Optimum Transfer to Mars Via Venus

The advantages of a transfer to Mars via Venus compared with a direct flight to Mars are becoming well understood. This paper investigates the advantages of a thrust maneuver during the flyby of Venus. Three types of free-fall transfers between Earth and Mars are compared. These are: (1) A direct, free-fall transfer from Earth to Mars. (2) A Venus flyby enroute to Mars. (3) A free-fall transfer which includes a thrust maneuver during a flyby of Venus enroute to Mars.

The specification of the launch date at Earth and the arrival date at Mars is sufficient to determine the a transfer of the first two types. The third type of trajectory is more complicated since it requires, in addition, the computation of the flyby thrust impulse at Venus. The date at Venus is a free parameter which can be chosen to minimize the total propulsive velocity requirement for the overall mission.

For each possible flyby date at Venus, it is also necessary to choose the optimum thrusting point. The constraint of a finite flyby planet radius is then important, since a computed optimum thrusting point may lie beneath the planet's surface. A simplified criterion is given for determining whether the optimum point lies above the planet's surface. For cases in which the optimum lies beneath the surface, a technique is presented for finding the best thrusting point lying above the surface.

The optimum thrust impulse must be computed for each possible flyby date for the given dates at Earth and Mars. The optimum thrusted flyby determined in this manner is compared with transfers of the first two types for most practical dates between 1970 and 1990. A simple method for predicting the dates of practical trips to Mars via Venus is employed. It is shown that the angular position (relative to the Earth) of Venus and Mars at the date of their planetary alignment with the Sun is sufficient to predict whether or not Venus is available for a flyby.

In comparing the three types of Earth-Mars transfers for practical dates between 1970 and 1990, it was found that the transfer using thrust during the flyby of Venus is usually better than one which does not use thrust, but the saving is small because the optimum date for a flyby with thrust is always close to the date for a pure (unthrusted) flyby of Venus.

It was also found that there exist some flyby dates for which a thrusted flyby of Venus is more economical than a direct transfer, and, in addition, a flyby of Venus without thrust would require that the vehicle pass beneath the surface of the planet. However, when this situation arises there are usually neighboring dates for which transfers of the first two types are more economical.

As a result, the use of thrust during a flyby of Venus does offer savings in the overall propulsive velocity requirement for an Earth-Mars mission, but from a practical point of view the savings do not appear significant. This conclusion applies only to the specific orbital transfer which was investigated: the Earth-Mars transfer for a round-trip stop-over mission. The method of analysis described, however, is applicable to any interplanetary flyby trajectory. Since, in any flyby transfer, the thrusted flyby can potentially be more economical than a pure flyby, the use of a thrusted flyby should be investigated for other types of missions, such as a non-stop, round-trip mission which includes thrusted flybys of both Venus and Mars.