TAB 7

GRAVITY ASSISTED BI ELLIPTIC TRANSFER ORBIT

ABSTRACT

Bi-Elliptic trajectories are known to be more efficient than Hohmann Transfer orbits, although energy efficiency is typically achieved at the cost of a much longer time in transit. (see illustration below). This report proposes a bi-elliptic transfer orbit of a different kind. The first ellipse is identical to the first half of the Hohmann Transfer and the second ellipse is similar to the second half of the Hohmann Transfer, but with a shorter transit time and more favorable geometry upon approach to the target. Both trajectories are assumed to be a heliocentric ellipse. The program is designed to also take advantage of gravity assist "fly by" phenomena near each planet to make the overall trajectory even more efficient. Overall, the GRABET Transfer Orbit is faster and more efficient than the Hohmann Transfer. In the case of an Earth to Mars mission, the GRABET Transfer either arrives at Mars using 25% less fuel, 40 days faster, or something in between.

The GRABET Transfer orbit is intended to take advantage of nature's proven ability to find the fastest path between two points. The Hohmann Transfer is shown to be most efficient in the Two Body Problem (2BP) system, and this fact is used to initiate the GRABET Transfer by designating the Hohmann Transfer as the initial, nominal trajectory upon Earth escape.

The program then seeks the optimal point from which to begin the second elliptical orbit, using a thrust along some existing velocity vector. The objective is not a Lambert type transfer in which an exorbitant amount of thrust is used to make a rapid transfer to another orbit, but rather something intermediate between a Lambert and a Hohmann, minimizing energy use while making the transfer as fast as possible.

The advantage of using transfer ellipses that are slight variations off the minimum energy Hohmann Transfer is that the trajectory near the primary bodies, Earth and Mars, approximates the minimum energy paths nature predicates. Integrating the conjunction to Earth part of the trajectory, the spacecraft literally falls effortlessly - i.e. without the need for any flight path corrections - into the gravity well of the Earth. Integrating from conjunction to Mars, the spacecraft trajectory is adjusted until it finds the free return trajectory of the sun-Mars system, and the combined gravity of these two bodies moves the spacecraft into a simple, robust approach path to Mars. Again, there is virtually no need for any trajectory correction maneuvers once this "free return" approach trajectory is achieved.

A Traditional Bi-Elliptic Transfer Orbit

The final approach to Mars is especially critical. The spacecraft is moving at half the speed of Mars, Mars being on a nearly circular orbit and the spacecraft being near the apoapse of a highly eccentric transfer ellipse, so the typical approach maneuver is to place the spacecraft in Mar's path and to wait for the planet to approach, for all practical purposes just like driving onto a railroad track and waiting for the freight train to come barreling down the tracks toward you. It's no wonder that 85% of all attempts to land on Mars have failed, crashing into the surface at the last moment ~ unable to make that delicate last second evasion into a safe parking orbit as Mars suddenly looms.

The GRABET Transfer orbit finesses the approach to Mars. The approach geometry is optimized to match the "free return" trajectory, and the program actually puts the spacecraft upon this flight path without the need for any flight path corrections near Mars at the very last moment, but just the single thrust at conjunction months before. The spacecraft then follows a heliocentric ellipse right to Mars, slips into the "free return" trajectory, and loops effortlessly around the rapidly approaching Mars along a trajectory that makes it virtually impossible to crash into the planet. Instead, the spacecraft follows a graceful arc almost all the way around the planet at a constant altitude, that brings it along a "free return" path to an effortless loop around the sun. This loop can either be modified into a large ellipse for aerobraking into a high parking orbit, or adjusted for a low parking orbit and an expeditious maneuver to bring the spacecraft safely down to the planet surface.

In this instance, the notion of nature always finding the minimum energy path also includes the safest path, for the simple reason that crashing the spacecraft on Mars or missing Mars completely and ejecting out into deep space are the worse possible results, not only at the extreme of "minimum" but the total loss of all energy from the system. The difference between success and disaster is admittedly subtle, but the path itself is well defined in Three Body Theory as a closed zero velocity curve looping in a figure eight around Mars and the sun, with the crossing at a Lagrange Point.

Perhaps one day when Mars missions are routine, a small satellite will be placed in a halo orbit around the L2 Lagrange Point, giving approaching spacecraft a physical target; although it is likely that a series of such targeting orbits will be needed to ensure that the spacecraft is on the correct trajectory, matching the "free return" approach in both magnitude and direction of velocity. Something like the Babylon 5 "Jump Gate" architecture, and with a similar purpose - at least for approaching spacecraft. This would be especially important, since the L2 point may diverge from the Mars orbital plane.

________________________________
your banner could be here

© 2004 WH Clark