# Homework Help: Satellite following circular orbit.

1. May 11, 2010

### dator

1. The problem statement, all variables and given/known data
A satellite with a mass of 5.00 x 10^2kg is in a circular orbit, whose radius is 2r_e, around earth. Then it is moved to a circular orbit with a radius of 3r_e.

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.

2. Relevant 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)

3. The attempt at a solution
I worked out all the questions but I am wondering about the wording and if I should have considered a few things.

Questions a+b:
For the radius it lists 2r_e that is basically 2*(Radius of earth) correct?
And when calculating the potential gravitational energy, E_p will the radius be (2r_e+Radius of earth)? The question says "whose radius is 2r_e, around Earth" implying that you would add the radius of earth on top of the multiplication.

So E_p_i = -(G*m_earth*m_satellite)/(2*r_e+r_e)

Question c:
Isn't this just the result of question b?

d+e:
no problems here just plug into the eqn and solve.

2. May 11, 2010

### D H

Staff Emeritus
Radius means distance from the center. Altitude means height above the surface.

3. May 11, 2010

### dator

Thank you!

4. May 11, 2010

### BishopUser

an orbital radius is typically measured from the center of the object that it is orbiting. if the orbital radius is 2r_e then use 2*(radius of earth) not 3*. I understand your interpretation, but I think it's incorrect.

question c: looks like it to me. your teacher probably wants some statement or equation as proof though.

5. May 11, 2010

### D H

Staff Emeritus
No. Question (b) is about gravitational potential energy only. There is also kinetic energy to consider.