Planetary Formulas

Kepler’s Laws

Kepler’s Laws for planetary motion is found by Johannes Kepler and is stated as below.

Kepler’s first law: Law of Orbits

Kepler’s first law

Kepler’s first law states that “All planets move around the sun in elliptical orbits with the sun at one focus”.

Explanation: An ellipse traced out by a planet around the sun. The closest point is P and the farthest point is A, P is called the perihelion and A the aphelion. The semimajor axis is half the distance AP.

Kepler’s second law states that “The line joining a planet to the Sun sweeps out equal areas in equal interval of time”.

Kepler’s second law


P is the planet that moves around the sun in an elliptical orbit

∆A is the area swept

∆t is the time interval

Kepler’s Third Law states that “The square of the time period of the planet is directly proportional to the cube of the semimajor axis of its orbit”

\(\begin{array}{l}P^{2}\alpha a^{3}\end{array} \)

Kepler’s third law is generalised after applying Newton’s Law of Gravity and laws of Motion.

\(\begin{array}{l}P^{2}=\frac{4\pi^{2}}{G(M1+M2)}(a^{3})\end{array} \)


M1 and M2 are the masses of the orbiting objects

Orbital Velocity Formula

Orbital velocity formula is used to calculate the orbital velocity of planet with mass M and radius R.

\(\begin{array}{l}V_{orbit}=\sqrt{\frac{GM}{R}}\end{array} \)


G = Gravitational constant = 6.67 × 10-11 m3/s2 kg

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