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Gravitational force near and away from earth's surface

  1. Feb 16, 2014 #1
    So, I asked myself the question, "why does the earths force of gravity effect us so dramatically on the surface of the earth, but seems nonexistent while just a couple hundred miles up?"

    I answered that question myself, after thinking more about it, because the idea of an orbit is that you constantly fall towards the earth. So just like the simulated weightless environment a plane can create, so is a space station a simulated weightless environment.

    However, in trying to answer this question I tried to calculate the newtonian gravitational force one one would feel at the surface, and here's what I got: (m1=earth, m2=unity)

    F = G * m1 * m2 / r^2 = 6.67e-11 * 5.97e24 * 1 / (6378.1 / 2)^2 = 39191036.5 N/kg

    So if I weighed 80kg, I would experience 39191037*80 = 3135282921 N

    So, what did I do wrong? My feet obviously aren't holding up 314e6 N.

    Also, knowing that we feel 9.81*m newtons sitting on the surface, it would follow that G*m1/r^2 = 9.8:
    G = 9.8*r^2/m1 = 9.8* (6378.1 / 2)^2 / 5.97e24 = 1.6705e-17

  2. jcsd
  3. Feb 16, 2014 #2


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    Staff: Mentor

    1. You're using Kilometers for R. Use meters instead.
    2. Don't divide your value by 2. 6,378 is the radius of the Earth in Km, not the diameter.
  4. Feb 16, 2014 #3
    The radius of the Earth needs to be expressed in meters not kilometers also do not divide the radius by 2?
  5. Feb 16, 2014 #4
    Oh man, I'm bad. Thanks guys, lol....
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