This paper defines the basic constraints for interplanetary round trip travel or, equivalently, for round trip travel from and to a natural or artificial satellite, such as round trips from the International Space Station to another satellite and back. While the constraints are straightforward, they do not seem to have been discussed previously in the literature, perhaps because round trip travel has not been a realistic option for most missions.
We call the location that we are leaving and returning to the home planet or satellite and the spacecraft which makes the round trip the traveler. In round trip space travel, the traveler and the home planet must begin and end at the same true anomaly. Consequently, the fundamental constraint for mission design is as follows:
Over the duration of the mission the difference in the change in true anomaly for the home planet and the change in true anomaly for the traveler must be an integral number of revolutions.
This fundamental constraint implies a number of interesting properties for round trip travel to other locations in the solar system. For example:
- For Hohmann minimum energy transfers, going to nearby objects takes longer than going to some which are further.
- The shortest Hohmann round trip to a destination further from the Sun is a 2-year trip to a heliocentric distance of 2.2 AU, i.e., 1.2 AU outward from the Earth.
- Increasing the transfer velocity has only a very small effect on total trip time, except at discrete “jumps” where the total trip time can change by a year or more.
- One way to reduce the round trip time is to go beyond the target planet and visit the target “on the way back.”
- Some scenarios that go above a ∆V threshold can dramatically reduce the total round trip time, i.e., a reduction in round trip time for a Mars mission from the traditional 2.5 years to less than 6 months.
This paper discusses the general constraint equations and the resulting implications for round trip mission design. These equations provide very fundamental constraints on solar system travel in which people or equipment want to visit another planet and return.
Wertz, J.R. 54th International Astronautical Congress, Bremen, Germany. September 29–October 3, 2003.