A hypothetical spherical planet consists entirely of iron. what is the period of a satellite that orbits this planet just above its surface?

Question

Taylor Hickman

Physics

27 April, 14:47

A hypothetical spherical planet consists entirely of iron. what is the period of a satellite that orbits this planet just above its surface?

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Pudge · Answer 1

Newton states: F=G*M*m / r^2, where M = ρ * (4/3) * pi*r^3 is mass of iron planet, r is radius of the planet;

the same gravity force F=m*w^2*r is the centripetal force for the orbiting satellite, where angular speed w=2pi/T, T is period;

thus F=F; G*M*m / r^2 = m*w^2*r; or;

G * (ρ * (4/3) * pi*r^3) / r^2 = (2pi/T) ^2*r; or;

G*ρ/3 = pi/T^2, hence T = √ (3pi / (G*ρ)) =

= √ (3pi / (6.6742E-11 * 7860)) = 4238.62s = 70h 38’;