Question

Two satellites of a planet have periods 32 days and 256 days. If the radius of orbit of former is R,find the orbital radius of the latter

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

Answer 2

Answer:

           4R

Explanation:

                        256 days ⇒ R = ?

            Keplers 3ʳᵈ law ⇒  

                               T²∝R³

             

             (T₁/T₂)² = (R₁/R₂)³

             (32/256)² = (R₁/R₂)³

             (1/8)² = (R₁/R₂)³

             

             1/64 = (R₁/R₂)³

 

             1/4 ⇒ R₁/R₂

             R₂ = 4R