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Escape velocity and formulas for circular orbits

  1. Sep 16, 2003 #1
    In my class, we developed a list of formulas for circular orbits. One of them is E/m=1/2v2-GM/r=constant. To derive escape velocity we find for what v does E=0. But an orbit of this nature is certainly not circular! How can we apply the formula?
     
  2. jcsd
  3. Sep 16, 2003 #2

    chroot

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    Bound orbits are those with E < 0.

    - Warren
     
  4. Sep 16, 2003 #3

    Janus

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    The formula given is true for all orbits; whether they be circular, eliptical, parabolic or hyperbolic.

    As Warren pointed out, circular or eliptical orbits will have E<0

    A parabolic orbit (the one followed by an object traveling exactly at escape velocity) E=0

    For E > 0, you get a hyperbolic orbit.

    One thing about circular orbits:

    v= [squ](GM/r) at all points. if you substitute this for v in the formula you have it reduces to

    E=-GMm/2r

    Now, this turns out to be also true for eliptcal orbits if you substitute the semi-major axis(a) for r. (the semi-major axis is half of the longest dimension of the ellipse. It is also the Average length of the radius vector over the course of an orbit. )

    This gives

    E = -GMm/2a
     
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