6. 'help fsolve' in matlab and reading the help would be helpful.
(a) A spacecraft is observed at r = 7,000 km and with a v = 7.56 km/s in its orbit around
Earth ? = 398,600 km³/s². It is also determined that the spacecraft has no radial velocity
at this epoch. Use Kepler's Equation and find the distance and velocity of the spacecraft
one day after this epoch. To solve the Kepler's equation, use MATLAB fsolve. Read
about fsolve from MATLAB Documentation.
(b) Assuming that e is small, show that the expression E = M + e\sin(M) is a solution to
Kepler's equation. Using this expression, solve the problem in part (a) analytically and
compare the results.