LET KINETIC ENERGY OF A SATELLITE IS X,THEN ITS TIME OF REVOLUTION T IS PROPORTIONAL TO - Physics - Gravitation

Question

LET KINETIC ENERGY OF A SATELLITE IS X,THEN ITS TIME OF REVOLUTION
T IS PROPORTIONAL TO

Sayantan · Accepted Answer

Dear Student,

We have,

12mv2=x  or v2=2xm
(i)Now, mv2R=GMmR2   ( for a satellite )or v2=GMR
(ii)from (i) and (ii)GMR=2xmor R=GMm2x
(iii)Now Time Period:  T=Perimeter of Circlevelocity⇒2πRv  ( Assuming its a circular orbit)using (i) and (iii)T=2π×GMm2x×m2xor, T=πGM2m321x3   Note: The bracket term is a constantor, T=const×1x3Or, T∝1x3   ⇒T∝x-32
Regards