Question

derivation of Kepler's third law of gravitation




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Answer 1

Explanation:

Derivation of Kepler’s Third Law

Now if we square both side of equation 3 we get the following:

T^2 =[ (4 . π^2)/(R^2)]. r^3/g ……………………………(4)

Here, (4. π^2)/(R^2) and g are constant as the values of π (Pi), g and R are not changing with time.

So we can say, T^2 ∝ r ^3. …………….. (5) .[Kepler’s Third Law equation]

Here this Kepler’s Third Law equation says that square of the Orbital Period of Revolution is directly proportional to the cube of the radius of the orbit.

If the orbit is not circular in the truest sense and rather elliptical, then this law states like this,

square of the Orbital Period of Revolution varies with the cube of the semi-major axis of the orbit.

This is known as Kepler’s third Law.

From this equation of Kepler’s Third Law it comes out clearly that the mass of the object in revolution has no effect on the Period of Revolution.