Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Hyperbolic, Parabolic or Elliptical Orbit?

  1. Aug 31, 2004 #1


    User Avatar

    A comet is first seen at a distance of d AUs from the Sun and is travelling with a speed of q times the Earth's speed.

    Apparently it can be shown that if q2·d is greater than, equal to, or less than 2, then the comet's orbit will be hyperbolic, parabolic or elliptical respectively.

    Any idea how this can be shown??

    I know that, in general, ε (eccentricity) is less than, equal to, or greater than 1 for an ellipse, parabola, and hyperbola respectively.
  2. jcsd
  3. Aug 31, 2004 #2


    User Avatar
    Science Advisor
    Homework Helper

    Yes, see post: https://www.physicsforums.com/showthread.php?t=40525

    Just substitute the heliocentric gravitational constant for the geocentric gravitational constant.

    The specific energy of object (energy per unit of mass) is just:

    where v is velocity, r is position and [tex]\mu_{sun}=1.327124421\times 10^{11}km^3/sec^2[/tex]

    If the specific energy is less than 0, the object will orbit the Sun. If equal to 0, the object will follow a parabola. If greater than 1, the object will follow a hyperbola.

    'e' is normally used to represent eccentricity (depends on the book you're using)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook