This page will contain a moderately detailed discussion of the topics noted in more detail below. However, the orbital mechanics are very complex, especially in the case of gravitational assist encounters, so although the concepts involved will be discussed in detail in the final version of this page, mathematics will be essentially abandoned in favor of greater clarity for the vast majority of people who are not involved in the actual calculations required for spacecraft engineering and support.
Launching spacecraft to other planets requires immense amounts of energy. To reduce the energy requirements, various techniques can be used. One of the earliest and simplest methods is to use a Hohmann Transfer Orbit, named after Walter Hohmann, a German scientist who published a description of the method in Die Erreichbarkeit der Himmelskörper (or in English, The Accessibility of Celestial Bodies), which was published in 1925, long before we could reach any other celestial body.
Although Hohmann orbits are the most energy-efficient way to reach other planets along "direct" paths, there are other methods that can allow far lower energies, using gravitational assist (often called "gravitational slingshot") encounters with planets (usually other planets, but sometimes even the Earth). Such encounters can be used to greatly increase (as in the case of the New Horizons voyage to Pluto and the Galileo voyage to Jupiter) or greatly decrease (as in the case of the MESSENGER spacecraft's complex trip to Mercury) the speed of spacecraft, allowing us to send spacecraft to otherwise unreachable objects (such as Mercury, which cannot be reached by any direct orbit using current technology), or to greatly increase the size and weight of spacecraft that can be launched by current launch vehicles. For unmanned spacecraft, where launch energy is among the greatest constraints on the construction of the spacecraft, gravitational encounters are invaluable. But using such trajectories often increases the time required to reach the target planet far beyond any acceptable value for human space travel, so Hohmann transfer orbits will almost certainly be the primary approach for manned flight to other planets, especially the most likely first target, Mars (whence the title for this page).
The trajectory of the Mercury MESSENGER, which flew by Mercury in 2008 and 2009, and entered orbit around the planet in 2011. (A long discussion of the complexities of the planetary flybys and gravitational assists required to achieve this goal, which required a considerable amount of time to write, was lost in uploading files; and as a result of the lost time and frustration involved in that loss rewriting it was put off until another day. However, a placeholder (Orbital Perturbations and Gravitational Assists
was created as a prod to enlarge on this sooner rather than later. When complete, part of that page may be incorporated into this page and vice versa, or the two may be merged into a single page. All current links to either page will then be directed to the appropriate target(s)) Although both this and the other page are currently labeled as placeholders, they do provide a reasonable preview of where they are headed. (Image Credit Johns Hopkins, Carnegie Institution, NASA)