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Cant solve this question on kepler's 3rd law equation (1 Viewer)

Cujo10

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For some reason my rearrange the formulae does not work to solve this question, so can you show me how to solve this question WIN_20180818_09_08_15_Pro.jpg
 

jazz519

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So basically if planets are orbiting the same star the value of GM/(4pi^2) will be constant (because M is the mass of the central planet), so this means that r1^3/T1^2 = r2^3/T2^2 (basically like doing a simultaneous equation),
rearrange for T2, giving T1^2/r1^3=T2^2/r2^3
so T2 = sqrt(T1^2*r2^3/r1^3)
substitute ur values in where T1 = 8.75*10^7 (I think its power to 7 but a bit blurry) and r2=8*10^11, r1=4*10^11

therefore T2 = sqrt((8.75*10^7)^2*(8*10^11)^3/(4*10^11)^3)
which should give u 2.47*10^8 seconds which is A

its just an exercise of understanding which variables represent what in the equation as half the columns there are useless info (i..e the mass of the planets, radius of planets and length of day none of which are actual variables) as M=central mass and T = the period of orbit around the central mass
 

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