Sling-shotting Energy

[Oddt]

Hey everyone,

 

I've heard that with many mechanical devices that we place into space, we first loop them around the Earth to build up velocity, allowing for them to 'rocket' out of our gravitational pull and to gain some momentum. I've also heard that light curves around gravity; since light is a form of energy, I was wondering if energy is uniformly affected by gravity as well. If so, would it be possible to slingshot a minimal amount of energy around, say, a star, and to have it 'recharge' and return to it's point of origin? This is some really sci-fi stuff, I realize, but I'm just curious if it's at all feasible.

 

Thanks,

Oddt

[lemur]

It's interesting to imagine how it would look from the perspective of a pilot doing this. Imagine you used a body without atmosphere, like the moon, so you could come very close to the ground without air-friction. You would basically accelerate toward a planned-point just above the horizon and swoop very close to the ground as you fly by and see the planet disappear behind you (assuming I understand this idea right). It would be a dramatic and exciting way to leave orbit.

Edited May 10, 2011 by lemur

[DrRocket]

Hey everyone,

 

I've heard that with many mechanical devices that we place into space, we first loop them around the Earth to build up velocity, allowing for them to 'rocket' out of our gravitational pull and to gain some momentum. I've also heard that light curves around gravity; since light is a form of energy, I was wondering if energy is uniformly affected by gravity as well. If so, would it be possible to slingshot a minimal amount of energy around, say, a star, and to have it 'recharge' and return to it's point of origin? This is some really sci-fi stuff, I realize, but I'm just curious if it's at all feasible.

 

Thanks,

Oddt

 

Gravity is a conservative force. Any ncrease in velocity that occurs when approaching a body is lost again when departing from it.

 

So, you ask, how do spacecraft take advantage of a "slingshot effect" ?

 

The answer is that the "slingshot effect" takes advantage of the velocity, hence kinetic energy, associated with the orbit of a planet around the sun. The spacecraft approaches the planet from "behind" and gains some energy from the planet's speed, using gravity as a "rope". The key is that one is not considering the planet in isolation, but rather in a heliocentric coordinate system.

 

While light is affected by a strong gravitational field and is red-shifted when climbing out, and blue-shifted when falling in, the effects compensate.

[Oddt]

Thanks Lemur! Haha, yeah it would be pretty exhilarating

Gravity is a conservative force. Any ncrease in velocity that occurs when approaching a body is lost again when departing from it.

 

 

And hello again, DrRocket- you just answered a different one of my posts (quite well, at that). Now, this point you've made is fascinating. I wasn't aware of this, but upon reading it the notion does make total sense. You mentioned a rope; does the same temporary increase in velocity apply to, say, centrifugal force situations? Thanks

[DrRocket]

. I wasn't aware of this, but upon reading it the notion does make total sense. You mentioned a rope; does the same temporary increase in velocity apply to, say, centrifugal force situations? Thanks

 

I'm not quite sure what you have in mind, but it sounds like an old sling (David and Goliath kind) and yes, it works there.

[Airbrush]

Gravity is a conservative force. Any increase in velocity that occurs when approaching a body is lost again when departing from it.

 

Not exactly. When Voyager missions were sling-shotted by Jupiter's gravity, the spacecraft took advantage of Jupiter's gravity to pull it faster, but timed it right so speed was not lost when departing Jupiter. Maybe a little velocity was lost when departing Jupiter, but there was a big net gain in speed and thus gain in energy. The trick is to approach from the proper angle and disengage at the right moment. All the outer planets may be used this way sending probes to the outer solar system.

Edited May 12, 2011 by Airbrush

[Spyman]

Not exactly. When Voyager missions were sling-shotted by Jupiter's gravity, the spacecraft took advantage of Jupiter's gravity to pull it faster, but timed it right so speed was not lost when departing Jupiter. Maybe a little velocity was lost when departing Jupiter, but there was a big net gain in speed and thus gain in energy. The trick is to approach from the proper angle and disengage at the right moment. All the outer planets may be used this way sending probes to the outer solar system.

From an external view like from Earth the spacecraft gains momentum from Jupiter, but from an local view on either Jupiter or aboard the spacecraft there is no difference in arriving and departing speed according to conservation laws.

 

Explanation

A gravity assist or slingshot maneuver around a planet changes a spacecraft's velocity relative to the Sun, though the spacecraft's speed relative to the planet on effectively entering and leaving its gravitational field, will remain the same - as it must according to the law of conservation of energy. To a first approximation, from a large distance, the spacecraft appears to have bounced off the planet. Physicists call this an elastic collision even though no actual contact occurs. A slingshot maneuver can therefore be used to change the spaceship's trajectory and speed relative to the Sun viz. its velocity.

 

Suppose that you are a "stationary" observer and that you see: a planet moving left at speed U; a spaceship moving right at speed v. If the spaceship is on the right path, it will pass close to the planet, moving at speed U + v relative to the planet's surface because the planet is moving in the opposite direction at speed U. When the spaceship leaves orbit, it is still moving at U + v relative to the planet's surface but in the opposite direction, to the left; and since the planet is moving left at speed U, the total velocity of the rocket relative to you will be the velocity of the moving planet plus the velocity of the rocket with respect to the planet. So the velocity will be U + ( U + v ), that is 2U + v.

 

Over-simplified example of gravitational slingshot: the spacecraft's velocity changes by up to twice the planet's velocity

 

It might seem that this is oversimplified since the details of the orbit have not been covered, but it turns out that if the spaceship travels in a path which forms a hyperbola, it can leave the planet in the opposite direction without firing its engine, the speed gain at large distance is indeed 2U once it has left the gravity of the planet far behind.

 

This explanation might seem to violate the conservation of energy and momentum, but we have neglected the spacecraft's effects on the planet. The linear momentum gained by the spaceship is equal in magnitude to that lost by the planet, though the planet's enormous mass compared to the spacecraft makes the resulting change in its speed negligibly small. These effects on the planet are so slight (because planets are so much more massive than spacecraft) that they can be ignored in the calculation.

http://en.wikipedia.org/wiki/Gravity_slingshot#Explanation

Edited May 12, 2011 by Spyman

[DrRocket]

Not exactly. When Voyager missions were sling-shotted by Jupiter's gravity, the spacecraft took advantage of Jupiter's gravity to pull it faster, but timed it right so speed was not lost when departing Jupiter. Maybe a little velocity was lost when departing Jupiter, but there was a big net gain in speed and thus gain in energiy. The trick is to approach from the proper angle and disengage at the right moment. All the outer planets may be used this way sending probes to the outer solar system.

 

Yes exactky. But read my entire post rather than an isolared sentence out of context for the explanation as to how this really works.

[Airbrush]

Nice explanation Spyman. Does this mean that when a probe uses Jupiter to gain speed, the probe is using Jupiter's speed in orbit to pull it faster and not Jupiter's gravity?

 

Can you tell us how much percentage increase in speed, relative to the Sun, a probe can gain if using Jupiter to speed up? Would it be possible to use Jupiter, then Saturn, and maybe one or two of the outer giants, one after the other?

[DrRocket]

Nice explanation Spyman. Does this mean that when a probe uses Jupiter to gain speed, the probe is using Jupiter's speed in orbit to pull it faster and not Jupiter's gravity?

 

Can you tell us how much percentage increase in speed, relative to the Sun, a probe can gain if using Jupiter to speed up? Would it be possible to use Jupiter, then Saturn, and maybe one or two of the outer giants, one after the other?

 

http://en.wikipedia....tary_Grand_Tour

 

http://en.wikipedia.org/wiki/Gravitational_slingshot

Edited May 12, 2011 by DrRocket

[Airbrush]

Thanks for the good links DrRocket. It is astonishing to learn that they would sling shot probes around inner planets to throw they towards outer planets, and I suppose around outer planets to get shot towards the inner solar system, or around the sun in a polar orbit.

 

My question for anyone is how much increase in speed can a probe get when getting whipped around Jupiter on the way towards the outer solar system? Like from about 15 miles per second to 20 miles per second? Or double?

Edited May 14, 2011 by Airbrush

[Spyman]

According to Wikipedia Jupiter has an average orbital speed of 13.07 km/s, 1 mile is 1.609 km and since a spacecraft on a trajectory for a gravitational slingshot can gain twice the planets orbital speed, it can increase its speed with 2 × 13.07 / 1.609 = 17 miles per second on each slingshot around Jupiter.