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Theory of Gravity

  1. Jun 5, 2009 #1
    1. The problem statement, all variables and given/known data

    The space shuttle orbits 366.1 km above the surface of the earth. What is the gravitational force on a 1.09 kg sphere inside the space shuttle?

    2. Relevant equations

    U=Gm1m2/Re
    U=-W
    W=m(freefall)

    3. The attempt at a solution

    I am starting to understand the theory behind gravity now, am I setting this problem up correctly? I am making U=-W and then solving for the free fall so I come up with ......

    G*M/(radius of earth+ distance of how far it is from earth)=g

    G=6.67X10^-11
    M=5.98X10^24
     
  2. jcsd
  3. Jun 5, 2009 #2

    Cyosis

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    What is the formula of the gravitational force between two objects?
     
  4. Jun 5, 2009 #3

    CompuChip

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    I assume that by W you mean work (e.g. work done against the gravitational force to lift the sphere from the center of the earth to its current position). In that case, W is not given by m, but by m g h where h = radius of earth + distance above the surface. It is probably easier, however, to go from the potential energy directly to the force through F = - U', where U denotes differentiation with respect to the distance, giving
    F = G M m / r^2
    where M, m are the mass of the earth and sphere and r is the distance between the sphere and the center of the earth (= radius of earth + distance above the surface).

    You can also use the first two formulas you gave complemented with W = m g r as I explained above to derive an expression for g first, and then use F = m g for the gravitational force. That will give you the same result.
     
  5. Jun 5, 2009 #4
    So all I have to do is ues F=G*M*m/r^2.......? Was I just over thinking things?
    Where F is the gravitational force?
     
  6. Jun 5, 2009 #5

    Cyosis

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    Yep.
     
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