Express the kinetic energy K in terms of the potential energy U.

K=GMm/2R

K = - ½U

Explanation:

From Newton's law of gravitation, the formula for gravitational potential energy is;

U = - GMm/R

Where,

G is gravitational constant

M and m are the two masses exerting the forces

R is the distance between the two objects

Now, in the question, we are given that kinetic energy is;

K = GMm/2R

Re-rranging, we have;

K = ½ (GMm/R)

Comparing the equation of kinetic energy to that of potential energy, we can derive that gravitational kinetic energy can be expressed in terms of potential energy as;

K = - ½U