The "Grabet Transfer" Orbit
(Gravity Assisted Bi-Elliptic)
by
Bill H. Clark, PE, MSE

The purpose of this posting is to present my PhD research at the
Aerospace Engineering Department of the University of Texas at Austin
on optimizing the Earth to Mars trajectory. I have created a computer
model of a two body Hohmann Transfer orbit to Mars, with Earth and
Mars in circular orbits and all motion in the same plane. The nominal
trajectory matches exactly a Hohmann Transfer in total thrust and time
of flight. This confirms the accuracy of the model, which is
integrated to 13 significant digits using a Runge Kutta 7/8 variable
step integrator. The half of the trajectory that is an approach to
Mars is then optimized and a is solution found that uses 20% less fuel
arriving in the Hohmann time of flight; or arrives 30 days faster
using the Hohmann thrust. The complete Fortran source code is only 9
pages long, is easy to follow, and requires no third party
optimization software (although using this would presumably result in
an even better solution). Moreover, the problem I have solved is
essentially the ballistic trajectory targeting problem; exactly what
they have been having problems with solving for the Strategic Defense
Initiative missile defense project. The University did not think this
project was suitable for even a Masters' Report, much less a Thesis or
Dissertation, as indicated by their letter of dismissal. If you have
any questions please direct them to the University officials who
signed the dismissal letter.

http://home.earthlink.net/~whcii/