This came from an article on the Stardust spacecraft:
The Stardust spacecraft started the Earth Gravity
Assist (EGA) phase of its mission on November
28, 2000, 48 days from closest approach to
Earth. The final targeting maneuver for Earth
flyby was successfully performed on January 5,
2001. The primary objective of the EGA phase
is to provide Stardust with an energy boost from
flying past the Earth. The boost, which comes
from "sling-shoting" around the Earth, i.e. a
"gravity assist," will increase the spacecraft's
orbital period around the Sun from 2 years to
2-1/2 years and alter its flight path to intercept
Comet P/Wild 2 on January 2, 2004.
I’m a bit mystified by this slingshot effect. If I remember conservation of energy principles correctly, any kinetic energy a body gains entering a field is lost upon leaving. Does this effect have more to do with altering trajectory than providing an “energy boost”? Can any of you physicists provide clarity?
The slingshot boost does work and it does increase the speed of the spacecraft. Energy is conserved because, as the speed of the spacecraft increases the orbital speed of the Earth (or whatever planet you are using) decreases. Of course, the mass of the Earth is much, much larger than the mass of the spacecraft, so the effect on our orbit is negligable.
If the Earth were sitting still (relative to whatever overall system you’re interested in), then the spacecraft would have the same speed coming out that it had going in, and there would be no slingshot effect.
But think of the solar system. The Earth is zipping along around the sun, and if the spacecraft’s path passes just behind it, it will be slung around to a faster speed. As tanstaafl said, the Earth is slowed very slightly, and energy is conserved. Spacecraft frequently use the slingshot effect off different planets to get to where they want to go, since they can just use a small amount of fuel to maneuver into the right position, and get most of the energy “free.”
This site is from Jet Propulsion Labs talking about gravity assists. It is more complexly stated than as described by tanstaafl and CurtC, however it says essentially the same thing. It uses the motion of the planet orbiting the Sun to cause the assist, not the gravity of the planet pulling on the spacecraft.
Good link Irishman. If I read it correctly jebert is partially correct in his assessment.
The spacecraft has the same velocity relative to the planet leaving as it did coming in but it has more velocity relative to the sun.
In other words, from the planet’s perspective all of the energy the spaceship gained coming in was lost on its way out. But from the sun’s perspective the spaceship gained the angular momentum of the orbiting planet hence it is moving faster (remember from the planet’s perspective it is standing still and the spaceship is moving but from the sun’s perspective both planet and ship are moving so the ship gains the planet’s orbital velocity).
I’d wondered about that as well. Cool…learned something new today!
In some slingshot scenarios, the spacecraft fires rockets during the manuever. This uses fuel, and may involve dropping off part of the craft (rocket stages). Thus, the craft leaves the gravity well with less mass than it entered with.
The greater mass going in brings a lot of speed, and the lesser mass leaving means the gravity well doesn’t strip off as much as was gained.
This doesn’t really describe a pure gravity-assist, but it is another way they use gravity to help out.
I don’t think dropping mass during the slingshot would allow it to get more speed on the way out. Gravity’s acceleration doesn’t depend on mass. For maneuvering, they’d want the mass to be smaller so they can use less fuel. Maybe this is why they do that.
I disagree that dropping mass won’t effect speed. True, 2 objects with different masses will have the same acceleration due to the force of gravity (Galileo proved that at Pisa), but if you apply energy to an object, then alter it by subtracting mass (without having the subtracted mass take its portion of energy with it, i.e. dropping a stage, but instead fire the thrusters and leave the expended mass with no potential energy), it should travel farther, even disregarding the additional energy provided by the thrust. Wouldn’t that be analogous to a spinning skater reducing their radius, so the speed increases to maintain the angular momentum?
Saltire and fortifier are correct about deep-well burns: You want to burn as much of your fuel as possible (and discard as many stages as possible) as low as possible in a gravity well. Essentially, the effect is that you get to leave some mass behind on or near Earth (little or no energy expenditure), and put the energy you have into your payload and important stuff.
I think the critical matter is not the mass of the vehicle, but the time it spends in each aspect of the fly by. As Chronos noted the maneuver requires firing the rockets at the point of closest approach, when the planetary gravity is having the greatest effect. By increasing the speed relative to the planet at this point in the trajectory, the time spent decelerating is less than the time spent accelerating and the result is a net increase in speed.
By timing a maneuver carefully with respect to the relative final vectors, the planets own orbital speed can be used to increase the first portion of the fly by, and decrease the second portion. In that way the amount of fuel can be much less, and the effect still considerable, for the vehicle, with respect to the rest of the system.
I’m not sure I buy this explanation. If my rocket were starting out outside a planet’s gravity well, and I were doing a slingshot by the planet, I think I’d still want to drop off those extra stages as soon as possible, rather than carry (and spend fuel to accelerate) the extra weight with me to drop deeper in the planets’s gravity well.
Triskadecamus’s explanation makes more sense to me (although I’m still thinking about it).