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

Question

Makovka662 [10]

3 years ago

15

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

its surface?

Physics

1 answer:

san4es73 [151] · Answer 1 · 2022-04-06T21:00:11+03:00

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’;