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 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”.
Explanation:
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”
Kepler’s third law is generalised after applying Newton’s Law of Gravity and laws of Motion.
Where,
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.
Where,
G = Gravitational constant = 6.67 × 10-11 m3/s2 kg
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