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 of planetary motion equation. Kepler s third law examples. This physics video tutorial explains kepler s third law of planetary motion. All planets move in elliptical orbits with the sun at one focus. Kepler s third law implies that the period for a planet to orbit the sun increases rapidly with the radius of its orbit.

A derivation of kepler s third law of planetary motion is a standard topic in engineering mechanics classes. It provides physics problems where you have to calculate the period of mars or t. With the help of. Substitute the values in the below satellite mean orbital radius equation.

The law of orbits. Kepler s third law states that the square of the period is proportional to the cube of the semi major axis of the orbit. 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. 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.

See for example pages 161 164 of meriam j l. Mass of the earth 5 98x10 24 kg t 2 35x10 6 s g 6 6726 x 10 11 n m 2 kg 2. The period of the moon is approximately 27 2 days 2 35x10 6 s. Determine the radius of the moon s orbit.

The sun and the planet are separated by distance r. In satellite orbits and energy we derived kepler s third law for the special case of a circular orbit. Kepler proposed the first two laws in 1609 and the third in 1619 but it was not until the 1680s that isaac newton explained why planets follow these laws. Newton showed that kepler s laws were a consequence of both his laws of motion and his law of gravitation.

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. 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. Equation 13 8 gives us the period of a circular orbit of radius r about earth.