You need to know the radius of the planet to answer this.
I have no idea what your "pressure formula" means. It is incorrect, and pressure has nothing to do with this problem.
Im sorry! I meant density! It was represented by a small p, so i thought pressure >_<
Anyways, density = mass/volumne. My teacher gave me a hint about radius cancelling each other off in the formula manipulation. Hope this helps!
Time required for 1 revolution,
T= (2πr^(3/2))/√(G∙M) (p. 146 of 7th ed Cutnell & Johnson)
Volume of a sphere,
V=4πr^3 (book inside cover)
Formula for mass density,
T: the time period
G: universal gravitational constant, 6.673 E-11 (N∙m^2)/kg^2
r: distance from center of planet to satellite, aka planetís radius
ρ: mass density of planet.
Iron density = 7860 kg/m^3
V: Volume of planet
Substitute formula for volume of a sphere into equation for mass:
M = ρ∙ 4πr^3
Then substitute this into the equation for time period
T= (2πr^(3/2))/√(G∙ρ∙ 4πr^3)
The r^(3/2) in the numerator cancels the √(r^3) in the denominator,
So the equation simplifies to
Plug in the known value of G and given value of ρ.
For a planet made of iron, satellite period
T ≈ 2447.39 seconds
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