# Homework Help: Short Grade 12 Gravitational Problem

1. Jan 22, 2012

### TheSerpent

The Question
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.

2. Jan 22, 2012

### SammyS

Staff Emeritus
Do you mean that the radius of the orbit of planet X is triple that of planet V ?

Does the mass of the planet matter? Is the M in the equation, v = sqrt ( GM/r ), the mass of the planet, or the mass of some other object?

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