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Circular Orbit / Practice Quiz #4, Question 27

  1. Oct 6, 2014 #1
    1. The problem statement, all variables and given/known data


    What is the acceleration due to gravity at an altitude of 1.00 x 10^6 above the earth's surface, given that the radius of the earth is 6.38 x 10^6 m?


    2. Relevant equations
    Using g = GMm/r^2
    Fc = mv^2/r
    3. The attempt at a solution
    Fc = mv^2/r

    How can I solve this equation if I am missing m and v?
     
  2. jcsd
  3. Oct 6, 2014 #2
    The only force acting upon the object in this example is the force of earths gravity. You only need to use the equation F=GMm/r^2...remember F=ma, which means that acceleration=G*M/r^2 and mass =m. F=m*a=m*(GM/r^2)
     
  4. Oct 6, 2014 #3

    berkeman

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    Staff: Mentor

    Write the 2 equations, one at the surface of the Earth where you know the value of g, and the other at altitude. You should be able to cancel a lot of things out... :-)
     
  5. Oct 6, 2014 #4

    and mass =m. F=m*a=m*(GM/r^2)[/QUOTE]

    I don't understand this last part. Are you saying
    m= m
    F = ma = m * (GMr^2)

    where did you get the mass from? I thought the equation for acceleration is G*M/r^2
     
  6. Oct 6, 2014 #5
    If the formula is a= GM/R^2

    then i only need the value of M
     
  7. Oct 6, 2014 #6
    yes exactly...M in this case is the mass of the earth...it appears that they want you to look it up yourself...it happens to be 5.972*10^24 kg

    ALSO! dont forget that your radius is actually radius of earth + objects distance from earth
     
  8. Oct 7, 2014 #7

    gneill

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    Staff: Mentor

    If you have the acceleration due to gravity at one radius (like the surface of the Earth), then you can find the acceleration due to gravity at another radius using ratios. No need to know the actual mass of the Earth or the value of G.

    Write the expression for the acceleration due to gravity for both locations using appropriate variables (so R1 and g for one, R2 and a for the other). Then make a ratio of the equations. All the common variables will cancel.
     
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