Gravity Assists

[arkie87]

How exactly do gravity assists work? What's confusing me is this:

Consider a stationary object in space. Along comes a wild planet and zips by it, just barely missing it. All the kinetic energy/velocity the object gains by falling towards the planet should be lost as the planet zips away, since gravity is a conservative force.

What am i missing?

[Dkmdlb]

You're missing that the planet is orbiting the sun. The object getting a gravity assist gains velocity relative to the sun as it is pulled along in the orbit by the planet.

[Jonboy]

As a probe or other spacecraft approaches a planet, it begins to speed up as it is pulled by the planet's gravity. As it "zips" past the planet and moves away, it again slows down. However, the planet is moving in relation to the Sun, and as the probe flies by the planet, some of that momentum and kinetic energy is transferred to the probe. In other words, the planet pulls the probe along for a sjort time in its orbit around the sun, giving it a boost in speed relative to the sun.

The total amount of kinetic energy and momentum is conserved. The planet loses some momentum and kinetic energy. But the effect on the planet is not noticable because of its large mass in relation to the probe.

Edit: Gravity assists can also slow a spacecraft down in relation to the sun. If a boost in velocity is required, the spacecraft will travel alongside the planet in the same direction as the planet's orbit. If a decrease in velocity is required, it will travel in opposite direction of the planet's orbit and the planet will "drag it back" in relation to the sun.

Edited May 21, 2015 by Jonboy

[Guest]

Ok, empty universe, small object (0), heavy object (1) appears on trajectory, that just misses object 0.

I ran a simulation in my mind, and found that small object will get some velocity change, but there is big probability of collision. Actually both object's velocities would change ... but since object 0 have tiny mass, and object 1 is extra heavy ...

[Bill Phil]

You're gaining energy from the SOI of the planet.

[AngelLestat]

[Slam_Jones]

You're gaining energy from the SOI of the planet.

Gaining energy?

The conservation of energy is a fundamental concept of physics along with the conservation of mass and the conservation of momentum. Within some problem domain, the amount of energy remains constant and energy is neither created nor destroyed.

So is the small object siphoning off some of the energy from the larger object? I'm a little confused.

[Jonboy]

Gaining energy?

So is the small object siphoning off some of the energy from the larger object? I'm a little confused.

Yes. The planet transfers some of its kinetic energy to the spacecraft. Since the spacecraft is FAR less massive than the planet, the effects of this kinetic energy transfer are far more noticeable. There is no net change in energy between the planet and the spacecraft, the planet loses as much energy as the spacecraft gains.

[Kerbart]

It's the change of direction. A "slingshot maneuver" doesn't really speed up or down the ship itself (as you're falling towards the gravity well and then away from it in a symmetrical trajectory in reference to that well). But it changes the angle of the orbit you were in before the assist, and that's what makes the difference.

[PakledHostage]

The planet transfers some of its kinetic energy to the spacecraft. Since the spacecraft is FAR less massive than the planet, the effects of this kinetic energy transfer are far more noticeable. There is no net change in energy between the planet and the spacecraft, the planet loses as much energy as the spacecraft gains.

@Slam Jones: Another way to think about Jonboy's response is by the analogy shown in the image below:

The train transfers momentum in the collision with the ball such that, relative to the Sun at "Solar Junction", the ball has been accelerated. Because the train is much more massive than the ball, it is only slowed by a miniscule amount.

Relative observers on the train, the ball approaches and recedes at the same speed (80 mph). From the perspective of an observer on the train, only the ball's direction changes when the ball bounces off the front of the locomotive. However, from the perspective of the Sun sitting at Solar Junction, the ball has been accelerated from 30 mph to 130 mph.

[Slam_Jones]

Yes. The planet transfers some of its kinetic energy to the spacecraft. Since the spacecraft is FAR less massive than the planet, the effects of this kinetic energy transfer are far more noticeable. There is no net change in energy between the planet and the spacecraft, the planet loses as much energy as the spacecraft gains.

@Slam Jones: Another way to think about Jonboy's response is by the analogy shown in the image below:

http://i.stack.imgur.com/8Chpu.jpg

The train transfers momentum in the collision with the ball such that, relative to the Sun at "Solar Junction", the ball has been accelerated. Because the train is much more massive than the ball, it is only slowed by a miniscule amount.

Relative observers on the train, the ball approaches and recedes at the same speed (80 mph). From the perspective of an observer on the train, only the ball's direction changes when the ball bounces off the front of the locomotive. However, from the perspective of the Sun sitting at Solar Junction, the ball has been accelerated from 30 mph to 130 mph.

Awesome, thank you for the explanations! I understand much better now.

+rep for both of you

[arkie87]

@Slam Jones: Another way to think about Jonboy's response is by the analogy shown in the image below:

http://i.stack.imgur.com/8Chpu.jpg

The train transfers momentum in the collision with the ball such that, relative to the Sun at "Solar Junction", the ball has been accelerated. Because the train is much more massive than the ball, it is only slowed by a miniscule amount.

Relative observers on the train, the ball approaches and recedes at the same speed (80 mph). From the perspective of an observer on the train, only the ball's direction changes when the ball bounces off the front of the locomotive. However, from the perspective of the Sun sitting at Solar Junction, the ball has been accelerated from 30 mph to 130 mph.

Thanks for the answer/analogy! I'm still digesting the answer...

In the example i gave, where the ball/object is initially moving at 0 mph relative to the sun and the planet/train is coming in at 50 mph, what will happen exactly? The ball will slingshot around up to 50 mph so it will have 50 mph relative to the planet/train, and 100 mph relative to the sun?

- - - Updated - - -

@Slam Jones: Another way to think about Jonboy's response is by the analogy shown in the image below:

http://i.stack.imgur.com/8Chpu.jpg

The train transfers momentum in the collision with the ball such that, relative to the Sun at "Solar Junction", the ball has been accelerated. Because the train is much more massive than the ball, it is only slowed by a miniscule amount.

Relative observers on the train, the ball approaches and recedes at the same speed (80 mph). From the perspective of an observer on the train, only the ball's direction changes when the ball bounces off the front of the locomotive. However, from the perspective of the Sun sitting at Solar Junction, the ball has been accelerated from 30 mph to 130 mph.

I guess what's going on is "slingshots" are like perfectly elastic collisions (and why shouldnt they be? they are conservative and there is no friction in space). Any slingshotted object will gain all the momentum of the heavier one, plus retain its initial momentum...

I think the angle around which the slingshot occurs also matters. If there is no curling around the planet, the slingshot wouldnt do anything, right?

I guess basically: at the border of the SoI, your velocity magnitude will be the same relative to the planet (since gravity is conservative); however, the gravity assist will allow you to change the direction of that velocity vector

Edited May 21, 2015 by arkie87

[Mr Shifty]

In the example i gave, where the ball/object is initially moving at 0 mph relative to the sun and the planet/train is coming in at 50 mph, what will happen exactly? The ball will slingshot around up to 50 mph so it will have 50 mph relative to the planet/train, and 100 mph relative to the sun?

Can't really happen because if an object is at 0 mph relative to the Sun, it will immediately start accelerating directly toward the sun because of the Sun's gravity.

I guess what's going on is "slingshots" are like perfectly elastic collisions (and why shouldnt they be? they are conservative and there is no friction in space). Any slingshotted object will gain all the momentum of the heavier one, plus retain its initial momentum...

They're not really like collisions; the train photo was an analogy (and the photo is misleading because the ball wouldn't be thrown toward the train, but in the same direction as the train. In a real orbital situation, crossing retrograde orbits would have far too much relative velocity for the planet to affect the spacecraft at any distance.) The situation is determined by 1) the relative velocity of the spacecraft and planet, 2) how close the spacecraft will pass to the planet, 3) the mass of the planet and 4) the initial angle of the spacecraft's trajectory relative to the planet's orbit around its primary. Roughly, the faster a vessel is going, the less influence a planet can exert. The closer it passes to the planet and the more massive the planet, the more influence the planet exerts. And the closer a vessel approaches the planet from directly ahead, the more the planet can change its resulting sun-relative velocity. The maximum velocity change occurs when a vessel enters a planet's SOI from directly ahead, loops around the planet in a 180°, and leaves its SOI directly ahead. It gains 2x the difference between their sun-relative velocities. (This is what happens in the train image, where the train is going 50 mph and the ball is going -30 mph, for a relative difference of 80 mph. 2x80 mph=160 mph, which when added to -30 mph gives 130 mph.)

Edited May 21, 2015 by Mr Shifty

[arkie87]

Can't really happen because if an object is at 0 mph relative to the Sun, it will immediately start accelerating directly toward the sun because of the Sun's gravity.

That is true, but its a theoretical example, and theoretically, if the planet was closer than the sun (or far enough away from the sun), it could start falling towards the planet first

They're not really like collisions; the train photo was an analogy (and the photo is misleading because the ball wouldn't be thrown toward the train, but in the same direction as the train. In a real orbital situation, crossing retrograde orbits would have far too much relative velocity for the planet to affect the spacecraft at any distance.) The situation is determined by 1) the relative velocity of the spacecraft and planet, 2) how close the spacecraft will pass to the planet, 3) the mass of the planet and 4) the initial angle of the spacecraft's trajectory relative to the planet's orbit around its primary. Roughly, the faster a vessel is going, the less influence a planet can exert. The closer it passes to the planet and the more massive the planet, the more influence the planet exerts. And the closer a vessel approaches the planet from directly ahead, the more the planet can change its resulting sun-relative velocity. The maximum velocity change occurs when a vessel enters a planet's SOI from directly ahead, loops around the planet in a 180°, and leaves its SOI directly ahead. It gains 2x the difference between their sun-relative velocities. (This is what happens in the train image, where the train is going 50 mph and the ball is going -30 mph, for a relative difference of 80 mph. 2x80 mph=160 mph, which when added to -30 mph gives 130 mph.)

Yeah, you have to control how much you arc around the planet (by controlling periapsis), and if your velocity is too high, you wont be able to change your path very much at all. But the key thing is your velocity relative to the planet will not change upon entering and exiting the SoI.

On that note, is it possible to change it 180°? What is the maximum?

[Jonboy]

Thanks for the answer/analogy! I'm still digesting the answer...

In the example i gave, where the ball/object is initially moving at 0 mph relative to the sun and the planet/train is coming in at 50 mph, what will happen exactly? The ball will slingshot around up to 50 mph so it will have 50 mph relative to the planet/train, and 100 mph relative to the sun?

- - - Updated - - -

I guess what's going on is "slingshots" are like perfectly elastic collisions (and why shouldnt they be? they are conservative and there is no friction in space). Any slingshotted object will gain all the momentum of the heavier one, plus retain its initial momentum...

I think the angle around which the slingshot occurs also matters. If there is no curling around the planet, the slingshot wouldnt do anything, right?

I guess basically: at the border of the SoI, your velocity magnitude will be the same relative to the planet (since gravity is conservative); however, the gravity assist will allow you to change the direction of that velocity vector

Although the objects technically do not collide, you can think of them as colliding if it helps you. The gravity assist is essentially a perfectly elastic collision, just as noted. Just like in a perfectly elastic collision, so conservation of energy/momentum applies.

- - - Updated - - -

It's the change of direction. A "slingshot maneuver" doesn't really speed up or down the ship itself (as you're falling towards the gravity well and then away from it in a symmetrical trajectory in reference to that well). But it changes the angle of the orbit you were in before the assist, and that's what makes the difference.

It can in fact change your overall velocity relative to the sun. You are "stealing" kinetic energy from the planet as you swing alongside it (and the planet loses an equal amount of kinetic energy), and this increases your velocity relative to the sun.

[arkie87]

It can in fact change your overall velocity relative to the sun. You are "stealing" kinetic energy from the planet as you swing alongside it (and the planet loses an equal amount of kinetic energy), and this increases your velocity relative to the sun.

I think you are saying the same thing but from different perspectives.

Since your velocity magnitude (relative to the planet) at SoI crossing is the same (since its conservative), all it does is re-direct your velocity relative to the sun since the planet deflects your path, which changes your orbit of the Sun.

Edited May 21, 2015 by arkie87

[Mr Shifty]

On that note, is it possible to change it 180°? What is the maximum?

Yeah, it's possible. You have to be on a parabolic trajectory, which means you have to be going exactly escape velocity. So for instance, for Eve:

r_SOI =85,109,365 m

r_Eve = 700,000 m

h_atm = 90,000 m

µ = 8.1717302×10¹² m³/s²

Escape velocity at Eve's SOI edge is:

v_esc = (2*µ/r)^1/2 = (2 * 8.1717302x10¹² m³/s² / (85,109,365 m) )^1/2 = 438 m/s

So you'd have to be going that speed relative to Eve when you encounter it, and also encounter it from directly ahead in its orbit. You can find the relevant math here.

[PakledHostage]

Yeah, it's possible. You have to be on a parabolic trajectory, which means you have to be going exactly escape velocity.

Interestingly, in KSP's physics you can even be on an elliptical trajectory that has its Ap outside the body that you're orbiting's SOI. That's almost certainly also true in real-world orbital mechanics because you don't need to reach a point infinitely far from one celestial body before another celestial body's gravity dominates.

A couple of years ago, I hosted a challenge to reach the Mun's surface from a 100 km orbit about Kerbin using the minimum delta-V possible. I recall that Stochasty won by building a lander that could make a roll-on landing at high speed (one restriction of the challenge was that you had to land in one piece). I got close to Stochasty's result by using multiple munar gravitational assists to match orbits with the Mun before making my final approach. On my best attempt, I entered the Mun's SOI on an elliptical orbit. Unfortunately, the thread was lost during the great forum derp in April 2013, so I can't link to it here.

Edited May 21, 2015 by PakledHostage

[Mr Shifty]

Although the objects technically do not collide, you can think of them as colliding if it helps you. The gravity assist is essentially a perfectly elastic collision, just as noted. Just like in a perfectly elastic collision, so conservation of energy/momentum applies.

In a perfectly elastic collision of an object against a wall, say, the angle the object bounces off the wall is determined by drawing a line normal to the wall at the collision point and reflecting the object's approach vector around that line. (Another way of saying this is to say that the velocity of the object tangent to the wall doesn't change, while the velocity normal to the wall reverses direction.) In a gravity assist, the angle is determined only by the initial velocity of the vessel relative to the planet at a given distance, not by the angle of approach. It only functions like an elastic collision in a very limited set of cases.

[magnemoe]

It's the change of direction. A "slingshot maneuver" doesn't really speed up or down the ship itself (as you're falling towards the gravity well and then away from it in a symmetrical trajectory in reference to that well). But it changes the angle of the orbit you were in before the assist, and that's what makes the difference.

This, think of grabing an rope and swing around.

It can still be very useful and save loads of fuel. Last time I used it I an Jool aerobrake to get into Jool orbit, then I used two Laythe flyby and an Tylo flyby to raise my Pe, this also lowered my Ap who was far to high, this set me on an nice orbit from Val to outside Tylo who was nice to get an Pol intercept for 200 m/s