A satellite orbiting Earth at an orbital radius r has a velocity v. Which represents the velocity if the satellite is moved to an orbital radius of 5r?

The new velociry is v/√5

Explanation:

The orbital velocity of something that orbits the planet is:

v = √(G*M/r)

where G is the gravitational constant, M is the mass of the earth, and r is the orbital radius.

If we now have a radius equal to 5r, then the new velocity will be:

v2 = √(G*M/5r)

we can take the 1/√5 out, and get:

v2 = √(G*M/5r) = √(G*M/r)*(1/√5)  

The first part is equal to the initial velocity, so we can write this as:

√(G*M/r)*(1/√5) = v/√5

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