ASTR 1210 (O'Connell) Study Guide


STS-105 Launch

Space Shuttle Discovery launches on
a mission to the Space Station, 2001

"There will certainly be no lack of human pioneers when we have mastered the art of [space] flight....Let us create vessels and sails adjusted to the heavenly ether, and there will be plenty of people unafraid of the empty wastes. In the meantime we shall prepare, for the brave sky-travelers, maps of the celestial bodies."
---- Johannes Kepler (1610)

Newton's theories of dynamics and gravity provided a complete understanding of the interaction between gravitating bodies and the resulting orbits for planets and satellites. This guide first describes the nature of possible gravitational orbits and some implications of those.

In the mid-twentieth century, Newton's work became the key conceptual element in space technology, which is introduced in the second part of the guide. Space technology---rockets, the Space Shuttle, dozens of robot spacecraft, the human space program---has provided most of our present knowledge of the Solar System and most of the material we will discuss in the rest of this course.

A. Newtonian Orbit Theory

Orbital Dynamics

Newton's theory can accurately predict gravitational orbits because it allows us to determine the acceleration of an object in a gravitational field. Acceleration is the rate of change of an object's velocity.

Kinds of Gravitational Orbits

In the case of two gravitating objects (for example, the Earth and the Moon, the Sun and a planet, or the Earth and an artificial satellite), Newton found that the full solutions of his equations give the following results:

You can interactively explore the relation between the orbit and the initial velocity vector using the Flash animation Gravity Chaos.

Newton's Mountain

Newton illustrated orbital behavior for a simple idealized situation where a powerful cannon is fixed in position on top of a high mountain on the Earth. Since both the distance from Earth's center and the direction of initial flight is fixed, the cannonball follows an orbit that depends only on the muzzle velocity of the cannon as shown below:

The gravitational force of a spherical body like the Earth acts as though it originates from the center of the sphere, so elliptical orbits have the center of the Earth at one focus.


"Newton's Mountain": orbit type depends on initial velocity.
From lower to higher velocities, orbit shapes are: ellipse, circle, ellipse, parabola, hyperbola.
"Escape velocity" (which is 25,000 mph at Earth's surface) produces a parabolic orbit.

General Relativity

Much later (1916), Newton's theory was shown to be inadequate by Albert Einstein in the presence of large masses or over large distances and has been replaced by the General Theory of Relativity in such situations. Relativity theory profoundly changed our understanding of space and time, for example by demonstrating that mass and energy can affect the structure of space and time. It is much more complicated mathematically than Newton's formulation. But as a practical matter, Newton's theory is an entirely satisfactory description of "everyday" gravity. Only very minor corrections to the Newtonian predictions are necessary, for example, to send spacecraft with high accuracy throughout the solar system.

B. Important Implications of Newtonian Orbits

"Free-Fall" Orbits

The Russian "Mir" space station (1986-2001) orbiting Earth at an altitude of 200 miles with a velocity of 17,000 mph

Geosynchronous Orbits

Applications of Kepler's Third Law

Rocket Engine

Schematic diagram of a liquid-fueled rocket engine. The thrust of the engine is
proportional to the velocity of the exhaust gases (Ve).

C. Space Flight

If the primary technology enabling space flight is Newtonian orbit theory, the second most important technology is the rocket engine.

D. Interplanetary Space Missions

Beginning in the early 1960's, NASA and foreign space agencies developed a series of ever-more sophisticated robot probes to study the Sun, Moon, planets, and the interplanetary medium. These included flyby spacecraft, orbiters, landers, rovers, and sample-return vehicles.

By 2012, only 55 years after the first successful satellite launch (Sputnik), we had flown at close range past every planet except Pluto; had placed robotic observatories into orbit around the Moon, Mercury, Venus, Mars, Jupiter, Saturn, and the asteroids Eros and Vesta; had soft-landed on the Moon, Venus, Mars, and Saturn's moon Titan; had returned to Earth samples obtained from the coma of the comet Wild 2 and from a soft-landing on the asteroid Itokawa; and had sent probes into a comet nucleus and the atmosphere of Jupiter. At right is an artist's concept painting of the Cassini mission in orbit around Saturn. We also put a number of highly capable observatories for studying the distant universe (such as the Hubble Space Telescope and the Chandra X-Ray Observatory) into orbit around the Earth and the Sun.

Of course, the Apollo program in the 1960's also sent human beings to the Moon. This was very fruitful in learning about lunar geology and surface history. But, by far, most of what we know about the denizens of the Solar System has come from the powerful robot observatories.

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Last modified January 2015 by rwo

Text copyright © 1998-2015 Robert W. O'Connell. All rights reserved. Orbital animation copyright © Jim Swift, Northern Arizona University. Conic section drawings from ASTR 161, University of Tennessee at Knoxville. Newton's Mountain drawing copyright © Brooks/Cole-Thomson. These notes are intended for the private, noncommercial use of students enrolled in Astronomy 1210 at the University of Virginia.