Finding orbital altitude 30 min after perigee passage using Kepler's equation

  • Thread starter Thread starter Logarythmic
  • Start date Start date
  • Tags Tags
    Calculations Orbit
Join the discussion
Registration is free. Start your own thread to ask a follow-up.
Sign up Log in
1 reply · 2K views
Logarythmic
Messages
277
Reaction score
0

Homework Statement


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.


Homework 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]


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?
 
Physics news on Phys.org

Discussion

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.