Kepler S Third Law Of Planetary Motion Formula

A derivation of kepler s third law of planetary motion is a standard topic in engineering mechanics classes.

Kepler s third law of planetary motion formula.

Kepler s third law kepler s third law of planetary motion. 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. 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 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.

Using the equations of newton s law of gravitation and laws of motion kepler s third law takes a more general form. Substitute the values in the below satellite mean orbital radius equation. The period of the moon is approximately 27 2 days 2 35x10 6 s. T 2 a 3.

Mass of the earth 5 98x10 24 kg t 2 35x10 6 s g 6 6726 x 10 11 n m 2 kg 2. 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. See for example pages 161 164 of meriam j l. P 2 frac 4 pi 2 g m1 m2 a 3 where m1 and m2 are the masses of the orbiting objects.

Kepler s third law examples. 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. 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. Orbital velocity formula is used to calculate the orbital velocity of planet with mass m and radius r.

Determine the radius of the moon s orbit. The semimajor axis is equal to half of the largest. 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. The area swept out by a line joining the centers of a planet and the sun is the same in equal units of time.

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. Murray and dermott solar system dynamics cambridge university press 1999 isbn 0 521 57597 4.