Trajectories

Trajectories are the paths followed by spacecraft as they travel from one point to another. They are governed by two key factors: the spacecraft's own propulsion system and the gravity of the Sun, Earth, and other planets and moons. Because even the most powerful rockets have only a limited amount of thrust, engineers must carefully develop trajectories for spacecraft that will allow them to reach their intended destination. In some cases this can lead to complicated trajectories that get a boost from the gravity of other worlds.

The trajectory needed for a spacecraft to go into orbit around Earth is relatively straightforward. The spacecraft needs to gain enough altitude—typically at least 200 kilometers (124 miles)—to clear Earth's atmosphere and enough speed to keep from falling back to Earth. This minimum orbital velocity around Earth is about 28,000 kilometers per hour (17,360 miles per hour) for low Earth orbits and slower than that for higher orbits as Earth's gravitational pull weakens. Other parameters of the orbit, such as the inclination of the orbit to Earth's equator, can be altered by changing the direction of the spacecraft's launch.

Launching a spacecraft beyond Earth, such as on a mission to Mars or another planet, is more complicated. Because of the great distances between planets and the limited power of modern rockets, one cannot simply aim a spacecraft directly at its destination and launch it. Instead, trajectories must be carefully calculated to allow a spacecraft to travel to its destination given the limited amount of rocket power available. A common way to do this is to use a Hohmann transfer orbit, a type of orbit that minimizes the amount of propellant needed to send a spacecraft to its destination. A Hohmann transfer orbit is an elliptical orbit with its perihelion at Earth and aphelion at the destination planet (or the reverse if traveling towards the Sun). If launched at the proper time a spacecraft will spend only half an orbit in a Hohmann orbit, catching up with the destination world at the opposite point of its orbit from Earth. To do this, the spacecraft much be launched during a relatively short launch window. For a mission to Mars, such launch windows are available every twenty-six months, for only a couple months at a time.

Even a Hohmann orbit, however, may require more energy than a rocket can provide. Another technique, known as gravity assist, can allow spacecraft to reach more distant destinations by taking advantage of the gravity of other worlds. A spacecraft is launched on a Hohmann trajectory toward an intermediate destination, usually another planet. The spacecraft flies by this planet, gaining velocity by taking, though gravitational interaction, an infinitesimally small amount of the planet's angular momentum . This added velocity allows the spacecraft to continue on to its destination. Gravity assists allowed the Voyager 2 spacecraft, launched from Earth with only enough velocity to reach Jupiter, to travel on to Saturn, Uranus, and Neptune. Gravity assist flybys of Venus, Earth, and Jupiter will also allow the Cassini spacecraft to reach Saturn in 2004.

see also Orbits(volume 2).

Jeff Foust

Bibliography

Wertz, James R., and Wiley J. Larson, eds. Space Mission Analysis and Design. Dordrecht, Netherlands: Kluwer, 1991.

Internet Resources

Basics of Space Flight. NASA Jet Propulsion Laboratory, California Institute of Technology. <http://www.jpl.nasa.gov/basics/>.