Two satellites of a planet have time period 32 days and 256 days if the radius of orbit of first satellite is R find the radius of orbit of radius of second satellite
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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
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
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