectrum. Radio waves, received here on Earth, have been used since 1931 to investigate celestial objects. Starting with the emergence of space flight in 1957, instruments operating above Earth's obscuring atmosphere could take advantage not only of light and radio, but virtually the whole spectrum (the electromagnetic spectrum is the subject of a later chapter). At last, with interplanetary travel, instruments can be carried to many solar system objects, to measure their physical properties and dynamics directly and at very close range. In the 21st century, knowledge of the solar system is advancing at an unprecedented rate.

The solar system consists of an average star we call the sun, the planets Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune, and Pluto. It includes the satellites of the planets, numerous comets, asteroids, meteoroids, and the interplanetary medium, which permeates interplanetary space. The sun is the richest source of electromagnetic energy in the solar system. The sun's nearest known stellar neighbor is a red dwarf star called Proxima Centauri, at a distance of about 4.2 light years. (A light year is the distance light travels in a year, at about 300,000 km per second.)

### Motions Within the Solar System

The sun and planets each rotate on their axes. Because they formed from the same rotating disk, the planets, most of their satellites, and the asteroids, all revolve around the sun in the same direction as it rotates, and in nearly circular orbits. The planets orbit the sun in or near the same plane, called the ecliptic (because it is where eclipses occur). Pluto is a special case in that its orbit is the most highly inclined (17 degrees) and the most highly elliptical of all the planets. Because its orbit is so eccentric, Pluto sometimes comes closer to the sun than does Neptune. It's interesting to note that most planets rotate in or near the plane in which they orbit the sun, since they formed, rotating, out of the same dust ring. Uranus must have suffered a whopping collision, though, that set it rotating on its side.

### Distances Within the Solar System

The most common unit of measurement for distances within the solar system is the astronomical unit (AU). The AU is based on the mean distance from the sun to Earth, roughly 150,000,000 km. JPL's Deep Space Network refined the precise value of the AU in the 1960s by obtaining radar echoes from Venus. This measurement was important since spacecraft navigation depends on accurate knowledge of the AU. Another way to indicate distances within the solar system is terms of light time, which is the distance light travels in a unit of time. Distances within the solar system, while vast compared to our travels on Earth's surface, are comparatively small-scale in astronomical terms. For reference, Proxima Centauri, the nearest star at about 4 light years away, is over 265,000 AU from the sun.

Light Time Approximate Distance Example
3 seconds 900,000 km ~Earth-Moon Round Trip
3 minutes 54,000,000 km ~Sun to Mercury
8.3 minutes 149,600,000 km Sun to Earth (1 AU)
1 hour 1,000,000,000 km ~1.5 x Sun-Jupiter Distance
12.5 hours 90 AU Voyager-1 (January, 2004)
1 year 63,000 AU Light Year
4 years 252,000 AU ~Next closest star

### Temperatures Within the Solar System

Select the above link for the Solar System Temperature Reference showing examples and comparing temperatures of objects and conditions from absolute zero through planet temperatures, to those of stars. The reference also includes temperature conversion factors and links to a conversion engine.

Mass Distribution Within the Solar System

 99.85% Sun 0.135% Planets 0.015% Comets Satellites Minor Planets Meteroids Interplanetary Medium

Units

Universe

### In Cosmic Perspective

Our whole solar system, together with all the local stars you can see on a clear dark night, orbits the center of our home galaxy. This spiral disk we call the Milky Way includes some 200 billion stars, thousands of gigantic clouds of gas and dust, and enormous quantities of mysterious dark matter

Interstellar/galactic Space

Interstellar space is the term given to the space between stars in the galaxy. We are beginning to find that many stars besides the sun harbor their own planets, called extrasolar planets. As of January 2004 astronomers have detected about 100 planets orbiting other stars. They are all giant, Jupiter-like planets, made mostly of gas, since current detection methods cannot reveal smaller worlds. Their formation process is still unclear.

Galaxies

The image at right shows a galaxy similar to the Milky Way, known as M100 (click the image for details). The Milky Way has two small galaxies orbiting it nearby, which are visible from the southern hemisphere. They are called the Large Magellanic Cloud and the Small Magellanic Cloud. Our galaxy, one of billions of galaxies known, is travelling through intergalactic space. On a cosmic scale, all galaxies are generally receding from each other, although those relatively close together may exhibit additional local motion toward or away from each other

Sun

### The Sun

The sun is a typical star. Its spectral classification is "G2 V." G2 basically means it's a yellow-white star, and the roman numeral V means it's a "main sequence" dwarf star (by far the most common) as opposed to supergiant, or sub-dwarf, etc. You can view current images of the sun as seen today by the suite of instruments aboard SOHO (Solar & Heliospheric Observatory) as it views the sun from the L1 Lagrange point between the Earth and the sun.

The sun dominates the gravitational field of the solar system; it contains about 99.85% of the solar system's mass. The planets, which condensed out of the same disk of material that formed the sun, contain only about 0.135% of the mass of the solar system. Satellites of the planets, comets, asteroids, meteoroids, and the interplanetary medium constitute the remaining 0.015%. Even though the planets make up only a small portion of the solar system's mass, they do retain the vast majority of the solar system's angular momentum. This storehouse of momentum can be utilized by interplanetary spacecraft on so-called "gravity-assist" trajectories.

The sun's gravity creates extreme pressures and temperatures within itself, sustaining a thermonuclear reaction fusing hydrogen nuclei and producing helium nuclei. This reaction yields tremendous amounts of energy, causing the material of the sun to be plasma and gas. These thermonuclear reactions began about 5 x 109 years ago in the sun, and will probably continue for another 5 x 109 years. The apparent surface of the sun has no clean physical boundary, as solid planets do, although it appears as a sharp boundary when seen from the distance of Earth. Click the SOHO solar image at right for more details about the image.

The sun rotates on its axis with a period of approximately 25.4 days. This is the adopted value at 16° latitude. Because the sun is a gaseous body, not all its material rotates together. (This solar fact sheet describes how rotation varies with latitude). Solar matter at very high latitudes takes over 30 days to complete a rotation. Our star's output varies slightly over an 11-year cycle, during which the number of sunspots changes.

The sun's axis is tilted about 7.25 degrees to the axis of the Earth's orbit, so we see a little more of the sun's northern polar region each September and more of its southern region in March. As viewed from the Earth's surface, the Sun subtends roughly half a degree of arc upon the sky (as does the Moon, at this period in cosmic time.)

The sun has strong magnetic fields that are associated with sunspots and coronal mass ejections, CMEs (also called solar flares). A sunspot is a relatively cool area that appears dark against the hotter face of the sun. Sunspots are formed when magnetic field lines just below the sun's visible surface are twisted, and reach though the photosphere. CMEs are huge magnetic bubbles of plasma that erupt from the sun's corona and travel through space at high speed. View this spectacular 5-Mbyte SOHO movie of CMEs in August, 1999.

The solar magnetic field is not uniform, and it is very dynamic. Solar magnetic field variations and dynamics are targets of major interest in the exploration of the solar system

### Our Bubble of Interplanetary Space

The "vacuum" of interplanetary space includes copious amounts of energy radiated from the sun, some interplanetary and interstellar dust (microscopic solid particles) and gas, and the solar wind. The solar wind, discovered by Eugene Parker in 1958, is a flow of lightweight ions and electrons (which together comprise plasma) thrown from the sun. The solar wind inflates a bubble, called the heliosphere, in the surrounding interstellar medium (ISM).

The solar wind has a visible effect on comet tails. It flows outward from our star at about 400 km per second, measured in the vicinity of Earth's orbit, and the Ulysses spacecraft found that it approximately doubles its speed at high solar latitudes.

Diagram courtesy Dr. Gary Zank, University of Delaware

The boundary at which the solar wind meets the ISM, containing the collective "solar" wind from other local stars in our galaxy, is called the heliopause. This is where the solar wind and the sun's magnetic field stop. The boundary is theorized to be roughly teardrop-shaped, because it gets "blown back" to form a heliotail, as the sun moves through the ISM (toward the right in the diagram above). The sun's relative motion may also create an advance bow shock, analogous to that of a moving boat. This is a matter of debate and depends partly on the strength of the interstellar magnetic field.

But before it gets out to the heliopause, the solar wind is thought to slow to subsonic speeds, creating a termination shock. This appears at the perimeter of the green circle in the diagram. Its actual shape, whether roughly spherical or teardrop, depends on magnetic field strengths, as yet unknown.

In the diagram above, temperatures are theorized; none have been actually measured beyond the termination shock. Note that even with the high particle temperatures, their density is so low that massive objects like spacecraft remain very cold (as long as they are shaded, or distant, from the sun).

The white lines in the diagram represent charged particles, mostly hydrogen ions, in the interstellar wind. They are deflected around the heliosphere's edge (the heliopause). The pink arrow shows how neutral particles penetrate the heliopause. These are primarily hydrogen and helium atoms, which are mostly not affected by magnetic fields, and there are also heavier dust grains. These interstellar neutral particles make up a substantial fraction of the material found within the heliosphere. The little black + in the green area represents the location of Voyager 1 at 80 AU in January of 2001. Voyager 1 is humanity's most distant object, and in 2004 the spacecraft is returning evidence that it is probably beginning to encounter the termination shock now, at a distance of just over 90 AU from the Sun.

The solar wind changes with the 11-year solar cycle, and the interstellar medium is not homogeneous, so the shape and size of the heliosphere probably fluctuate.

The solar magnetic field is the dominating magnetic field within the heliosphere, except in the immediate environment of planets which have their own magnetic fields. It can be measured by spacecraft throughout the solar system, but not here on earth, where we are shielded by our planet's own magnetic field.

The actual properties of the interstellar medium (outside the heliosphere), including the strength and orientation of its magnetic field, are important in determining the size and shape of the heliopause. Measurements that the two Voyager spacecraft will make in the region beyond the termination shock, and possibly beyond the heliopause, will provide important inputs to models of the termination shock and heliopause. Even though the Voyagers will sample these regions in discrete locations, this information will result in more robust overall models.

For further information on this vast subject and its many related topics, search the web for "heliosphere," "Alfven waves," "pickup ions," and "local interstellar cloud."

## Planets

### The Terrestrial Planets

The planets Mercury, Venus, Earth, and Mars, are called terrestrial because they have a compact, rocky surface like Earth's terra firma. The terrestrial planets are the four innermost planets in the solar system. None of the terrestrial planets have rings, although Earth does have belts of trapped radiation, as discussed below. Only Earth has a substantial planetary magnetic field. Mars and the Earth's Moon have localized regional magnetic fields at different places across their surfaces, but no global field.

Of the terrestrial planets, Venus, Earth, and Mars have significant atmospheres. The gases present in a planetary atmosphere are related to a planet's size, mass, temperature, how the planet was formed, and whether life is present. The temperature of gases may cause their molecules or atoms to achieve velocities that escape the planet's gravitational field. This contributes to Mercury's lack of a permanent atmosphere, as does its proximity to the source of the relentless solar wind.

The presence of life on Earth causes oxygen to be abundant in the atmosphere, and in this Earth is unique in our solar system. Without life, most of the oxygen would soon become part of the compounds on the planet's surface. Thus, the discovery of oxygen's signature in the atmosphere of an extrasolar planet would be significant.

Mercury lacks an atmosphere to speak of. Even though most of its surface is very hot, there is strong evidence that water ice exists in locations near its north and south poles which are kept permanently-shaded by crater walls. This evidence comes from Earth-based radar observations of the innermost planet. The discovery of permanently shaded ice at the poles of Earth's Moon strengthens arguments that the indications of ice on Mercury may be real.

Venus's atmosphere of carbon dioxide is dense, hot, and permanently cloudy, making the planet's surface invisible. Its best surface studies have come from landers and imaging radar from orbiting spacecraft.

Earth, as of November 2001, is still the only place known to harbor life. And life has flourished here since the planet was young. Our home planet is also unique in having large oceans of surface water, an oxygen-rich atmosphere, and shifting crustal sections floating on a hot mantle below, described by the theory of plate tectonics. Earth's Moon orbits the planet once every 27.3 days at an average distance of about 384,400 km. The Moon's orbital distance is steadily increasing at the very slow rate of 38 meters per millenium. Its distance at this point in its history makes the Moon appear in the sky to be about the same size as the Sun, subtending about half a degree.

Mars' atmosphere, also carbon dioxide, is much thinner than Earth's, but it sustains wispy clouds of water vapor. Mars has polar caps of carbon dioxide ice and water ice. The planet's surface shows strong evidence for extensive water coverage in its distant past, as well as possible evidence for water flow in small springs during recent times.

JPL's first spacecraft, Explorer 1, carried a single scientific instrument devised and operated by James Van Allen and his team from the University of Iowa. Early in 1958 the experiment discovered bands of rapidly moving charged particles trapped by Earth's magnetic field in toroidal, or doughnut-shaped regions surrounding the equator. The illustration below shows these belts only in two dimensions, as if they were sliced into thin cross-sections.

The belts that carry Van Allen's name have two areas of maximum density. The inner region, consisting largely of protons with an energy greater than 30 million EV, is centered about 3,000 km above Earth's surface. The outer belt is centered about 15,000 to 20,000 km up, and contains electrons with energies in the hundreds of millions of EV. It also has a high flux of protons, although of lower energies than those in the inner belt.

### Terrestrial Planetary Data

Mercury Venus Earth Mars
Mean distance from sun (AU) 0.387 0.723 1 1.524
Light minutes from sun 3.2 6.0 8.3 12.7
Mass (x Earth) 0.0553 0.815 1 0.107
Equatorial radius (x Earth) 0.383 0.949 1 0.533
Rotation period
(Earth days)
175.942 − 116.75
1 1.027
Orbit period (Earth years) 0.241 0.615 1 1.881
Mean orbital velocity (km/s) 47.87 35.02 29.78 24.13
Natural satellites 0 0 1 2
Surface atmospheric pressure (bars) Near 0 92 1 .0069
to .009
Global Magnetic field Faint None Yes None

#### Mean Distances of the Terrestrial Planets from Sun

Orbits are drawn approximately to scale.

### The Jovian Planets

Jupiter, Saturn, Uranus, and Neptune are known as the Jovian (Jupiter-like) planets, because they are all gigantic compared with Earth, and they have a gaseous nature like Jupiter's -- mostly hydrogen, with some helium and trace gases and ices. The Jovian planets are thus referred to as the "gas giants" because gas is what they are mostly made of, although some or all of them probably have small solid cores. All have significant planetary magnetic fields, rings, and lots of satellites.

Jupiter is more massive than all the other planets combined. It emits electromagnetic energy from charged atomic particles spiraling through its strong magnetic field. If this sizzling magnetosphere were visible to our eyes, Jupiter would appear larger then the full Moon in Earth's sky. The trapped radiation belts near Jupiter present a hazard to spacecraft as do Earth's Van Allen belts, although the Jovian particle flux and distribution differ from Earth's. Bringing a spacecraft close to Jupiter presents a hazard mostly from ionized particles. Spacecraft intended to fly close to Jupiter must be designed with radiation-hardened components and shielding. Spacecraft using Jupiter for gravity assist may also be exposed to a harsh radiation dose. Instruments not intended to operate at Jupiter must be protected by being powered off and by having detectors covered.

Saturn, the farthest planet easily visible to the unaided eye, is known for its extensive, complex system of rings, which are very impressive even in a small telescope. Using a small telescope one can also discern the planet's oblateness, or flattening at the poles. Continued study of Saturn's ring system can yield new understandings of orbital dynamics, applicable to any system of orbiting bodies, from newly forming solar systems to galaxies.

Uranus, which rotates on its side, and Neptune are of similar size and color, although Neptune seems to have a more active atmosphere despite its much greater distance from the sun. Both planets are composed primarily of rock and various ices. Their extensive atmosphere, which makes up about 15% the mass of each planet, is hydrogen with a little helium. Neither of these planets were known to the ancients; Uranus was discovered in 1781, Neptune in 1846.

### ...And Pluto

Pluto is neither a rocky terrestrial planet nor a Jovian gas giant. It is a Kuiper Belt Object, composed of material left over after the formation of the other planets (see Comets in the next section). Kuiper Belt Objects were never exposed to the higher temperatures and solar radiation levels of the inner solar system. Pluto has large quantities of nitrogen ice, and simple molecules of carbon, hydrogen and oxygen. They remain on Pluto as a sample of the primordial material that set the stage for the evolution of the solar system as it exists today, including life. Its nitrogen atmosphere will precipitate out onto the surface as snow when its orbit takes it much farther from the sun than it is today. Since it has not yet been visited by a spacecraft, comparatively little is known about this small, distant body. Objects that orbit the Sun beyond Neptune's orbit are known as trans-Neptunian objects.

MOONS

### Satellites of the Jovian Planets

The gas giants have numerous satellites, many of which are large, and seem as interesting as any planet. Small "new" satellites of the Jovian planets are being discovered every few years.

Jupiter's Galilean satellites, so named because Galileo Galilei discovered them in 1610, exhibit great diversity from each other. All four can be easily seen in a small telescope or binoculars. Io (pictured here) is the closest of these to Jupiter. Io is the most volcanically active body in the solar system, due to heat resulting from tidal forces (discussed further in Chapter 3) which flex its crust. Powerful Earth-based telescopes can observe volcanoes resurfacing Io continuously. Europa is covered with an extremely smooth shell of water ice. There is probably an ocean of liquid water below the shell, warmed by the same forces that heat Io's volcanoes. Ganymede has mountains, valleys, craters, and cooled lava flows. Its ancient surface resembles Earth's Moon, and it is also suspected of having a sub-surface ocean. Callisto, the outermost Galilean moon, is pocked all over with impact craters, indicating that its surface has changed little since the early days of its formation.

Saturn's largest moon, enigmatic Titan, is larger than the planet Mercury. Almost a terrestrial planet itself, Titan has a hazy nitrogen atmosphere denser than Earth's. The Huygens Probe executed a spectacurly successful mission in January 2005, revealing rivers and lakebeds on the surface, and extensive details of its atmosphere. Saturn also has many smaller satellites made largely of

water ice. The "front," or leading, side of Saturn's icy satellite Iapetus is covered in dark material of some kind, and an equatorial mountain range higher than Olympus Mons on Mars was recently discovered on this 1450-km diameter moon. Icy Enceladus orbits within the densest part of Saturn's E Ring, and may somehow be the source of that ring's fine ice-particle makeup.

All of Uranus's five largest moons have extremely different characteristics. The surface of Miranda, the smallest of these, shows evidence of extensive geologic activity. Umbriel's surface is dark, Titania and Ariel have trenches and faults, and Oberon's impact craters show bright rays similar to those on Callisto.

Neptune's largest moon Triton is partly covered with nitrogen ice and snow, and has currently active nitrogen geysers that leave sooty deposits on the surface downwind.

### Rings

 SATURN'S RINGS IN FALSE COLOR

Jupiter's equatorial dust rings can be detected at close range in visible light and from Earth in the infrared. They show up best when viewed from behind, in forward scattered sunlight. Saturn, Uranus, and Neptune all have rings made up of myriad particles of ice ranging in size from dust and sand to boulders. Each particle in a ring is an individual satellite of the planet in its own right. Ring particles interact with each other in complex ways, affected by gravity and electrical charge. They also interact with the thin extended atmospheres of the planets. Saturn's magnificent ring system, as visible from Earth, spans about 280,000 km, yet its thickness is only around 200 meters! The A-ring, measured at several points, was found to be only ten meters thick.

When two satellites occupy orbits very close to each other within a ring system, one orbiting farther from the planet than a ring, and the other one orbiting closer to the planet than that ring, they confine particles between their orbits into a narrow ring, by gravitationally interacting with the ring particles. Thus these satellites are called shepherd moons.

Jovian Planetary Data (Approximate)
Jupiter Saturn Uranus Neptune
Mean distance from sun (AU) 5.20 AU 9.58 AU 19.20 AU 30.05 AU
Light hours from sun 0.72 1.3 2.7 4.2
Mass (x Earth) 317.8 95.2 14.5 17.1
Radius (x Earth) 11.21 9.45 4.01 3.88
Rotation period (hours) 9.9 10.7 17.2 16.1
Orbit period (Earth years) 11.9 29.4 83.7 163.7
Mean orbital velocity (km/s) 13.07 9.69 6.81 5.43
Known natural satellites (2004) 63 33 27 13
Rings Dust Extensive system Thin, dark Broken ring arcs

#### Mean Distances of the Jovian Planets from Sun

Orbits are drawn approximately to scale.
Pluto omitted to accommodate scale.

### Inferior and Superior Planets

Mercury and Venus are referred to as inferior planets, not because they are any less important, but because their orbits are closer to the sun than is Earth's orbit. They always appear close to the sun in Earth's morning or evening sky; their apparent angle from the sun is called elongation. The outer planets, Mars, Jupiter, Saturn, Uranus, Neptune, and Pluto are all known as superior planets because their orbits are farther from the sun than the Earth's.

 Planet or Moon appears in crescent phase when nearly between observer and sun.

### Phases of Illumination

Inferior planets may pass between the Earth and the sun on part of their orbits, so they can exhibit nearly the complete range of phases from the earth's point of view... from the dark "new" phase, to slim "crescent" phase, to the mostly lit "gibbous" phase (approximating the fully illuminated "full" phase when approaching the other side of the sun). Our own Moon, of course, exhibits all the phases. Superior planets, though, usually appear gibbous, and appear full only when at opposition (see below), from our earthly point of view.

Viewed from superior planets, Earth goes through phases. Superior planets can be seen as crescents only from the vantage point of a spacecraft that is beyond them.

### Conjunction, Transit, Occultation, Opposition

When two bodies appear to pass closest together in the sky, they are said to be in conjunction. When a planet passes closest to the sun as seen from Earth and all three bodies are approximately in a straight line, the planet is said to be in solar conjunction. The inferior planets Venus and Mercury can have two kinds of conjunctions with the Sun: (1) An inferior conjunction, when the planet passes approximately between Earth and Sun (if it passes exactly between them, moving across the Sun's face as seen from Earth, it is said to be in transit); and (2) A superior conjunction when Earth and the other planet are on opposite sides of the Sun and all three bodies are again nearly in a straight line. If a planet disappears behind the sun because the sun is exactly between the planets, it is said to be in occultation.

Superior planets can have only superior conjunctions with the sun. At superior conjunction the outer planet appears near its completely illuminated full phase. The planet is said to be at opposition to the sun when both it and the Earth are on the same side of the sun, all three in line. (The Moon, when full, is in opposition to the sun; the Earth is then approximately between them.)

Opposition is a good time to observe an outer planet with Earth-based instruments, because it is at its nearest point to the Earth and it is in its fullest phase.

Inferior planets can never be at opposition to the sun, from Earth's point of view.

Occultations, transits, conjunctions, and oppositions offer special opportunities for scientific observations by spacecraft. Studies of the solar corona and tests of general relativity can be done at superior conjunctions. Superior conjunctions also present challenges communicating with a spacecraft nearly behind the sun, which is overwhelmingly noisy at the same radio frequencies as those used for communications. At opposition, such radio noise is at a minimum, presenting ideal conditions for gravitational wave searches. These special opportunities and challenges are further discussed in later chapters.

Earth

## Chapter 5. Planetary Orbits

Objectives:
Upon completion of this chapter you will be able to describe in general terms the characteristics of various types of planetary orbits. You will be able to describe the general concepts and advantages of geosynchronous orbits, polar orbits, walking orbits, sun-synchronous orbits, and some requirements for achieving them.

### Orbital Parameters and Elements

The terms orbital period, periapsis, and apoapsis were introduced in Chapter 3.

The direction a spacecraft or other body travels in orbit can be direct, or prograde, in which the spacecraft moves in the same direction as the planet rotates, or retrograde, going in a direction opposite the planet's rotation.

True anomaly is a term used to describe the locations of various points in an orbit. It is the angular distance of a point in an orbit past the point of periapsis, measured in degrees. For example, a spacecraft might cross a planet's equator at 10° true anomaly. Nodes are points where an orbit crosses a plane. As an orbiting body crosses the ecliptic plane going north, the node is referred to as the ascending node; going south, it is the descending node.

To completely describe an orbit mathematically, six quantities must be calculated. These quantities are called orbital elements, or Keplerian elements, after Johannes Kepler (1571-1630). They are:

1. Semi-major axis and

2. Eccentricity, which together are the basic measurements of the size and shape of the orbit's ellipse (described in Chapter 3. Recall an eccentricity of zero indicates a circular orbit).

3. Inclination is the angular distance of the orbital plane from the plane of the planet's equator (or from the ecliptic plane, if you're talking about heliocentric orbits), stated in degrees. An inclination of 0 degrees means the spacecraft orbits the planet at its equator, and in the same direction as the planet rotates. An inclination of 90 degrees indicates a polar orbit, in which the spacecraft passes over the north and south poles of the planet. An inclination of 180 degrees indicates a retrograde equatorial orbit.

4. Argument of periapsis is the argument (angular distance) of the periapsis from the ascending node.

5. Time of periapsis passage and

6. Celestial longitude of the ascending node are the remaining elements.

The orbital period is of interest to operations, although it is not one of the six Keplerian elements needed to define the orbit.

Generally, three astronomical or radiometric observations of an object in an orbit are enough to pin down all of the above six Keplerian elements. The following table gives a sense of the level of precision an interplanetary mission commonly deals with. These elements are measured during routine tracking by the Deep Space Network.

Elements of Magellan's Initial Venus Orbit
10 August 1990

 1. Semimajor Axis: 10434.162 km 2. Eccentricity: 0.2918967 3. Inclination: 85.69613° 4. Argument of Periapsis: 170.10651° 5. Periapsis Passage: DOY 222 19:54 ERT 6. Longitude of Ascending Node: -61.41017° ( Orbit Period: 3.26375 hr )

### Types of Orbits

#### Geosynchronous Orbits

A geosychronous orbit (GEO) is a prograde, circular, low inclination orbit about Earth having a period of 23 hours 56 minutes 4 seconds. A spacecraft in geosynchronous orbit appears to remain above Earth at a constant longitude, although it may seem to wander north and south.

#### Geostationary Orbits

 Geostationary Satellite CLICK IMAGE TO START / STOP ANIMATION

To achieve a geostationary orbit, a geosychronous orbit is chosen with an inclination of either zero, right on the equator, or else low enough that the spacecraft can use propulsive means to constrain the spacecraft's apparent position so it hangs motionless above a point on Earth. (Any such maneuvering on orbit is a process called station keeping.) The orbit can then be called geostationary. This orbit is ideal for certain kinds of communication satellites or meteorological satellites.

#### Polar Orbits

Polar orbits are 90 degree inclination orbits, useful for spacecraft that carry out mapping or surveillance operations. Since the orbital plane is nominally fixed in inertial space, the planet rotates below a polar orbit, allowing the spacecraft low-altitude access to virtually every point on the surface. The Magellan spacecraft used a nearly-polar orbit at Venus. Each periapsis pass, a swath of mapping data was taken, and the planet rotated so that swaths from consecutive orbits were adjacent to each other. When the planet rotated once, all 360 degrees longitude had been exposed to Magellan's surveillance.

To achieve a polar orbit at Earth requires more energy, thus more propellant, than does a direct orbit of low inclination. To achieve the latter, launch is normally accomplished near the equator, where the rotational speed of the surface contributes a significant part of the final speed required for orbit. A polar orbit will not be able to take advantage of the "free ride" provided by Earth's rotation, and thus the launch vehicle must provide all of the energy for attaining orbital speed.

#### Walking Orbits

Planets are not perfectly spherical, and they do not have evenly distributed surface mass. Also, they do not exist in a gravity "vacuum." Other bodies such as the sun, or natural satellites, contribute their gravitational influences to a spacecraft in orbit about a planet. It is possible to choose the parameters of a spacecraft's orbit to take advantage of some or all of these gravitational influences to induce precession, which causes a useful motion of the orbital plane. The result is called a walking orbit or a precessing orbit, since the orbital plane moves slowly with respect to fixed inertial space.

#### Sun Synchronous Orbits

A walking orbit whose parameters are chosen such that the orbital plane precesses with nearly the same period as the planet's solar orbit period is called a sun synchronous orbit. In such an orbit, the spacecraft crosses periapsis at about the same local time every orbit. This can be useful if instruments on board depend on a certain angle of solar illumination on the surface. Mars Global Surveyor's orbit is a 2-pm Mars Local Time sun-synchronous orbit, chosen to permit well-placed shadows for best viewing.

It may not be possible to rely on use of the gravity field alone to exactly maintain a desired synchronous timing, and occasional propulsive maneuvers may be necessary to adjust the orbit.

This remarkable image of a Martian aquifer was obtained by the Mars Global Surveyor spacecraft from its sun-synchronous Martian orbit in January 2000. The view is to the north. Click the image for more details.

#### Lagrange points

In line with the two large bodies are the L1, L2 and L3 points. The leading apex of the triangle is L4; the trailing apex is L5. These last two are also called Trojan points.

Galaxies

TEMPERATURES

## Solar System Temperature Reference

Kelvin Degrees C
(Celsius)
Degrees F
(Fahrenheit)
Remarks
0 -273.15 -459.67 Absolute Zero
20 nano-K -273.15~ -459.67~ Lowest achieved in a lab
2.7 -270.5 -454.8 Cosmic background microwave radiation
4.2 -268.95 -452.11 Liquid helium boils
14.01 -259.14 -434.45 Solid hydrogen melts
20.28 -252.87 -423.16 Liquid hydrogen boils
35 -235 -390 Neptune's moon Triton surface
63.17 -209.98 -345.96 Solid nitrogen melts
72 -201 -330 Neptune 1-bar level
76 -197 -323 Uranus 1-bar level
77.36 -195.79 -320.42 Liquid nitrogen boils
90 -180 -300 Saturn's moon Titan surface
90.188 -182.96 -297.33 Liquid oxygen boils
100 -175 -280 Planet Mercury surface, night
134 -139 -219 Saturn 1-bar level
153 -120 -184 Mars surface, night low
165 -108 -163 Jupiter 1-bar level
195 -78.15 -108.67 Carbon dioxide freezes ("dry ice")
273.15 0.0 32.0 Water ice melts
288 15 59 Mars surface, day high
288.15 15.0 59.0 Standard room temperature
373.15 100 212 Liquid water boils
635 362 683 Venus surface
700 425 800 Planet Mercury surface, day
750 475 890 Uranus hydrogen "corona"
1,337.58 1,064.43 1,947.97 Solid gold melts
3,500 3,200 5,800 Betelgeuse (red giant star) photosphere
3,700 3,400 6,700 Sunspots
5,700 5,400 9,800 Solar photosphere
10,000 10,000 18,000 Sirius (blue-white star) photosphere
15,000 15,000 27,000 Saturn core
30,000 30,000 54,000 Jupiter core
2,000,000 2,000,000 3,600,000 Solar corona
15,000,000 15,000,000 27,000,000 Solar core
Melting and boiling points are shown to precision, for pressure of 1 atmosphere. Values for stars, planet cloudtops, surfaces etc. are shown as round numbers rather than precise conversions.

Temperature Conversions
K = °C + 273.15 °C = (5/9) X (°F-32) °F = ( 9/5) X °C+32 -40°F = -40°C

Asteroids

Mechanics

Comets

Stars

### The Key to Space Flight

Basically all of space flight involves the following concept, whether orbiting a planet or travelling among the planets while orbiting the Sun.

As you watch the third cartoon's animation, imagine that the cannon has been packed with still more gunpowder, sending the cannonball out a little faster. With this extra energy, the cannonball would miss Earth's surface at periapsis by a greater margin, right?

Right. By applying more energy at apoapsis, you have raised the periapsis altitude.

 A spacecraft's periapsis altitude can be raised by increasing the spacecraft's energy at apoapsis. This can be accomplished by firing on-board rocket thrusters when at apoapsis.

And of course, as seen in these cartoons, the opposite is true: if you decrease energy when you're at apoapsis, you'll lower the periapsis altitude. In the cartoon, that's less gunpowder, where the middle graphic shows periapsis low enough to impact the surface. In the next chapter you'll see how this key enables flight from one planet to another.

Now suppose you increase speed when you're at periapsis, by firing an onboard rocket. What would happen to the cannonball in the third cartoon?

Just as you suspect, it will cause the apoapsis altitude to increase. The cannonball would climb to a higher altitude and clear that annoying mountain at apoapsis.

 A spacecraft's apoapsis altitude can be raised by increasing the spacecraft's energy at periapsis. This can be accomplished by firing on-board rocket thrusters when at periapsis.

And its opposite is true, too: decreasing energy at periapsis will lower the apoapsis altitude. Imagine the cannonball skimming through the tops of some trees as it flys through periapsis. This slowing effect would rob energy from the cannonball, and it could not continue to climb to quite as high an apoapsis altitude as before.

In practice, you can remove energy from a spacecraft's orbit at periapsis by firing the onboard rocket thrusters there and using up more propellant, or by intentionally and carefully dipping into the planet's atmosphere to use frictional drag. The latter is called aerobraking, a technique used at Venus and at Mars that conserves rocket propellant.

## Chapter 6. Electromagnetic Phenomena

Objectives:
Upon completion of this chapter you will be able to describe in general terms characteristics of natural and artificial emitters of radiation. You will be able to describe bands of the spectrum from RF to gamma rays, and the particular usefulness radio frequencies have for deep-space communication. You will be able to describe the basic principles of spectroscopy, Doppler effect, reflection and refraction.

Electromagnetic radiation (radio waves, light, etc.) consists of interacting, self-sustaining electric and magnetic fields that propagate through empty space at 299,792 km per second (the speed of light, c), and slightly slower through air and other media. Thermonuclear reactions in the cores of stars (including the sun) provide the energy that eventually leaves stars, primarily in the form of electromagnetic radiation. These waves cover a wide spectrum of frequencies. Sunshine is a familiar example of electromagnetic radiation that is naturally emitted by the sun. Starlight is the same thing from "suns" much farther away.

When a direct current (DC) of electricity, for example from a flashlight battery, is applied to a wire or other conductor, the current flow builds an electromagnetic field around the wire, propagating a wave outward. When the current is removed the field collapses, again propagating a wave. If the current is applied and removed repeatedly over a period of time, or if the electrical current is made to alternate its polarity with a uniform period of time, a series of waves is propagated at a discrete frequency. This phenomenon is the basis of electromagnetic radiation.

Electromagnetic radiation normally propagates in straight lines at the speed of light and does not require a medium for transmission. It slows as it passes through a medium such as air, water, glass, etc.

### The Inverse Square Law

Electromagnetic energy decreases as if it were dispersed over the area on an expanding sphere, expressed as 4πR2 where radius R is the distance the energy has travelled. The amount of energy received at a point on that sphere diminishes as 1/R2. This relationship is known as the inverse-square law of (electromagnetic) propagation. It accounts for loss of signal strength over space, called space loss.

The inverse-square law is significant to the exploration of the universe, because it means that the concentration of electromagnetic radiation decreases very rapidly with increasing distance from the emitter. Whether the emitter is a distant spacecraft with a low-power transmitter or an extremely powerful star, it will deliver only a small amount of electromagnetic energy to a detector on Earth because of the very great distances and the small area that Earth subtends on the huge imaginary sphere.

## Chapter 6. Electromagnetic Phenomena     CONTINUED

### Electromagnetic Spectrum

Light is electromagnetic radiation (or electromagnetic force) at frequencies that can be sensed by the human eye. The whole electromagnetic spectrum, though, has a much broader range of frequencies than the human eye can detect, including, in order of increasing frequency: audio frequency (AF), radio frequency (RF), infrared (meaning "below red," IR), visible light, ultraviolet (meaning "above violet," UV), X-rays, and finally gamma rays. These designations describe only different frequencies of the same phenomenon: electromagnetic radiation.

All electromagnetic waves propagate at the speed of light. The wavelength of a single oscillation of electromagnetic radiation means the distance the wave will propagate in vacuo during the time required for one oscillation.

The strength, or "loudness" or intensity of the wave is known as its amplitude. For wavelengths up through radio frequencies, this quantity is commonly expressed as a power ratio in decibels (dB).

 λ = c / f and f = c / λ

Frequency is expressed in Hertz (Hz), which represents cycles per second.

There is a simple relationship between the frequency of oscillation and wavelength of electromagnetic energy. Wavelength, represented by the Greek lower case lambda (λ), is equal to the speed of light (c) divided by frequency (f).

### Natural and Artificial Emitters

 Radio Image of Jupiter Click image for details.

Deep space communication antennas and receivers are capable of detecting many different kinds of natural emitters of electromagnetic radiation, including the stars, the sun, molecular clouds, and gas giant planets such as Jupiter. These sources do not emit at truly random frequencies, but without sophisticated scientific investigation and research, their signals appear as noise -- that is, signals of pseudo-random frequencies and amplitudes. Radio Astronomy is the scientific discipline which investigates natural emitters by acquiring and studying their electromagnetic radiation. The Deep Space Network participates in radio astronomy experiments.

Deep space vehicles are equipped with radio transmitters ("artificial emitters") and receivers for sending and receiving signals (electromagnetic radiation) to and from Earth-based tracking stations. These signals utilize pre-established discrete frequencies. On the other hand, various natural and human-made emitters combine to create a background of electromagnetic noise from which the spacecraft signals must be detected. The ratio of the signal level to the noise level is known as the signal-to-noise ratio (SNR). SNR is commonly expressed in decibels.

Relativity, Etc.

### Non-Newtonian Physics

We know from Einstein's special theory of relativity that mass, time, and length are variable and the speed of light is constant. And from general relativity, we know that gravitation and acceleration are equivalent, that light bends in the presence of mass, and that an accelerating mass radiates gravitational waves at the speed of light.

Spacecraft operate at very high velocities compared to velocities we are familiar with in transportation and ballistics here on our planet. Since spacecraft velocities do not approach a significant fraction of the speed of light, Newtonian physics serves well for operating and navigating throughout the solar system. Nevertheless, accuracies are routinely enhanced by accounting for tiny relativistic effects. Once we begin to travel between the stars, velocities may be large enough fractions of light speed that Einsteinian physics will be indespensible for determining trajectories.

For now, spacecraft do sometimes carry out experiments to test special relativity effects on moving clocks, and experiments to test general relativity effects such as the space-time warp caused by the sun, frame-dragging, the equivalence of acceleration and gravitation (more precisely the equivalence between inertial mass and gravitational mass) and the search for direct evidence of gravitational waves. As of July 2004 there has been no test by which an observer could tell acceleration from gravitation, nor has gravitational radiation been directly observed. Some of these subjects are explored in Chapter 8.