Question

Two satellite of a planet having period 32 and 256 days, if the radious of 1st satellite is 'R.Find the orbital radious of the 2nd satellite

Answer 1

Given :

Time Period of 1st Satellite = 32 Days
 
Time period of 2nd Satellite = 256 Days

Radius of First Planet = R

Let Other satellite Be At a height of 'h' From 1st Satellite

We Know That Time Period T = 2π√(R/g)

Time Period Of First Satellite =  T₁ = 2π√(R/g) = 32days

Time Period of Second Planet T₂ = 2π√[(R+h)]/g = 256days

T₁/T₂ = 32/256 = [2π√(R/g)] / [2π√[(R+h)]/g]
⇒1/8 = √(R)/(R+H)
⇒64 = (R+H)/R
⇒64 - 1 = H/R
⇒H = 63R

Orbital Raidius of Latter is 63R + R = 64R
 
∴ The Orbital Radius Of the Latter Satellite Is 64R