## Planetary Motion

Seen from a point north of the plane of Earth's orbitfor example, from the North Starthe planets travel counterclockwise in their orbits. All the orbits are nearly level with the plane of Earth's orbit, except those of Mercury and Pluto, which are more tilted. Seen with the unaided eye, the five clearly visible planets look much like stars. However, the planets do not twinkle like stars when overhead in the sky, although they may twinkle near the horizon. Through a telescope these planets can be easily distinguished from stars because they appear as discs while the stars are so far away that they appear as mere points of light.

While Copernicus correctly deduced that the planets revolve around the sun, he otherwise retained the Ptolemaic system. Planetary motion was first correctly described by Johannes Kepler.

The first two of Kepler's Laws were published in 1609, the third in 1619. They state that:

1. The orbit of every planet is an ellipse that has the sun as one of its foci.2. A straight line from the planet to the sun sweeps over equal areas of the ellipse in equal periods of time. (This means that the planet's speed is greatest when the planet is nearest the sun and lowest when it is at the point in its orbit farthest from the sun.) 3. The squares of the periods of any two planets are in the same proportion as the cubes of their mean distances from the sun. (A planet's period is the time it takes the planet to complete one orbit. Its mean distance from the sun is defined as half the length of the major axis of the ellipse.)

Kepler's Laws described planetary motion, but did not explain it. The explanation came in Isaac Newton's Principia (1687). His law of gravitation states:

Every particle of matter attracts every other particle of matter with a force proportional to the product of their masses and inversely proportional to the square of their distance apart.

His laws of motion, the three basic laws of classical mechanics, state:

1. A body at rest remains at rest, and a body in motion continues to move in a straight line at a uniform speed unless it is acted upon by some external force. 2. Change in the motion of a body is in proportion to, and in the direction of, the force causing the change. 3. The action of every force is accompanied by an equal action in the opposite direction (the reaction).

Newton's laws explain perturbations, or irregularities in orbits. They also show that Kepler's third law, to be strictly accurate, must be modified by multiplying the square of each period by the sum of the planet's mass and the sun's mass. Even without the modification, however, the law is reasonably accurate, because the planets' masses are so small compared to the sun's mass.

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