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Gravitation - Satellite in circular orbit

  1. Oct 9, 2008 #1
    1. The problem statement, all variables and given/known data

    A satellite of mass m, initially at rest on the earth, is launched into a circular orbit at a height equal to radius of the earth. What is the the minimum energy required for this purpose?


    2. Relevant equations

    GMm/r^2 = mv^2/r

    PE at surface = -GMm/R
    PE at orbit = -GMm/r

    where r = 2R

    3. The attempt at a solution

    I am not getting the logic, and I think my problem is more so related to circular motion, I mean if we launch a satellite ,then it will go up and if viewed from outside earth , follow an elliptical trajectory , then how does it get into a circular orbit?How does a force which is actually pulling it downward suddenly provide centripetal acceleration for rotational motion? How is the initial and final energy related. I did most of the problem but this has left me perplexed made me revisit circular motion but I didnt get the solution to my answer anywhere.
     
  2. jcsd
  3. Oct 9, 2008 #2
    Re: Gravitation

    To get you on the right track, think of this in terms of energy. You need to do a certain amount of work on the satellite to get it into orbit. That work goes into a change in potential energy - and - you have to get the satellite up to a certain velocity - so you also need to provide enough energy that goes into kinetic energy.
     
    Last edited by a moderator: Oct 9, 2008
  4. Oct 9, 2008 #3
    Re: Gravitation

    I understand that but thats not really my question but thanks.
     
  5. Oct 9, 2008 #4
    Re: Gravitation

    You are making it more difficult than it is. You don;t have to go into the technical details of the launching. And it does not have to be an elliptical orbit (unless you consider a circular orbit as a special case op ellipse).
    You may think about it in two steps:
    1. rise the satellite up to a height of 2r - you provide potential energy
    2. "kick-it" laterally so it gets the appropriate speed for that orbit - you provide kinetic energy
    Total energy provided = sum of the two.
    Now, for the orbital motion, you must have mv^2/r = F
    F is the centripetal force, here the gravitational force between satellite and Earth. This will give you the orbital speed.
     
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