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Homework Help: Orbit calculations

  1. Oct 29, 2007 #1
    1. The problem statement, all variables and given/known data
    The given data is the perigee altitude [itex]r_p[/itex], the apogee altitude [itex]r_a[/itex] and the period T. Mission: find the altitude 30 min after perigee passage.

    2. Relevant equations
    Semi-major axis a is calculated.
    Kepler's equation gives a relation for the eccentric anomaly E:

    [tex]E - \epsilon \sin{E} = \frac{2 \pi}{T} \left( t - t_p \right)[/tex]

    The radius of the orbit is given by

    [tex]r = a \left( 1 - \epsilon \cos{E} \right)[/tex]

    3. The attempt at a solution

    How do I solve for the eccentric anomaly E so I can use the formula for the radius? Or should I use another approach?
  2. jcsd
  3. Oct 29, 2007 #2

    D H

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    Staff Emeritus
    Science Advisor

    There are a number of ways to solve Kepler's equation for the eccentric anomaly given either the mean anomaly or time since periapsis, Newton's method being one of them.
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