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Elliptical orbit

  1. Dec 7, 2003 #1
    i was wondering, is there a particular formula to calculate the velocity of a object in an elliptical orbit. Lets say a satellite orbiting around the earth, and the orbit is elliptical, so how do u calculate the velocity at a certain distance from earth. I tried using the v^2=GM/r, but thats only for circular orbits.
    thx for ur time
  2. jcsd
  3. Dec 7, 2003 #2


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    Welcome to the forums!

    The generalized form is called the Vis-Viva equation:


    Where [itex]\mu[/itex] is G*M or 398600.4 km^3/sec^2 for Earth,
    r is the distance from the center of the Earth and
    a is the semimajor axis of the ellipse.

    You'll see that for a circular orbit, a = r for all points on the "ellipse" and you get the expected [tex]\sqrt{\frac{\mu}{r}}[/tex]. You can also get the escape velocity by plugging in infinity for a.
  4. Dec 8, 2003 #3
    There are two things that must be remembered

    1. Conservation of Angular Momentum
    2. Conservation of Energy at any moment

    Writing the above equations as function of r,v
    and calulate r or v whatever required
  5. Dec 8, 2003 #4
    THanx alot for the help, even though in high school we haven't learned that formula yet, but it was really helpfull.
  6. Dec 9, 2003 #5


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    Do you understand it? The way you worded that, it sounds like you didn't.

    It really isn't any more difficult than sqrt(mu/r). a is half the distance of the longest line in the ellipse, r is the current position. Plug and chug.
  7. Dec 9, 2003 #6
    i also found it using the conservation of energy, except with the formula i was a little confused but somehow i got the answer, with it, so i guess that's an alternate way of doing it as well. but the idea of conservation energy was good because thats how much we are taught so far. and i did understood too, n e ways. thnx again
  8. Dec 10, 2003 #7
    Yes those two equations are basic foundation for deriving formula
  9. Mar 24, 2004 #8
    General Math or Physics

    Each planet moves around the sun in an elliptical orbit. the orbital period, T,of a planet is the timeit takes the planet to go once around the sun. the orbital period of a planet is proportional to the 3/2 power of the length of its semi-major axis. what is the orbial period (in days) of Mercury whose semi-major axis is 58 million km? what is the period (in years) of Pluto whose semi-major axis is 6,000 million km? the semi-major axis of the Eart is 150 million km.
    how do you solve this
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