Question

explain keplers third law of motion, derivation of the formula along with figure.​

Answer 1

Please mark it as the Brainliest.

© manasikolhe11126

Kepler’s 3rdLaw: Law of periods

Statement: -

According to this law the square of time period of a planet is ∝ to the cube of the semi-major axis of its orbit.

Suppose earth is revolving around the sun then the square of the time period (time taken to complete one revolution around sun) is ∝ to the cube of the semi major axis.

It is known as Law of Periods as it is dependent on the time period of planets.

Derivation of 3rd Law: assumption: The path of the planet is circular.

Let m=mass of planet

M= mass of sun

According to Newton’s Law of Gravitation:

F= GMm/r2

Fc=mv2/r

where

Fc =centripetal force which helps the planet to move around sun in elliptical order.

F = Fc

GMm/r2= mv2/r where r=radius of the circle

GM/r= v2 (1)

v= 2 πr/T

Squaring both the sides the above equation

v2=4 π2r2/T2

putting the value (1)

GM/r=4 πr2/T2

T2= (4 π2 r3/GM) where (4 π2/GM) = constant

T2=r3 (In ellipse semi-major axis is same as radius of the circle)