Ballistic capture is a low energy method for a spacecraft to achieve an orbit around a distant planet or moon. Prior to ballistic capture, spacecraft would use a method called Hohmann transfer orbit, this requires the spacecraft to burn fuel in order to slow down at the distant planet. The requirement to carry fuel across space adds to the cost and complexity of the craft.
To achieve ballistic capture the spacecraft is placed on a flight path ahead of the target's orbital path. The spacecraft is then captured by the target planet's gravity allowing low power ion thrusters to complete the orbit. Ballistic capture was first used by the Japanese spacecraft Hiten in 1991 as a method to get to the Moon.
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A spacecraft moving at a lower orbital velocity than the target celestial body is inserted into an orbit similar to that of a planet or moon, allowing it to move toward it and gravitationally snag it into orbit with no need for an insertion burn.
Low energy transfer (LET) was proposed in the 80s. The spacecraft is launched into a transfer orbit that places it ahead of the target planet's orbital path. As the planet approaches the spacecraft, the planet's gravity draws the craft into a high circular orbit eliminating the need for an insertion burn. This orbit is a temporary one, eventually the spacecraft would leave it again - but then it uses low power thrusters to get into a lower orbit. It can use the much more efficient ion thrusters at this stage as there is no need for a high level of thrust.
With some target orbits the total fuel is less than for Hohmann transfer. Hohmann transfer is more fuel efficient if an orbit closer to Mars is targeted, but can only be done at particular times. Ballistic capture, on the other hand, can be used at any time.
In 2014, low-energy transfer was proposed as an improved orbital maneuver for future Mars missions. It can be performed anytime, not only once per 26 months as in other maneuvers and does not involve dangerous and expensive (fuel cost) braking. But it takes up to one year, instead of nine months for a Hohmann transfer.