Consider a satellite in a circular orbit around the earth. if it were at an altitude equal to twice the radius of the earth, 2re, how would its speed v relate to the earth's radius re, and the magnitude g of the acceleration due to gravity on the earth's surface?

Explanation:

Satellites experiment a force given by Newton's Gravitation Law:

where M is Earth's mass, m the satellite's mass, r the distance between their gravitational centers and G the gravitational constant.

We also know from Newton's 2nd Law that F=ma, so putting both together we will have:

If we are on the surface of the Earth, the acceleration would be g and (Earth's radius):

Which we will write as:

If we are on orbit the acceleration is centripetal (), so we have:

And if this orbit has a radius we have: