A satellite is in a circular orbit about the Earth at a distance of one Earth radius above the surface. What is the speed of the satellite? (The radius of the Earth is 6.4 x 10^6 m, and G = 6.67 x 10^−11 N * m^2 /kg^2 .)

As the satellite moves in a circular orbit, it keeps circling due to an external force that prevents it from moving in a straight line at constant speed: this force, is called the centripetal force, and can be expresssed as follows:

Fc = ms*v²/res, where r is the distance to center of the earth, in this case, a distance equal to two Earth radius.

As this force can´t be a new force, it must be equal to a known force acting on the satellite.

The only external force acting on the satellite, is the gravitational force due to Earth (neglecting attractive force from moon and another celestial bodies), which can be expressed as follows, according to Universal Law of gravitation:

Fg = G*me*ms/res²

Let set both equations equal:

Fc = Fg ⇒ ms*v²/res = Gme*ms/res²

Simplifying common terms, we can solve for v as follows:

v = √(G*me/res) = √(6.67*5.97/2*6.4)*10⁷ = 5,578 m/s