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Gravitational field strength at a point

  1. Jul 18, 2016 #1
    1. The problem statement, all variables and given/known data
    What is the gravitational field strength at a point 6.38x106 m above the earth's surface?

    2. Relevant equations
    r%5E2.gif
    3. The attempt at a solution
    Ok so I plug in all the known variables. G= 6.67x10-11. M= 5.98x1024. r= 6.38x106 and so I multiply that by 2 because the given point is the exact same number as r. Then I powered by two. I calculate both top an bottom of the equation to get g= 39.8866x1013/162.8176x1012. For the answer I get a field strength of 2.449 m/s2. But the answer says that it is 0.622 m/s2.

    Edit. I was looking at a wrong answer. You got to love my brain sometimes!
     
  2. jcsd
  3. Jul 18, 2016 #2

    Andrew Mason

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    There is an easy way to do this if you recognize what 6,380 km above the surface is in terms of the earth radii!

    AM
     
  4. Jul 19, 2016 #3
    Isn't 6,380 km above the surface just twice the radius of Earth?
     
  5. Jul 19, 2016 #4

    Andrew Mason

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    Right. So how should acceleration due to gravity there compare to the acceleration on the surface?

    AM
     
  6. Jul 19, 2016 #5
    Oh I see. So it would approximately be the square root of 9.8?
     
  7. Jul 19, 2016 #6

    Andrew Mason

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    ? Gravitational force and Gravitational force/unit mass (acceleration) is proportional 1/R2 so if R doubles from the surface, what happens to acceleration (ie. compared to acceleration at the surface, which is 9.8 m/sec2)?

    AM
     
  8. Jul 20, 2016 #7

    haruspex

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    This illustrates a benefit of always including units. In this case, the square root of 9.8m/s2 would be about ##3.1m^{\frac 12}s^{-1}##. Hmm.. I wonder what the square root of a metre looks like.
     
  9. Jul 20, 2016 #8
    It would diminish by 4x?
     
  10. Jul 20, 2016 #9

    Andrew Mason

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    Correct. Work that out and compare that to your answer.

    AM
     
  11. Jul 20, 2016 #10
    I actually figured this out when I had my test today it was one of the questions. I just put in some random masses and radius in the equation and saw that if you half the radius then the force of gravity increases by 4x.
     
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