Satellite and Earth

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  • #1
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How much work is required to lift a 1000-kg satelitte to an altitude of 2*10^6 m above the surface of the earth? The gravitational force is F = GMm/r^2, where M is the mass of the earth, m is the mass of the satellite, and r is the distance between them. The radius of the earth is 6.4*10^6m, its mass is 6*10^24kg, and in these units the gravitational constant, G, is 6.67*10^-11.

I know that the formula of work is W = F * d

d is distance. What is r here? The distance between the satellite and earth? Is it the 2*10^6 and what is d here? Thanks
 

Answers and Replies

  • #2
HallsofIvy
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Work= F*d if F is a constant. When F is a variable, you need
[tex]W= \int f(x)dx[/tex]

Here,
[tex]W= 6.67*10^{11} \int_{6.4*10^5}^{8.4*10^6}\frac{Mm}{r^2}dr[/tex]
 
  • #3
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M and m are also constant right? so we can pull that both outside from the integral??
 
Last edited:
  • #4
hage567
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Yes, the masses are constant.
 
  • #5
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why did I get the answer key from the text book:

I got GMm * ((-1/8*10^6) + (1/6.4*10^6))

is that right??
 
  • #6
hage567
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why did I get the answer key from the text book:

I got GMm * ((-1/8*10^6) + (1/6.4*10^6))

is that right??
Do you mean this is the answer in the book? Or this is the answer you got and it doesn't match the book?
 
  • #7
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this is the answer I got and it didn't matches the book
 
  • #8
hage567
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What's the answer in the book? How much are you off by?
 
  • #9
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the answer in the book is 1.489*10^10 and I got 1.042*10^10
 
  • #10
hage567
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I think you might be making a math error. I got the same answer as the book.
 
  • #11
hage567
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One thing I see is that in your answer you have the height of the satellite as 8x10^6, when it should be 8.4x10^6. I don't think it is really going to change it too much though.
 
  • #12
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where did you get 8.4 from?? there isn't 8.4 in the question
 
  • #13
hage567
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In your question, you have 6.4x10^6 m as the radius of the Earth. Add the 2x10^6 m altitude of the satellite to that, and you get 8.4x10^6 m as your upper limit.

You have to take all distances from the centre of the Earth.
 
Last edited:
  • #14
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okay the problem is solved if I change it to 8.4*10^6
 

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