When do I include the Earth's radius in questions involving satellites?

[checkerboard]

Homework Statement

A 722-kg satellite is in circular orbit 7380 km above the surface of Earth (ME= 5.98 ´1024kg). The gravitational force acting on the satellite is

Relevant Equations

Fg=(GMm)/r^2

The answer is 5.29 x 10^3N and I used r=7 380 000m to get it. However, in a different question like this one "If the mass of Earth is 5.98 x 10^24kg and the radius is 6.38 x10^6m, the gravitational potential energy of a 1.2x 10^3-kg satellite located in an orbit 230 km above the surface of Earth is" where the answer is –7.2 x 10^10 J, I had to use the 230 000m radius AND add Earth's radius of 6.38 x10^6m in the equation Eg= -(GMm)/r to get the answer.

Both questions say the 'satellite in orbit x km above the surface of the Earth' but I can't tell when I should add Earth's radius and when I should leave it out. I'd appreciate any help. Thank you c:

 

[gneill]

Satellite orbits are always taken to be about the center of the Earth, and the orbit radius is centered there. When they give you a height above the surface and you need the orbit radius, you must always include the radius of the Earth and add the height to that.

 

[checkerboard]

Satellite orbits are always taken to be about the center of the Earth, and the orbit radius is centered there. When they give you a height above the surface and you need the orbit radius, you must always include the radius of the Earth and add the height to that.

Thank you! Does that mean the first question's answer is wrong then? Or am I misunderstanding it

 

[gneill]

Does that mean the first question's answer is wrong then? Or am I misunderstanding it

Yes, you should have included the Earth's radius.

 

[checkerboard]

Yes, you should have included the Earth's radius.

Thank you very much!

 

[gneill]

Your welcome. And welcome to Physics Forums!