Asked by Rebecca
A satellite is placed in orbit, with a radius that is half the radius of the Moon's orbit. Find the period of the satellite in units of the period of the Moon. (sketch and analyze the situation, show all working so I can understand how you arrived at your answer).
Answers
Answered by
Damon
Ac = w^2 R
F = m a = m w^2 R = G m Me /R^2
so
w^2 = G Me/R^3
(2 pi /T)^2= G Me/R^3
(2 pi)^2/G Me = constant = T^2/R^3
so
Tmoon^2 / Rmoon^3 = Tsat^2/Rsat^3
Tsat^2 = Tmoon^2 (Rsat/Rmoon)^3
Tsat = Tmoon (1/2)^3/2 = 2sqrt 2 *Tmoon
F = m a = m w^2 R = G m Me /R^2
so
w^2 = G Me/R^3
(2 pi /T)^2= G Me/R^3
(2 pi)^2/G Me = constant = T^2/R^3
so
Tmoon^2 / Rmoon^3 = Tsat^2/Rsat^3
Tsat^2 = Tmoon^2 (Rsat/Rmoon)^3
Tsat = Tmoon (1/2)^3/2 = 2sqrt 2 *Tmoon
Answered by
Damon
Tsat = Tmoon (1/2)^3/2 = (1/2sqrt 2) *Tmoon
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