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## Homework Statement

A satellite with a mass of 5.00 x 10^2kg is in a circular orbit, whose radius is 2(radius of the earth), around earth. Then it is moved to a circular orbit with a radius of 3(radius of the earth).

a) Determine the satellite's gravitational potential energy from the first orbit to the second orbit.

b) Determine the change in gravitational potential energy from the first orbit to the second orbit.

c) Determine the work done in moving the satellite from the first orbit to the second orbit. Apply energy conservation.

d) Calculate the speed it would need in order to maintain its new orbit.

e) Calculate the escape velocity for the satellite if it is on the Earth's surface.

mass of Earth : 5.98 x 10^24 kg

radius of the Earth : 6.38 x 10^6 m

## Homework Equations

E_p = -1(G*m_1*m_2)/r

(delta)E_p = -((G*m_1*m_2)/r) - (-((G*m_1*m_2)/r))

v = sqrt((G*m_planet)/r)

v_escape = sqrt((2*G*m_planet)/r)

## The Attempt at a Solution

a) Epi=[(-G)(5.98x10^24kg)(5.00x10^2kg)]/2(6.38x10^6m)

Epi=-1.5637x1010J

Epf=[(-G)(5.98x10^24kg)(5.00x10^2kg)]/3(6.38x10^6m)

Epf=-1.042x10^10J

b)

Change in Ep= Epf-Epi

Change in Ep= (-1.042x10^10J)-(-1.5637x1010J)

Change in Ep=5.20x10^9J

c)

This is where I'm having trouble, in this case does Changes in Ep= Work ?

Or is Change in Ep+ Ek = Work ?

d)

v=Sqr[ [(G)(5.98x10^24kg)]/3(6.38x10^6m)]

v=4566m/s

e)

Vesp = Sqr [ [(2G)(5.98x10^24 kg)] / (6.38x10^6m) ]

Vesp =111.84.48 m/s

Could some verify my solutions, and shed some light on my problems in c)