Kepler S Third Law Of Planetary Motion Equation

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Kepler s third law of planetary motion equation.

Consider a planet of mass is moving in an elliptical orbit around the sun. Kepler s third law implies that the period for a planet to orbit the sun increases rapidly with the radius of its orbit. Newton showed that kepler s laws were a consequence of both his laws of motion and his law of gravitation. Kepler s third law sometimes referred to as the law of harmonies compares the orbital period and radius of orbit of a planet to those of other planets.

Kepler s third law examples. Determine the radius of the moon s orbit. It provides physics problems where you have to calculate the period of mars or t. Thus we find that mercury the innermost planet takes only 88 days to orbit the sun but the outermost planet pluto requires 248 years to do the same.

The sun and the planet are separated by distance r. A derivation of kepler s third law of planetary motion is a standard topic in engineering mechanics classes. Johannes kepler working with data painstakingly collected by tycho brahe without the aid of a telescope developed three laws which described the motion of the planets across the sky. Equation 13 8 gives us the period of a circular orbit of radius r about earth.

Also known as the law of harmonies kepler s third law of planetary motion states that the square of the orbital period represented as t of a planet is directly proportional to the cube of the average distance or the semi major axis of the orbit represented as r of a planet from the sun. The period of the moon is approximately 27 2 days 2 35x10 6 s. Kepler s third law states that the square of the period is proportional to the cube of the semi major axis of the orbit. Mass of the earth 5 98x10 24 kg t 2 35x10 6 s g 6 6726 x 10 11 n m 2 kg 2.

Substitute the values in the below satellite mean orbital radius equation. This physics video tutorial explains kepler s third law of planetary motion. In satellite orbits and energy we derived kepler s third law for the special case of a circular orbit. Kepler s second law of planetary motion a line joining any planet to the sun sweeps out equal areas in equal times or areal velocity of the planet around the sun is constant kepler s 2nd law equation.

All planets move in elliptical orbits with the sun at one focus. Unlike kepler s first and second laws that describe the motion characteristics of a single planet the third law makes a comparison between the motion characteristics of different planets. Murray and dermott solar system dynamics cambridge university press 1999 isbn 0 521 57597 4.