Question

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

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’;