Short Grade 12 Gravitational Problem

[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 = 3rvI 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.

 

[SammyS]

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:
T_V= 360days
T_X= ?
m_V = m_V
m_X = 1/2m_V
r_V = r_V
r_X = 3r_V

I derived a formula that incorporates time.
From which v = sqrt ( GM/r )
since T = 2(pi)r / v

sub v into that formula and you get:

T = sqrt (4 pi² r³ / 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 M_V.
Then I subbed M_V from one formula into another.

This is what results:

8pi²3rv³ / GTx² = 4pi²rv³/ GTv²

through cancellations I ended up getting:

T_X = 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.

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?

Use the subscript, X₂, & superscript, X², buttons above the "Go Advanced" message box.