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Acceleration of object at specific height?

  1. Mar 1, 2016 #1
    This stuff is so confusing! I really wish I were better at math.... I had to take precalc math twice, so please try and dumb this down for me.
    1. The problem statement, all variables and given/known data

    Communication satellites orbit the earth at a height of 35700km above the Earth's surface. What is the acceleration of an object due to the gravitational attraction by Earth at this height?
    The earth has a radius of 6.38x10^6m and a mass of 5.98x10^24kg

    Possible answers (m/s^2):
    0.0028
    0.0065
    0.044
    0.225
    8.55

    2. Relevant equations
    This is what I need to know??

    3. The attempt at a solution
    EDIT: I just found a table of varying g with altitude and it directly states that a satellite at that altitude has an acceleration of 0.225 m/s^2. Still, how are we supposed to find this without memorizing a table?
     
    Last edited: Mar 1, 2016
  2. jcsd
  3. Mar 1, 2016 #2

    SteamKing

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    Have you studied any formulas which might tell you the force due to gravitational attraction between two masses separated by a given distance?
     
  4. Mar 2, 2016 #3
    Force = G(m2+m1)/r^2 but this does not give acceleration. F=ma requires mass of the sattelite which i do not have.
     
  5. Mar 2, 2016 #4

    cnh1995

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    It's m1*m2, not m1+m2. You don't need mass of the satellite.
     
  6. Mar 2, 2016 #5
    Force = (6.6726x10^-11)(5.98x10^24)/(6.38x10^6)^2 .... this is not correct. What do I do? I tried adding the distance from the satellite to earth surface, and the distance from the satellite to the middle of the earth to r^2 and that didn't help. Plus, force isn't acceleration. Is that still the correct formula? what do I do with it?
     
  7. Mar 2, 2016 #6

    cnh1995

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    This is the formula for acceleration due to gravity at(and near) the surface of the earth. The satellite is at a height 37500km from the surface. How far is it from the center then? Calculate that distance and use it in place of r.
     
  8. Mar 2, 2016 #7
    Using that method, I got something like 0.207, which is not 0.225 but close? I don't like that it's not exact. This is really going to throw me off.
     
  9. Mar 2, 2016 #8

    cnh1995

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    I believe your answer is right. The values of mass of earth, G and radius of earth are slightly different in each textbook. So, 0.207 is close to 0.225.
     
  10. Mar 2, 2016 #9

    haruspex

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    .207 does seem somewhat off to me. Please post all your working.
    There are two routes you can take: apply GM/r2, where r=R+h, R being the radius of the earth and h the height; or you can just look at the ratio to surface gravity: gR2/r2. I tried both, and both gave me around .225.
     
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