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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.
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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#2
(Original post by dj_ad_1)
I think i have to use E=GMM/r but im not sure what the value of r would be as there is two.
I think i have to use E=GMM/r but im not sure what the value of r would be as there is two.
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(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?
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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#4
(Original post by dj_ad_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.
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.
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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(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.
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.
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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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.
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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#7
(Original post by dj_ad_1)
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.
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.
(Original post by dj_ad_1)
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.
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.
, where 
is the smallest radius and 
is the largest radius, which would give you the same result.
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#8
(Original post by dj_ad_1)
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.
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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(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
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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#10
(Original post by dj_ad_1)
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 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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#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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(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.
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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