Kepler's Problem: Time of Flight

Question 1

Shortcomings of Kepler’s Equation

Answer 1

1. ) Solving Kepler’s equation has numerical problems (e ≈ 1 which is near parabolic); slow convergence; lack of accuracy
   - as eccentricity approaches one, we have a highly elliptical orbit which comes into play when we look at geostationary transfer orbits (GTOs) or lunar orbit (e=0.99) start running into a problem because convergence goes really slow so get very little update with each iteration
2. ) Different formulation needed for elliptic/parabolic/hyperbolic orbits; inconvenient because could transition from one to the next; more convinent to have one formulation (universal formulation).