Question

The potential energy U of an object of mass m that is separated by a distance R from an object of mass M is given by U= -GMm/RA. What is the kinetic energy K of the satellite?Express your answer in terms of the potential energy .

B. Find an expression for the square of the orbital period.

Answer 1

The kinetic energy K of the satellite is GMm/RA. The expression for the square of the orbital period is T^2 = 4π^2(R^3/GM).

Step-by-step explanation:

The kinetic energy K of a satellite can be found using the equation:

KE = -U

Substituting the given potential energy equation U = -GMm/RA into the equation for kinetic energy, we get:

KE = -(-GMm/RA)

KE = GMm/RA

Therefore, the kinetic energy K of the satellite is GMm/RA.

To find the expression for the square of the orbital period, we need to use the equation for the orbital period T:

T = 2πR/v

where R is the radius of the satellite's orbit and v is the velocity of the satellite. Since the satellite is in a circular orbit, the velocity can be calculated using the equation:

v = sqrt(GM/R)

Substituting this expression for v into the equation for T:

T = 2πR/sqrt(GM/R)

T = 2πsqrt(R^3/GM)

Therefore, the expression for the square of the orbital period is T^2 = 4π^2(R^3/GM).