Kepler's third law states that square of period of
revolution (T) of a planet around the sun is proportional
to third power of average distance r between the sun
and the planet i.e. T2 = Kr3 (here K is constant). If the
masses of sun and planet are M and m respectively then
as per Newton's law of gravitation, force of attraction
between them is F = GMm/r2, here G is gravitational
constant.
The relation between G and K is described as
A K = G
B K = 1/G
C GK = 4π2
D GMK = 4π2
Ans 1:
Class : Class 9
Correct ans:D.
The gravitational force is equal to the centripetal force acting between the Sun and Planet.
GMm/r^2=Mv^2/r
=>v^2=Gm/r.
Also,T=2(pi)r/v.
Squaring both the sides we will get