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Homework Help: Can you assume that Jupiter has a circular orbit?

  1. Dec 30, 2003 #1
    When it is about the same distance from Jupiter, spacecraft on a mission to the outer planets has a speed that is 1.5 times the speed of Jupiter in its orbit. Why does the orbit of the spacecraft about the sun follow a hyperbolic orbit?

    Can you assume that Jupiter has a circular orbit? So far I've tried caltulating the total energies of the spacecraft and of Jupiter but I don't think that's correct.
     
  2. jcsd
  3. Dec 30, 2003 #2

    enigma

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    Use the Vis-Viva equation

    [tex]

    V=\sqrt{\frac{2}{r}-\frac{1}{a}}

    [/tex]

    It's a safe assumption (unless they give it to you explicitly) that the eccentricity of planetary orbits are very small. That means that r~=a.

    What is the semimajor axis of a parabolic (or hyperbolic) orbit? You can solve for escape velocity with that.
     
  4. Dec 30, 2003 #3

    enigma

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    I made a mistake.

    Vis Viva is:

    [tex]

    V=\sqrt{\mu*(\frac{2}{r}-\frac{1}{a})}

    [/tex]

    Where mu is the gravitational parameter, G*M or 398600.4 km^3/sec^2
     
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