A typical GPS (Global Positioning System) satellite orbits at an altitude of 4.0 107 m. (Astronomical data needed for this problem can be found on the inside back cover of the text.)

(a) Find the orbital period of such a satellite.
hours
(b) Find the orbital speed of such a satellite.
km/s

i cannot find the equation to use for this...please help?

1 answer

Add 4*10^7 m to the radius of the Earth to get the radial distance R from the center of the earth. Call this R.

Solve for the orbital speed V first.

GM/R^2 = V^2/R

G is the universal gravity constant and M is the mass of the earth.

V * P = 2 pi R

(solve for the period P in seconds)