A spacecraft is in a circular orbit at a height h h\,h above the surface of a spherical planet of radius RRR. The acceleration due to gravity at the surface of the planet is ggg. What is the orbital period T T\,T of the spacecraft?
2π(R+h)3gR22\pi \sqrt{\frac{(R+h)^3}{g R^2}}2πgR2(R+h)3
2πR+hg2\pi \sqrt{\frac{R+h}{g}}2πgR+h
2πgR2(R+h)32\pi \sqrt{\frac{g R^2}{(R+h)^3}}2π(R+h)3gR2
2π(R+h)3gR2\pi \sqrt{\frac{(R+h)^3}{g R}}2πgR(R+h)3