Kepler S Third Law Of Planetary Motion Formula

The semimajor axis is equal to half of the largest.

Kepler s third law of planetary motion formula.

Murray and dermott solar system dynamics cambridge university press 1999 isbn 0 521 57597 4. Kepler s third law kepler s third law of planetary motion. 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. 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 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. 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. 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.

See for example pages 161 164 of meriam j l. 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. 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. A derivation of kepler s third law of planetary motion is a standard topic in engineering mechanics classes.

Orbital velocity formula is used to calculate the orbital velocity of planet with mass m and radius r. Substitute the values in the below satellite mean orbital radius equation. Kepler s third law is generalised after applying newton s law of gravity and laws of motion. 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.

Determine the radius of the moon s orbit. 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. Mass of the earth 5 98x10 24 kg t 2 35x10 6 s g 6 6726 x 10 11 n m 2 kg 2. Using the equations of newton s law of gravitation and laws of motion kepler s third law takes a more general form.

The squares of the sidereal periods p of the planets are directly proportional to the cubes of their mean distances d from the sun. The period of the moon is approximately 27 2 days 2 35x10 6 s.