Help....on physics problem?
You are the science officer on a visit to a distant solar system. Prior to landing on a planet you measure its diameter to be 1.8*10^7m and its rotation period to be 22.3 hours. You have previously determined that the planet orbits 2.2*10^11m from its star with a period of 402 earth days. Once on the surface you find that the free-fall acceleration is 12.2m/s^2.
What is the mass of the planet?
What is the mass of the star?
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Verified answer
g (on surface) = G M (planet) / r ^2 (r= radius of planet)
solve:
M (planet) = g (on surface) * r^2/ G
period= Τ = 2 π/ω
ω= 2 π/Τ
G m (planet) M(star) / R^2 = m(planet) Rω^2 = m R 4 π^2 / Τ^2
(R = distance between star and planet)
M(star)= 4 π^2 R^3 /(G Τ^2)