Gravity’s Helping Hand

Apollo 13 was crippled. Two hundred thousand miles from Earth, an oxygen tank had exploded. Damage to the Command Mod­ule was so extensive that the crew of three retreated to the Lunar Module, which they then had to use as a “lifeboat” to return home. Flight Director Gene Kranz aborted the Moon landing and consid­ered the options. The simplest would have been to use the Com­mand Module engines to reverse its direction and head for home, but it was unclear if the engines could be used safely, and Apollo 13 was already in the grip of the Moon’s gravity. So instead, Kranz authorized use of the Lunar Module engines to steer a course that would take the spacecraft behind the Moon and get a gravitational “assist” from the Moon that would send it on the correct trajec­tory for an Earth landing. It was a gutsy call. The world waited tensely as the spacecraft got a helping hand from gravity to bring the astronauts home safely.6

Traveling in the Solar System is a tussle with gravity, every as­pect of which affects the amount of fuel required for a mission and so also its cost. The initial problem is leaving Earth’s gravity. This is accomplished in two steps: first, by a large, expendable chemical rocket that can get the spacecraft into orbit, and then is jettisoned; second, by rockets onboard the spacecraft which give it the extra 40 percent of velocity needed to escape the Earth’s pull. The es­cape velocity of the Earth is 11.2 kilometers per second, or 25,000 mph. Once achieved, the spacecraft is in the Sun’s grip. Going to Venus or Mercury seems like the easy choice since the spacecraft can swoon into the Sun’s gravity, which will pull it inward. But the problem emerges when the destination is reached. How do you slow down enough to carefully study or land on your target? Going to Mars and the outer planets means swimming against the tide of the Sun’s gravity. The Sun is remote but extremely massive. So having left the Earth, it takes an extra 12.4 kilometers per sec­ond to reach Jupiter and an extra 17.3 kilometers per second to reach Saturn. Compared to what it took to leave the Earth, that’s a similar amount of extra energy to get to Jupiter and twice as much extra energy to reach Saturn. Leaving the Solar System entirely

requires a velocity of 42.1 kilometers per second, or a whopping 94,000 mph. Where is all this energy going to come from?

The answer to both questions lies in gravitational assist. Rus­sian theorists Yuri Kondratyuk and Friedrich Zander pioneered the idea in the early twentieth century, and American Michael Mi – novitch added important refinements later.7 Gravity assist was first used by the Russians to let Luna 3 photograph the far side of the Moon in 1959. NASA reprised the maneuver in 1970 to rescue Apollo 13. Here’s how it works. Imagine standing beside a railroad track as a train approaches. You throw a tennis ball at the front of the train and it comes back in your direction at a higher speed because the train transfers some energy to the ball. Similarly, if the train was traveling away from you and you threw the ball, it would come back more slowly because the train took away some of the ball’s energy. Notice that energy doesn’t appear or disappear mysteriously. When the train is coming toward you, hitting it with the ball actually slows it down, but by an incredibly tiny amount because it’s so massive. When the train is going away from you, hitting it with the ball speeds it up by a tiny amount. In the case of gravity, there’s no physical contact as the force operates through a vacuum. When a spacecraft approaches a slower moving planet from behind, the spacecraft slows down by transferring some en­ergy to the planet. Conversely, when a faster-moving planet ap­proaches a spacecraft from behind, the spacecraft speeds up by gaining some energy from the planet. The idea works with moons as well as planets.8

Pioneer 10 was the first NASA spacecraft to benefit from gravity assist, using an encounter with Jupiter in 1973 to double its speed and send it someday out of the Solar System. Pioneer 11 followed suit a year later. Also in 1974, Mariner 10 passed close by Venus on its way to exploring Mercury. More recently, the MESSENGER probe needed one flyby of Earth, two flybys of Venus, and three flybys of Mercury to lose enough energy to be captured into an orbit of the innermost planet in 2011. For probes heading into the outer Solar System, it’s worth going out of your way to get a boost from gravity. Galileo and Cassini both took inward detours to Venus to get a “kick” that helped them explore the gas giants. Energy truly is conserved in this gravitational ballet. When MES-

SENGER used Mercury to slow down and go into an orbit, it gave the planet some energy and nudged it a tiny bit farther from the Sun. And when Pioneer “robbed” Jupiter of some of its energy, it pushed the giant planet very slightly closer to the Sun.

The two Voyagers launched from Cape Canaveral in Florida in the summer of 1977. Their Titan III/Centaur launch vehicle only provided enough energy to get to the distance of Jupiter. Without Jupiter’s help the spacecraft would have remained in elliptical or­bits that never got closer to the Sun than Earth and never got far­ther from the Sun than Jupiter. But NASA engineers had planned for Jupiter to be coasting by at the right time to give each of the spacecraft a boost. Although Voyager 1 left second, it took a faster and more direct route that got it to Jupiter first, and then Saturn, but at the cost of not visiting the outermost planets. It could have visited Pluto, but this possibility was sacrificed for a close look at Titan. In 1998, Voyager 1 overtook the slower moving Pioneer 10 to become the most distant human artifact. Voyager 2 took a more circuitous route through the Solar System, flying by each of the four gas giants and gaining a modest gravity boost from each encounter (figure 4.1).9 The Voyagers were originally con­ceived to take advantage of a once-i n-176-year opportunity: the near-perfect alignment of all four gas giants and Pluto. Aerospace engineer Gary Flandro pushed for NASA to take advantage of the alignment with a planetary “Grand Tour,” but the vision was com­promised by budget cuts so the Voyager executed a scaled-back version of the concept.