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How do you find the radius

  1. Jun 18, 2009 #1
    1. The problem statement, all variables and given/known data
    A 129 kg satellite experiences a gravitational force by the Earth of 790 N. What is the radius of the satellite's orbit?


    2. Relevant equations
    F=GM/R^2


    3. The attempt at a solution
     
  2. jcsd
  3. Jun 18, 2009 #2
    For an object of mass m under the effect of earth's gravitational pull, the force pulling it towards the center of the earth is of a magnitude:

    |Fgravity| = m((GMearth)/r²)
    where r is the distance of the object from the center of the earth.

    Another formula you'll find helpful if there are any follow-up questions is the following:
    An object in simple circular motion around a fixed point, is being pulled towards the center of its orbit by a force of magnitude:
    |Fcentripetal| = mv²/r
    Where v is the tangential speed of the object, and r is the radius of its circular orbit.

    Please make an attempt at the solution before asking us to help.
     
    Last edited: Jun 18, 2009
  4. Jun 18, 2009 #3
    r^2=G(m1m2)/F
    r^2=6.67x10^-11(129x5.98x10^24)/790
    r^2=6.67x10^-11(7.7142x10^26)/790
    r^2=6.67x10^-11(9.764810127x10^23)
    r^2=6.513128355x10^13
    r=8070395.501

    thats the answer i got but it is still wrong...i need some serious help...
     
  5. Jun 18, 2009 #4
    Final answer is 8068.29466 kilometers, according to Google calculator, so you're in the ball-park. Rounding errors could account for the difference in our answers.
    Why do think you're wrong?
     
  6. Jun 18, 2009 #5
    so did i use the proper formula?
     
  7. Jun 19, 2009 #6
    Yes, I think so. But can you explain to me why that was the proper formula?
     
  8. Jun 19, 2009 #7
    hey guys i need some more opinions on this problem...and i just took a guess at the formula...
     
  9. Jun 19, 2009 #8

    ideasrule

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    Homework Helper

    Why do you need more opinions? You got the right answer.

    As for why the formula is right, F=Gm1m2/r^2 is Newton's law of gravitation, relating gravitational force to mass and distance. You know F; that was given in the question. You know m1 and m2; one is the mass of the Earth and the other is the astronaut's mass. G is a constant. With one equation and one unknown (r), you can solve for r, which is what the question asks for.
     
  10. Jun 19, 2009 #9

    Redbelly98

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    Staff Emeritus
    Science Advisor
    Homework Helper

    Not to sound nitpicky, but RoyalCat gave you the correct formula in Post #2. Your formula in Post #1 was wrong.
     
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