Kepler S Third Law Of Planetary Motion Formula

The area swept out by a line joining the centers of a planet and the sun is the same in equal units of time.

Kepler s third law of planetary motion formula. The square of the orbital period of a planet in orbit around the sun is proportional to the cube of the semimajor axis of the orbit. Kepler s third law in fact all three works not only for the planets in our solar system but also for the moons of all planets dwarf planets and asteroids satellites going round the earth etc. P 2 frac 4 pi 2 g m1 m2 a 3 where m1 and m2 are the masses of the orbiting objects. T 2 a 3.

Kepler s third law examples. The semimajor axis is equal to half of the largest. Kepler s third law kepler s third law of planetary motion. Substitute the values in the below satellite mean orbital radius equation.

Determine the radius of the moon s orbit. Encyclopædia britannica inc patrick o neill rileythe usefulness of kepler s laws extends to the motions of natural and artificial satellites as well as to stellar systems and extrasolar planets. 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.

A derivation of kepler s third law of planetary motion is a standard topic in engineering mechanics classes. Kepler s third law is generalised after applying newton s law of gravity and laws of motion. Murray and dermott solar system dynamics cambridge university press 1999 isbn 0 521 57597 4. The period of the moon is approximately 27 2 days 2 35x10 6 s.

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. According to kepler s law of periods the square of the time period of revolution of a planet around the sun in an elliptical orbit is directly proportional to the cube of its semi major axis. 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 squares of the sidereal periods p of the planets are directly proportional to the cubes of their mean distances d from the sun.

Using the equations of newton s law of gravitation and laws of motion kepler s third law takes a more general form. 2 a radius vector joining any planet to sun sweeps out equal areas in equal intervals of time 3 the square of the period of any planet about the sun is proportional to the cube of the planet s mean distance from the sun.