Concepts of Planetary Motion

What is planetary motion?

Planetary motion describes the pattern in which planets travel through the solar system and the forces that propel them.

Kepler's Laws of Planetary Motion

The German astronomer, Johannes Kepler (1571 - 1630), arrived with his first two laws of planetary motion while studying the orbit of Mars. Using Tycho Brahe's accurate records, Kepler discovered that the orbit of Mars was not a perfect circle. It was in fact, an ellipse. This became Kepler's first law of planetary motion.

Kepler also observed variations in Mars' speeds. At certain areas of its orbit, Mars would appear to travel faster than it usually would. Kepler soon discovered that the sun was controlling Mars' orbiting speed. As Mars got closer to the sun, its orbiting speed increased. When Mars was farthest away, its orbiting speed decreased. This became Kepler's second law of planetary motion.

In order to illustrate his second law, imagine a line connecting a planet to the Sun. The line sweeps over equal areas in equal intervals of time at any part of the orbit.
Kepler's third law of planetary motion (Harmonic Law) was discovered ten years later. It states that the cube of a planet's average distance from the Sun, a, is equal to the square of the time it takes that planet to orbit the Sun once, p. Notice below how p squared equals a cubed.

 Planet P (years) A (AU) p2 a3 Mercury 0.24 0.39 0.06 0.06 Venus 0.62 0.72 0.39 0.37 Earth 1.00 1.00 1.00 1.00 Mars 1.88 1.52 3.53 3.51 Jupiter 11.9 5.20 142 141 Saturn 29.5 9.54 870 868

Kepler's third laws also work for any celestial body and its orbiting satellites.

1) The orbit of each planet is an ellipse, with the Sun at one focus of the ellipse.
2) A planet moves faster when closer to the sun and slower when farther away.

The Orbit

An orbit is the motion of one object around another. Some examples include the Earth's orbit around the sun and the moon's orbit around the Earth. Observing these behaviors led Isaac Newton to wonder what kept these celestial bodies from keeping their path in space. Why the moon didn't fall to the Earth was one of the few questions involving orbits.

Newton explained that the moon remained in its orbit because of its forward momentum and its balance between the Earth's gravitational pull on the moon. In other words, the moon would continue to move in a straight line away from the Earth, but at the same time, gravity would pull the moon back in. Therefore, the moon would never appear to get farther or closer to the Earth as it orbited around it.

Aspects of the Ellipse

An ellipse has an oval shape and looks like a squashed circle.

• Foci are the two points symmetrically located on major axis on either side of center

• Major axis is the longest axis of the ellipse (semi-major axis is half of major axis)

• Minor axis is perpendicular to the major axis and is the shortest axis of the ellipse

• Eccentricity describes the shape of the orbit. It is a ratio of distance of either foci from center to length of semi-major axis. For closed orbits, the number would be between 0 (a perfect circle) and 1 (a parabolic escape orbit).

Aspects of the Orbit

• Inclination is the angle the orbit makes relative to the equator. An orbit around the equator has an inclination of 0 degrees and an orbit around the north and south poles has an inclination of 90 degrees. An inclination between 90 and 180 degrees means that the satellite is going from east to west. This type of orbit is called "retrograde orbit".

• Period is the length of time it takes a satellite to orbit once.

• Perigee is the point on the orbit where the satellite is closest to Earth. A satellite moves fastest at perigee.

• Apogee is the point on the orbit where the satellite is farthest to Earth. A satellite moves slowest at perigee.

• Trajectory is used to describe the path of one orbit or a planet to another. By increasing speed, a satellite can get to a higher orbit. By decreasing speed, a satellite can get to a lower orbit.

• Geosynchronous Earth Orbit is an orbit 22,300 miles above the Earth's surface. At this height, the period of the orbit is 24 hours, the same time it takes the Earth to orbit once.

• Geostationary Orbit is a geosynchronous orbit with an inclination of 0. This means that the satellite will orbit around the equator every 24 hours. It will appear to remain stationary in the sky as seen from Earth.

• Sun-Synchronous Orbit is an orbit that causes the satellite to pass over every place on Earth the same local time of day. This is done by choosing the proper inclination for the orbit.

• Interplanetary Orbit is an orbit around the sun. The inclination is measured relative to the Earth's equator. The farthest point in its orbit is called the "aphelion" and the closest is called the "perihelion".

• Slingshot Orbit is when a spacecraft is sent near a planet in order to use its gravity to change its trajectory. This is also called gravity-assist trajectories.