This sort of maneuver is often used by interplanetary probes. Encounters with the Moon have also been used, for sending spacecraft towards the Lagrangian L1 point or the L2 point in the tail, for modifying missions (such as that of Geotail) and on December 22, 1983 for sending ISEE-3 away from Earth towards Comet Giacobini-Zinner (the figure above describes its orbit, which includes several encounters with the Moon, on the dates given). Even encounters with the Earth itself have been used this way, by the space probe Galileo now orbiting Jupiter: the probe first went to Venus, then came back to swing by Earth. All this looks like a cosmic game of billiards, except that the "cue ball," the satellite making the encounters, carries its own small rocket engine, to correct its course as needed and thus make complex shots possible.
The first use of this maneuver was by Mariner 10 launched in 1973 towards Venus, which used that planet's gravity to extend its own orbit to the planet Mercury. The probe Ulysses used an encounter with Jupiter in order to fling itself out of the ecliptic, into an orbit passing above both poles of the Sun. And NASA's "solar probe," intended to come within 4 solar radii of the center of the Sun, may use a tight "hairpin" trajectory around Jupiter as well.
One vocal proponent of using gravity assist maneuvers for economical flights between Earth and Mars has been the astronaut Buz Aldrin. His ideas are described in the article "A Bus Between the Planets" by James Oberg and Buzz Aldrin, p. 58-60, "Scientific American," March 2000.
An interesting parallel exists between Planetary swing-by maneuvers and the operation of the Pelton water turbine. More on this in section #35a, Planetary Swing-by and the Pelton Turbine.
...And This Just In
Some correction to Newton's equations of motion nay exist, and just possibly explaining some baffling observations, e.g those attributed to "dark energy" or to "dark mass." A study by John Anderson and co-workers at NASA's Jet Propulsion Lab in Pasadena California has analyzed gravity-assist maneuvers by past spacecraft, and uncovered subtle discrepancies (as described in "Wanted: Einstein Jr." in The Economist of 8 March 2008, to appear soon in Physical Review Letters). The difference is extremely small, but since many space probes are tracked a long time after any "gravity assist" encounter, their results accumulate.
What Anderson and his crew uncovered was a tiny extra velocity, of the order of 4 millimeters per second. Its significance is unknown, but it comes in addition to another discrepancy known for some time, in the push received by the Pioneer 10 and 11 spacecraft, tracked since the 1970s. Keep posted!
To the Stars
Close encounters with attracting planets have another use: the effect of any rocket thrust applied at closest approach is greatly amplified. A proposed "Profile" mission to the Earth's magnetosphere calls for a dozen small satellites placed initially aboard a "mother ship" in a long elliptical orbit. At each closest approach ("perigee") one satellite is tossed out, at no more speed than that of a runner in a footrace, yet that boost is enough, by the next closest approach, to make it lag by one hour. The next satellite is then tossed out, and so on, one at each closest approach. In the end all satellites are strung out one hour apart in the new orbit (drawing on right), which differs slightly from the orbit of the mother ship. A rather gentle push does it all, but it must be delivered at the right place.
Some day in the far future humanity will probably want to send robot explorers to the distant stars, journeys that may require many thousands of years. Long ago it was proposed that a good way to achieve the required speed would be to first pass close to the Sun, and at the closest approach fire a rocket. Even a modest increase in speed near the Sun then translates to a great increase in the ultimate velocity far away.
Unfortunately, this requires getting rather close to the Sun, and the space probe is likely to melt. A more reasonable start for a mission to a star may be from a comet, because the trajectories of comets already extend to the edge of the solar system, and the ice found on them may provide hydrogen and oxygen for fueling rocket motors.
In this manner the stars nearest to Earth might be reached. To reach more distant parts of the galaxy, however, may require close encounters like those proposed with the Sun. Dwarf stars exist which are as compact as Earth and as massive as the Sun, and perhaps some can be located that are burned out, dark and cold. If so, they would be a perfect target for such a maneuver. All that is now just pure fantasy: but humanity has the time, its venture into space is just beginning.
Added note: According to recent surveys, dim dwarf stars are surprisingly abundant in the Sun's neighborhood, at least 60% of the total count. See Science, 11 June 2004, p. 1587.
"The Art of the Orbit" by Gary Taubes, Science, p. 620-2. vol 283, 29 January 1999. A review of unusual orbits for solar-system exploration.
"The Starflight Handbook" (subtitle: "A Pioneer's Guide to Interstellar Travel"), by Eugene F. Mallove and Gregory L. Matloff, John Wiley & Sons, 1989.
"Voyager 2" is currently on its way out of the solar system. On the off-chance that some day in the distant future, an alien civilization might find it, a message was sent with it. See here for details
Questions from Users:
Rebounding ping-pong balls
*** Could Earth capture a second moon?.
Circumnavigation of the Sun
Fantasy spaceflight vs. reality
Flying to other planets