# Satellite physics question

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#1
Earth has a mass of 6.0 × 10^24 kg and a radius of 6400km.
A satellite of mass 320kg is lifted from the Earth’s surface to an orbit 1200km above its surface.

What is the change in the gravitational potential energy of the satellite?

How do i solve this? I think i have to use E=GMM/r but im not sure what the value of r would be as there is two.
Last edited by username3754758; 3 months ago
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3 months ago
#2
I think i have to use E=GMM/r but im not sure what the value of r would be as there is two.
The question asks you to calculate CHANGE in gravitational energy, so can you use the two radii to formulate that difference?
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#3
(Original post by lordaxil)
The question asks you to calculate CHANGE in gravitational energy, so can you use the two radii to formulate that difference?
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3 months ago
#4
Earth has a mass of 6.0 × 10^24 kg and a radius of 6400km.
A satellite of mass 320kg is lifted from the Earth’s surface to an orbit 1200km above its surface.

What is the change in the gravitational potential energy of the satellite?

How do i solve this? I think i have to use E=GMM/r but im not sure what the value of r would be as there is two.
Calculate using V = GM/r the gravitational potential at the Earth's surface using 6400 km in metres. Using M as Mass of Earth

Then calculate using V = GM/r the gravitational potential in orbit using 6400 km + 1200 km in metres. Using M as Mass of Earth

The difference is the change in the gravitational potential between the two positions. It is closer to zero the further from Earth you get.

The change in gravitational potential energy is the difference in the gravitational potential multiplied by the mass of the satellite, W = m (delta)V.

The answer you get should be roughly answer C, let me know if you need anymore help with this.
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#5
(Original post by khix)
Calculate using V = GM/r the gravitational potential at the Earth's surface using 6400 km in metres. Using M as Mass of Earth

Then calculate using V = GM/r the gravitational potential in orbit using 6400 km + 1200 km in metres. Using M as Mass of Earth

The difference is the change in the gravitational potential between the two positions. It is closer to zero the further from Earth you get.

The change in gravitational potential energy is the difference in the gravitational potential multiplied by the mass of the satellite, W = m (delta)V.

The answer you get should be roughly answer C, let me know if you need anymore help with this.
Thanks I got the answer. This was really explained nicely.
Could you also explain this question please i think its similar concept to what you explained above. I always get confused on what radius to use.

A satellite of mass 3000 kg moves from a parking orbit of radius 6800 km to a geostationary
orbit of radius 42 000 km. The mass of the Earth is 6.0 × 1024 kg.
What is the magnitude of the change in gravitational potential?

Update below
Last edited by username3754758; 3 months ago
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#6
Update: Never mind i figured the answer out myself its the same method you explained but i was a bit worried when i wasnt using the mass of the satellite. I feel like every time they give a number or figure in the question i have to use it somewhere along the line but in this case i didnt use it.

I did v=GM/r for both values using mass of earth and worked out the difference between them. I didnt use the mass of satellite at all.

P.S I think there is a method to use the mass of satellite using E=GMM/r but im not sure on what radius to use. And then after i would need to rearrange for v from the formula E=m x (delta) v. So change in gravitational potential= E/M where m is the mass of the satellite. If you could tell me what radius to use for this method it would be really helpful. As it could be useful to use in other questions.
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3 months ago
#7
Update: Never mind i figured the answer out myself its the same method you explained but i was a bit worried when i wasnt using the mass of the satellite. I feel like every time they give a number or figure in the question i have to use it somewhere along the line but in this case i didnt use it.

I did v=GM/r for both values using mass of earth and worked out the difference between them. I didnt use the mass of satellite at all.
You did use it - in the last step, you must have multiplied by mass of satellite to get its change in potential energy.

P.S I think there is a method to use the mass of satellite using E=GMM/r but im not sure on what radius to use. And then after i would need to rearrange for v from the formula E=m x (delta) v. So change in gravitational potential= E/M where m is the mass of the satellite. If you could tell me what radius to use for this method it would be really helpful. As it could be useful to use in other questions.
It does not really make sense to use a single "radius" because you are calculating a change in potential energy. However, if you wanted a number to plug into the equation, you could use , where is the smallest radius and is the largest radius, which would give you the same result.
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3 months ago
#8
Update: Never mind i figured the answer out myself its the same method you explained but i was a bit worried when i wasnt using the mass of the satellite. I feel like every time they give a number or figure in the question i have to use it somewhere along the line but in this case i didnt use it.

I did v=GM/r for both values using mass of earth and worked out the difference between them. I didnt use the mass of satellite at all.

P.S I think there is a method to use the mass of satellite using E=GMM/r but im not sure on what radius to use. And then after i would need to rearrange for v from the formula E=m x (delta) v. So change in gravitational potential= E/M where m is the mass of the satellite. If you could tell me what radius to use for this method it would be really helpful. As it could be useful to use in other questions.
hi there sorry for the late reply, I don't check student room that often. I am struggling to this question which you have managed to figure out, I have used the same method which I explained to you so please could you explain your method and the number used. Thanks
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#9
(Original post by khix)
hi there sorry for the late reply, I don't check student room that often. I am struggling to this question which you have managed to figure out, I have used the same method which I explained to you so please could you explain your method and the number used. Thanks
I did v=GM/r for both distances using mass of earth and worked out the difference between gravitational potential. In this question I didnt use the mass of satellite at all only mass of earth. I cant remember the exact answer and values sorry as I was doing this in preparation for my test which was on friday.
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3 months ago
#10
I did v=GM/r for both distances using mass of earth and worked out the difference between gravitational potential. In this question I didnt use the mass of satellite at all only mass of earth. I cant remember the exact answer and values sorry as I was doing this in preparation for my test which was on friday.

I also used v=GM/r and did 6.67x10^-11 x 6x10^24/6800000 = 58852941.18
Then I did v=GM/r and did 6.67x10^-11 x 6x10^24/6800000 + 42000000 = 8200819.672
Then I found the difference which was -50652121.51 and then multiplied this by the mass of the satellite as Ep = m x v. But I get answer D which is wrong as its C the answer.
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3 months ago
#11
Update: My bad I didn't read the question it asked for the change in gravitational potential, not gravitational potential energy. In regards to using E=GMm/r its the same method but then when you have found the difference you just divide the answer by the mass of the satellite. You would just use the same radius 6800km and 42000km but the reason you don't use E=Gmm/r+h is that the question already gives you r+h as the 42000km. Hope this kind of makes sense.
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#12
(Original post by khix)
Update: My bad I didn't read the question it asked for the change in gravitational potential, not gravitational potential energy. In regards to using E=GMm/r its the same method but then when you have found the difference you just divide the answer by the mass of the satellite. You would just use the same radius 6800km and 42000km but the reason you don't use E=Gmm/r+h is that the question already gives you r+h as the 42000km. Hope this kind of makes sense.
Aha yeah its the same method you used for the other question in a way. Just need to work out the change in gravitational potential instead of gravitational potential energy. I feel like if they had put both of those questions next to each other in a paper people wouldve definitely got 1/2 marks as they would've misread the question.
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3 weeks ago
#13
why do you multiply by the mass of the satellite at the end ?
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