Question

Hi please explain question and answer properly.. any intelligent moderater tell this
A satellite X moves round the earth in a circular orbit of radius R. If another satellite y of the
same mass moves round the earth in a circular orbit of radius 4R, then the speed of X is..........times that of Y.​

Answer 1

Equate gravitational acceleration with centripetal acceleration  

g = G*M/R^2 = v^2/R  

Express the orbital speed in terms of the orbit circumference and period  

v = 2*pi*R/P  

And insert the expression for v into the first equation  

G*M/R = 4*PI^2*R^2/P^2  

G*M/R^3 = 4*pi^2/P^2  

R^3/P^2 = 4*pi^2/(G*M) = constant = C  

We can do the above since G and M are constants for all earth orbits  

So we can write a second equation of the same form for another satellite and equate to get:  

R^3/P^2 = r^3/p^2  

r^3 = R^3*p^2/P^2  

r = R*(p^2/P^2)^(1/3)  

For the second satellite we have p = 8*P  

r = R*(8^2)^(1/3) = R*(64)^(1/3) = 4*R

Hope it helps!

Answer 2

ANSWER :

ANSWER REFER TO THE ATTACHMENT