Due: October 24, 2003

Assignment

As described in lecture and on the web, Kepler's equation is:

M = E-e*sin(E)

where M is the mean anomaly, e is the orbital eccentricity, and E is the eccentric anomaly. We need to know E so that we can predict the location of the GPS satellites. Kepler's equation is used to solve for E numerically. One method that can be used is called Newton's method. Say F is a function of x. We can determine successive values of x by the following:

x_i+1 = x_i - F(x_i)/F'(x_i)

Rewriting:

F(E) = M -E + e*sin(E)

F'(E) = -1 + e*cos(E)

E_i+1 = E_i -F(E)/F'(E)

Given e and M, find E (in degrees):

1. e = 0.4; M = 235.4 deg
2. e = 0.01; M = 165 deg
3. e = .8; M = 45 deg

You are required to solve Kepler's equation in a function. E should be returned in radians. The inputs to your Kepler function are to be defined in your main program.

Turn in:Your Kepler function and answers (to 6 decimal places).