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The Planet V has a year lasting 360 days. In the same star system is the Planet X. The Planet X has half the mass and triple the radius. A planet X year would be approximately _____ days

The attempt at a solution

Givens:

Tv= 360days

Tx= ?

mv = mv

mx = 1/2mv

rv = rv

rx = 3rv

I derived a formula that incorporates time.

From which v = sqrt ( GM/r )

since T = 2pir / v

sub v into that formula and you get:

T = sqrt (4 pi^2 r^ 3 / GM )

with that I had two sets of values, Vulcan and X:

I plugged them into the formula and arranged for a common values such as Mv.

Then I subbed Mv from one formula into another.

This is what results:

8pi^23rv^3 / GTx^2 = 4pi^2rv^3/ GTv^2

through cancellations I ended up getting:

Tx = sqrt ( (2)(3)^3(360)^2 )

which was that amount of days.

Not sure if this method would be the correct way to go with this question or not.

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# Homework Help: Short Grade 12 Gravitational Problem

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