Kepler S Third Law Of Planetary Motion Formula

Kepler laws of planetary motion are expressed as 1 all the planets move around the sun in the elliptical orbits having the sun as one of the foci.

Kepler s third law of planetary motion formula.

Substitute the values in the below satellite mean orbital radius equation. The squares of the sidereal periods p of the planets are directly proportional to the cubes of their mean distances d from the sun. Kepler s third law examples. 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 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. Orbital velocity formula is used to calculate the orbital velocity of planet with mass m and radius r. 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. A derivation of kepler s third law of planetary motion is a standard topic in engineering mechanics classes.

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. Kepler s third law is generalised after applying newton s law of gravity and laws of motion. 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. Using the equations of newton s law of gravitation and laws of motion kepler s third law takes a more general form.

See for example pages 161 164 of meriam j l. Determine the radius of the moon s orbit. The semimajor axis is equal to half of the largest. 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.

Murray and dermott solar system dynamics cambridge university press 1999 isbn 0 521 57597 4. 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. 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. 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. P 2 frac 4 pi 2 g m1 m2 a 3 where m1 and m2 are the masses of the orbiting objects.