Rendezvous
Rendezvous is the procedure by which space vehicles in differing flight paths and orbits can be placed into the same orbital space, with relative zero velocity, at a preselected location and time. Various types of rendezvous maneuvers have been developed, but all depend on orbital mechanics. Fundamentally, a satellite in orbit moves in an elliptical path created by the gravitational force of a celestial body such as a planet. The speed of the satellite is inversely proportional to the square root of the radius of the orbit (or more strictly the semimajor axis of the orbit). This means that larger orbits have slower speeds than smaller orbits. For example, a satellite orbiting 8,000 kilometers (4,960 miles) from the center of Earth (about 1,500 kilometers [930 miles] above the surface) moves twice as fast as a satellite in an orbit with a radius of 32,000 kilometers (19,840 miles; about 25,500 kilometers [15,810 miles] above the surface.)
The fact that lower orbits are faster than higher orbits has important implications for rendezvous maneuvers. Imagine two satellites in the same orbit but separated by some distance. In order for the trailing satellite to rendezvous with the leading satellite, it must fire its engines toward the leading satellite. This drops the trailing satellite into a lower and faster orbit, so that it catches up to the leading satellite. Once the trailing satellite has nearly caught up, it fires its engines away from the leading satellite to achieve the same orbit again. Of course, rendezvousing is more complicated if the two satellites are not in the same orbital plane; that is, if they do not orbit at the same angle to the equator. In such cases, one satellite must fire its engines at an angle to its line of flight to match the orbital plane of the satellite it is chasing. Plane changes are the most fuel-expensive orbit adjustments that can be made.
The Launch Window
Typically, a satellite on the ground must be launched within a certain period of time—called a "launch window"—in order to be correctly positioned to rendezvous with another satellite. The launch window is the time or set of times that a launch can occur and still meet mission objectives and stay within safety guidelines. Essentially, the launch window is defined by the position of an orbiting satellite relative to the launch site of the satellite set to rendezvous with it. To help understand this relationship, visualize an imaginary line on the ground that traces the orbital motion of a satellite—its so-called ground track. The ground track of all low-altitude, easterly launched satellites looks like a sine wave. The wave, however, is in a different place on the map on each successive trace, mainly because Earth rotates. There is also some rotation of the orbital plane about Earth's spin axis that causes the ground track to move because Earth is not a perfect sphere.
The space shuttle Atlantis docked to Russia's Mir space station. The techniques allowing space vehicles to rendezvous and dock were based on theories developed by scientists, engineers, and astronauts working together.Eventually, however, the ground track of an orbiting satellite will trace a path directly over the launch site. This is the moment when a spacecraft on the ground must be launched in order to rendezvous with the satellite in orbit. Of course, some passes are better than others. The closer the ground track comes to the launch site the more efficient the launch will be. If launch occurs a couple of minutes early or late or if the satellite does not go directly over the launch site, it is still possible to achieve a rendezvous, but this requires changing the orbital plane and using a significant amount of fuel. That is why the space shuttle has only a five-minute launch window to rendezvous with the International Space Station. The shuttle has only a limited supply of fuel to use in aligning the plane.
Pioneering Orbital Rendezvous
It was recognized very early that rendezvous and docking between space vehicles were essential for a trip to the Moon. Gemini flights provided the first experience in the tricky business of rendezvousing two craft in space with the minimum expenditure of fuel. The first rendezvous between twopiloted spacecraft occurred in December 1965 when Gemini 6 lifted off and approached Gemini 7, which was already in orbit. Later, during the Apollo program, the Lunar Module lifted off from the lunar surface and rendezvoused with an orbiting Command Module. Orbital rendezvous techniques were based on theories developed by scientists, engineers, and astronauts working together. Edwin "Buzz" Aldrin, Apollo 11 Lunar Module pilot, did his doctoral thesis on guidance for piloted orbital rendezvous. Aldrin's procedures were tested and refined during the Apollo flights.
Guidance and Control Systems (Volume 3);; Navigation (Volume 3);; Orbits (Volume 2).
Bibliography
Compton, William D. Where No Man Has Gone Before: A History of Apollo Lunar Exploration Missions. Washington, DC: National Aeronautics and Space Administration, 1989.
Cortright, Edgar M., ed. Apollo Expeditions to the Moon. Washington, DC: National Aeronautics and Space Administration, 1975.
Dewaard, E. John, and Nancy Dewaard. History of NASA: America's Voyage to the Stars. New York: Exeter Books, 1984.
Lewis, Richard S. Appointment on the Moon. New York: Viking Press, 1968.
Internet Resources
Apollo Rendezvous Docking Simulator. NASA Langley Research Center. <http://lisarwww.larc.nasa.gov/A BSTRACTS/EL-2000-00439.html>.
Launch Windows. NASA Marshall Space Flight Center. <http://liftoff.msfc.nasa.gov/ac ademy/rocket_sci/launch/launch_window.h tml>.
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