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Gravity Assists/Flybys A Quick Gravity Assist Primer

Gravity Assists/Flybys A Quick Gravity Assist Primer

The "gravity assist" concept has proven to be a fundamental technique to help in exploring our "back yard" -- the solar system. The technique has also been employed to rescue an Earth-orbiting communication satellite whose launch vehicle failed to place it in its intended orbit.

A Little History:

Several robotic spacecraft have taken advantage of the "gravity assist" technique to reach their targets of exploration in distant areas of the solar system. For example, Voyager 2 launched in August 1977 and flew by Jupiter, using "gravity assist" for a trajectory boost to Saturn. Voyager 1 launched the following month and did the same (reaching Jupiter before Voyager 2 did). Voyager 2 then obtained an assist from Saturn and another one later from Uranus, climbing all the way to Neptune and beyond. Galileo used "gravity assist" to get one boost from Venus and two from Earth, while orbiting the Sun en route to Jupiter, its final destination. The Cassini-Huygens spacecraft took two "assists" from Venus, one from Earth, and another from Jupiter to gain enough momentum to reach Saturn.

The "gravity assist" flyby technique can add or subtract momentum to increase or decrease the energy of a spacecraft's orbit. Generally it has been used in solar orbit, to increase a spacecraft's speed and propel it outward in the solar system, much farther away from the Sun than its launch vehicle would have been capable of doing. A flyby can also decrease a spacecraft's orbital momentum, such as in the case of Galileo, where the spacecraft used a "gravity assist" flyby in front of Jupiter's largest moon, Io. In this way, it was possible for Galileo to decrease its energy and mass of rocket propellant needed to insert into Jupiter's orbit. Comets and other bodies in solar orbit naturally experience orbital changes as they happen to pass close by to a planet or moon.

The two Voyager spacecraft provide a classic example of utilizing gravity assist flybys to reach their destinations. They were launched aboard a Titan-III/Centaur, with destinations of Saturn and beyond. But their launch vehicles could provide only enough energy to get them to Jupiter (halfway out to Saturn). Had Jupiter not been present, and had the two spacecraft not encountered the giant gas planet, they would have remained in solar orbit indefinitely, farthest from the sun (known as aphelion) of Jupiter's orbital distance (5 AU or 750,000,000 km). Conversely, the spacecraft would have been closest to the sun (known as perihelion) at Earth's orbital distance (1 AU or 150,000,000 km).

The two Voyager launch times were planned so that Jupiter would coast by at just the right time. Therefore, they were influenced by Jupiter's gravitational pull and began falling toward it. Fortunately, their speeds were controlled by careful positioning of how close they came to Jupiter's orbit without impacting the planet. As the two Voyager spacecraft climbed "up" away from Jupiter, they slowed down again with respect to the gas giant, eventually reaching the same speed they had on their way in.

How It Works

From Jupiter's point of view, the situation is similar to a bicyclist speeding up going downhill into a valley, then slowing down again on the uphill part of the road.

Gravity Assist Figure 1

In the diagram on the right, the situation is described in two dimensions. One can see the magnitude and direction of the spacecraft's velocity on its way toward Jupiter in the lower right corner of the diagram. In the upper left corner, the accelerating force of Jupiter's gravitation has made a significant change in the direction of the spacecraft's velocity, but not in its magnitude. (These represent velocity at "infinity," from Jupiter, that is, before and after being noticeably changed by Jupiter's presence.) Near the middle of the diagram, the long arrow shows that there's a significant, but temporary, increase in the magnitude (speed).

To look at the same phenomenon in terms of a cyclist, "V-in" shows the cyclist approaching a downhill grade into a canyon. "V-out" shows that the cyclist slowed down again at the top of the ensuing uphill grade. Indeed, after negotiating the canyon, the cyclist's direction has changed, but in the end the cyclist has not increased or decreased the speed of the bicycle.

Gravity Assist Figure 2

The planet's motion is one key. A gravity assist with Jupiter involves not a stationary planet as illustrated above, but a planet with enormous angular momentum as it revolves around the Sun. In the diagram on the left, Jupiter's motion along its solar orbit has been simply illustrated with a red-colored vector. The spacecraft acquires this vector, or a significant portion of it, during its interaction with Jupiter. The red vector is added to "V-in" and "V-out." The result shows how the spacecraft's velocity, relative to the Sun, gets an adequate boost from Jupiter.

A concept called "trajectory bending" is the other key. Notice how rotation of the vector from "V-in" to "V-out" (the bending of the spacecraft's path by the planet's gravity) helps increase the result. The spacecraft is a physical mass, so it has its own gravitation. That's how the spacecraft can tug on Jupiter and actually decrease the planet's orbital momentum by a tiny amount. In exchange, the spacecraft acquires a significant amount of momentum from Jupiter, compared to the momentum the spacecraft already had.

In the analogy of tossing a ping-pong ball into an electric fan, the ball would take energy from the fan blade, and we can presume it would bounce off at a speed greater than it had coming in. In this case, the ball interacts with the fan blade directly rather than gravitationally, and it slows the fan slightly as it hits. (If the fan's motor were on, the blade's lost momentum would instantly be replaced, which of course is not true in the case of a freely orbiting planet.)

The Slingshot Myth

Individuals have often compared gravity assist with the effects of a slingshot. But in reality, gravity assist is, in terms of physics, a different example. Using a slingshot, a person would sling a projectile around a few times, stronger and better aimed each time, before letting it go. At that point, the projectile's centrifugal force becomes the same as its propulsion force. On the other hand, using a gravity assist, a spacecraft comes up and steals some angular momentum during a single flyby of a planet in motion, removing momentum from that planet. Gravity assist is really much more like a ping-pong ball hitting the revolving blade of a ceiling fan than it is like a slingshot.