Posted by ALan on Tuesday, March 2, 2010 at 6:30pm.
A hypothetical spherical planet consists entirely of iron (p=7860 kg/m^3). Calclate the period of a satellite that orbits just above its surface.
I started out with the pressure formula P=M/V, but i kept subbing in other formulas, but i get stuck..can someone help me? thanks.

Physics  Marianne, Tuesday, April 12, 2011 at 6:05pm
Time required for 1 revolution,
T= (2πr^(3/2))/√(G∙M)
(if you have 7th ed Cutnell & Johnson, its on p. 146)
Volume of a sphere,
V=4πr^3 (book inside cover)
Formula for mass density,
M=ρ∙V (p.321)
Where
T: the time period
G: universal gravitational constant, 6.673 E11 (N∙m^2)/kg^2
note: N=(kg∙m)/s
r: distance from center of planet to satellite, aka planet’s 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
T= 2π/√(G∙ρ∙4π)
Plug in the known value of G and given value of ρ.
For a planet made of iron, satellite period
T ≈ 2447.39 seconds
~Marianne
Answer This Question
Related Questions
 Physics, help please!  A hypothetical spherical planet consists entirely of ...
 Physics  A hypothetical spherical planet consists entirely of iron (p=7860 kg/m...
 physics help!!  A hypothetical spherical planet consists entirely of iron (p=...
 physics help!!!  A hypothetical spherical planet consists entirely of iron (p=...
 Physics  A hypothetical spherical planet consists entirely of iron (p=7860kg/m^...
 Physics  A satellite has a mass of 5750 kg and is in a circular orbit 3.6 * 10^...
 Physics  A satellite has a mass of 6179 kg and is in a circular orbit 4.83 × ...
 PHYSICS PLEASE HELP  A satellite has a mass of 5850 kg and is in a circular ...
 Physics  A satellite has a mass of 5600 kg and is in a circular orbit 3.70*10^5...
 physics  A satellite has a mass of 5950 kg and is in a circular orbit 3.80 10^5...
More Related Questions