Gravity Boost

[gigaforce90]

So I've been experimenting with gravity boost's lately, namely Duna though Eeloo, and through experimenting my results have been inconclusive

A.

B.

Now my gut and mathematical degree tells me that image A. should raise my orbit but my results haven't been very conclusive Ive also been able to boost my orbit with a B. type flyby but in both instances I've only been able to boost my orbit back to Kerbin and the DeltaV required to get to Duna would have been more than a direct trip from Kerbin.

I guess my two questions are:

1. is this type of maneuver not beneficial by a limitation of the game

2. which encounter is ideal for a gravity assist

Edited May 10, 2013 by gigaforce90

[gigaforce90]

It seems my images didn't show up...

A.

B.

I know they are crude but i hope they are clear enough

Edited May 10, 2013 by gigaforce90

[Nachtengel]

Hai, im an aerospace engineer so i might be able to help you here, first of all, both cases A and B are the same. you are increasing speed with a gravity assist, or swing-by. however, the common misconception here is that your speed on the instruments must increase, and it wont. your speed entering the planet encounter will equal the speed leaving the encounter if no thrusters were burned. gravity assists find no use in standard orbital mechanics within one body systems or systems with one moon. but they find many uses in systems with more bodies. like a solar system. gravity assists are used for interplanetary travel, to conserve time and fuel.

first you need to understand that the speed we are considering here is not the speed of the orbit but the speed relative to the sun. start with a heliocentric reference frame. now, consider that your spacecraft and the planet pull on each other, its not just the planet pulling you, but also you pulling the planet, but the mass of planets is so large its negligible, but the principle is important. the idea is that the velocity vector of the planet and your spacecrafts entering velocity become an added vector Vin (you're in mathematics so i know you know how to add vectors, the arrow method will suffice.) now, the velocity vector of the planet and your spacecraft also form a resultant the moment you reach the escape node. construct the two resultants and observe the difference, in both cases A and B you will find the resultant Vout to be larger. meaning, you have assisted in increasing your speed relative to the sun, and thus are travelling to wherever youre going faster in terms of the solar system.

gravity assists can also be used to slow down your craft if the planet is moving in the opposite direction of your spacecraft. and the manipulation of the encounter vectors Nin and Nout is what determines this, for example, case A is a large increase in velocity relative to the sun, while case B is a much smaller change. and depending on how exact the points i took from your drawing are, case B could also be a negative assist.

regardless the understanding should be that you are trying to manipulate your vector, not your speed. because the resultant of the planets vector and your own will determine where and how fast your interplanetary travel will be. remember according to the planet, no matter the strength of the assist. the velocity on your screen will be the same at encounter point and escape unless any burns were made. so for quick analysis, arbitrary arrow lengths are acceptable, the spacecraft's and the planet's. find your encounter on the map, and work out your velocity vector and the planets and draw them on a sheet of paper for the resultant, if the assist does not benefit your flight, change early to minimize fuel usage. when the desired resultant is reached. enjoy the ride.

[Crown]

Flying as shown in picture A, which means tangential to the planet you want to use to boost, will only barley increase your speed.

The best angle to get the maximum of your planet is different and depending on factors as the planet's characteristics and the spacecraft's speed.

But most visible is it at about 90°:

For deceleration the opposite:

Basically when you want to go faster get "behind" the planet. If you wanna go slower go "ahead" the planet.

[wilt57]

I think I understand the basic concepts of gravity assists, but I'm still learning in practice! How ever, it got me thinking, could I reduce the amount of Delta-V needed to close my orbit if I enter my target planet's SoI on its prograde side? A sort of reverse gravity assist into its own orbit. Or is this really only changing my velocity is regard to the Sun/Kerbol and not in relation to my target planet?

[Crush]

The general rules about gravity assists:

1. Pass in front of a moon (on its orbital path) to lose speed and behind a moon to gain speed.

2. the closer the better

I wrote a tutorial on the wiki: http://wiki.kerbalspaceprogram.com/wiki/Tutorial:_Gravity_Assist

Edited May 10, 2013 by Crush

[Kromey]

I think I understand the basic concepts of gravity assists, but I'm still learning in practice! How ever, it got me thinking, could I reduce the amount of Delta-V needed to close my orbit if I enter my target planet's SoI on its prograde side? A sort of reverse gravity assist into its own orbit. Or is this really only changing my velocity is regard to the Sun/Kerbol and not in relation to my target planet?

Nope.

Let's say that your interplanetary transfer speed is X, relative to Kerbol; your target planet's speed is Y relative to Kerbol. If you approach from the planet's prograde vector, your speed relative to the planet is X+Y, but if you approach from "behind" the planet (it's retrograde vector), your relative speed is X-Y!

In both cases you have to slow down to orbital speeds; as should be obvious, then, it takes less delta-V to slow down from the slower speed. As was noted above by Nachtengel gravity assists only help with your speed relative to other bodies, not the body you're boosting around -- law of conservation of energy tells us energy in equals energy out, so relative to your target body you're going just as fast as you leave as you were when you entered. Gravity boosts work because you're "borrowing" energy from the target body's own orbital velocities, so they do alter your speeds with respect to the body your target body is orbiting (so a planet alters your speed relative to its sun, or a moon relative to its planet).

[Crown]

[...]could I reduce the amount of Delta-V needed to close my orbit if I enter my target planet's SoI on its prograde side? A sort of reverse gravity assist into its own orbit.[...]

I am not sure about this. Apollo did an figure-8 shape around the moon. So I think it's kind of a thing, because they approached the moon on the prograde (-speed) side and left it on the retrograde side (+speed).

[wilt57]

Let's say that your interplanetary transfer speed is X, relative to Kerbol; your target planet's speed is Y relative to Kerbol. If you approach from the planet's prograde vector, your speed relative to the planet is X+Y, but if you approach from "behind" the planet (it's retrograde vector), your relative speed is X-Y!.

I don't think I made myself clear. I'm not talking about a clockwise Kerbol orbit to approach, say Duna. I know that's bad! I'm talking about whether I'm trying to catch Duna from behind, thus having it add its Y to my X, or getting "out in front" of Duna and having it catch up to me, thus subtracting its Y from my X. I'm suspecting it doesn't matter either way. No matter where I enter Duna's SoI, when my orbital speed switches from Kerbol to Duna, my Duna speed will be the same, regardless of whether I had added or subtracted velocity to Kerbol. I'm just a noob so I thought I may have stumble across a way to reduce needed Delta-V, but I suppose the real scientists would have already thought of that! Thanks for your help!

[Kromey]

I don't think I made myself clear. I'm not talking about a clockwise Kerbol orbit to approach, say Duna. I know that's bad! I'm talking about whether I'm trying to catch Duna from behind, thus having it add its Y to my X, or getting "out in front" of Duna and having it catch up to me, thus subtracting its Y from my X. I'm suspecting it doesn't matter either way. No matter where I enter Duna's SoI, when my orbital speed switches from Kerbol to Duna, my Duna speed will be the same, regardless of whether I had added or subtracted velocity to Kerbol. I'm just a noob so I thought I may have stumble across a way to reduce needed Delta-V, but I suppose the real scientists would have already thought of that! Thanks for your help!

No, I think I didn't my myself clear.

Gravity boosting around Duna will neither help nor hurt you achieving orbit around Duna. The direction you approach, however, will -- if you approach from prograde, you will be going a lot faster (relative to Duna) than if you approach from retrograde, because it is the difference between adding or subtracting Duna's velocity from your own. The direction you approach Duna's SOI will always affect your Duna speed.

Gravity boosts only help you relative to the body being orbited by the body you're boosting around. That is, gravity boosting around Duna would help with speed relative to Kerbol (e.g. speeding you up for an encounter with Jool), or gravity boosting around Ike could help with achieving orbit around Duna. Gravity boosting around any body will never help you relative to that body, because you're going just as fast as you leave as when you arrive (relative to that body).

[wilt57]

Ok, I understand what you're saying, for the most part. Essentially, encountering Duna with a vector as similar to Duna's vector around Kerbol will give me the cheapest (in Delta-V) capture I can achieve.

Sorry, I have derailed the OP's thread a bit, but I can bring it back! In this same example of going to Duna, how do I time a gravity assist with Ike? Is it purely luck if Ike is positioned well enough in its orbit or do I have more control over whether I get an encounter with Ike or not? On a similar note, when I use ksp.olex.biz to give me my phase and ejection angles for a trip from Kerbin to Duna, how to I manipulate these to add a Mun or Minmus gravity assist? Conceptually, I understand what's happening. Controlling what's happening, by how much it's gonna happen, and when it's gonna happen is the hard part!

[Nao]

I don't think I made myself clear. I'm not talking about a clockwise Kerbol orbit to approach, say Duna. I know that's bad! I'm talking about whether I'm trying to catch Duna from behind, thus having it add its Y to my X, or getting "out in front" of Duna and having it catch up to me, thus subtracting its Y from my X. I'm suspecting it doesn't matter either way. No matter where I enter Duna's SoI, when my orbital speed switches from Kerbol to Duna, my Duna speed will be the same, regardless of whether I had added or subtracted velocity to Kerbol. I'm just a noob so I thought I may have stumble across a way to reduce needed Delta-V, but I suppose the real scientists would have already thought of that! Thanks for your help!

If you transferring from Kerbin you can only catch Duna from the front (it catches you since it has more Kerbol orbital speed). If you would like to approach Duna from behind you'd need to start from Jool.

And on that note:

The general rules about gravity assists:

1. Pass in front of a moon (on its orbital path) to lose speed and behind a moon to gain speed.

image snip

Nice tutorial! But looking at the picture the "loose speed" path is almost impossible to create. It tries to look like its in Mun SOI but to encounter Mun from behind you need to have more orbital speed (in relation to main body - Kerbin) than it. And while it shows properly how slingshots works it's not applicable to example you are mentioning in the tutorial.

I think it's actually impossible to slow down Kerbin orbit by Mun slingshot if starting orbit around Kerbin have Pe below Mun orbit.

In general, the direction of ship's approach to a body you want to slingshot from is based on main body orbital speed. If you are faster than the slingshot body, you come from behind it, if you are slower you start at the front of it.

For example starting from Kerbin: you can increase your (Kerbol) orbital speed with Duna slingshot or decrease orbital speed with Eve slingshot, but not the other way around.

I'll try to create some pictures for this (as i'm pretty bad with writing on the subject) when I get to my desktop.

Cheers!

[Crush]

I think it's actually impossible to slow down Kerbin orbit by Mun slingshot if starting orbit around Kerbin have Pe below Mun orbit.

It is?

Without the mun encounter, that orbit would be outside of Minmus, as can be seen in the tracking station where gravity assists aren't considered:

[Nao]

It is?

Yeah i messed up. It's not possible to start behind Mun (in that setup) but that doesn't mean there aren't any slowing trajectories from the front. They are kind of hard get in interplanetary space and i never encountered one while trying to do a useful slingshot.

I suspected could be possible but seeing a working example is great. Thanks!

[Temstar]

If you transferring from Kerbin you can only catch Duna from the front (it catches you since it has more Kerbol orbital speed). If you would like to approach Duna from behind you'd need to start from Jool.

That's not true, you can approach either in front or from behind for any planets both superior and inferior, it's a simple matter of arriving at the same point in space slightly earlier vs slightly later, you can easily switch between the two types of encounter with minimal change in delta-V after Kerbin ejection.

For example, here is an approach to Jool from Kerbin from behind. Jool's massive gravity then pulls the spacecraft forward for a huge increase in prograde velocity, hence a gravity assist:

[Nao]

That's not true, you can approach either in front or from behind for any planets both superior and inferior, it's a simple matter of arriving at the same point in space slightly earlier vs slightly later, you can easily switch between the two types of encounter with minimal change in delta-V after Kerbin ejection.

For example, here is an approach to Jool from Kerbin from behind. Jool's massive gravity then pulls the spacecraft forward for a huge increase in prograde velocity, hence a gravity assist:

img snip

It looks like you are coming to Jool from its front rather than back.

I made a simple drawing in paint with touchpad earlier today while thinking about this and it actually fits the Kerbol-Jool example.

My point is with standard Hoffman transfers (without excessive vertical velocity) it's not possible to approach outward planet from behind as well as inward one from the front. As at the point of meeting, the two velocity vectors of planet and ship are almost parallel. So the side from which the ship approaches planet is defined only by direction of the sum of their velocity. In simpler terms, you cannot catch a bus from behind by running after it, you can only get splattered on the windshield .

I have a feeling that i can be horribly wrong as you guys have a lot more experience in this but i'll stand my ground on this one

Edit: Actually the bus thing gave me an idea on how to visualize the concept.

Suppose the ship is a person that can run, and object he is getting slingshot on is somebody else on a heavy bike. At the point of meeting they can catch each other's hands briefly and exchange velocities in similar way you can do by catching a pole while running and rotating 180deg around it.

If both go in one direction, bike driving faster than man, when they meet the man can get flung by the bike forward. But there is no way for a man to catch the bike in such a way to get flung backwards.

The possibility of getting backward acceleration from the encounter, comes only when the man is running at an angle to bike's motion (ie: perpendicular). So that its possible for a man to arrive in reach of the biker's hand right after it passes him. And the resulting velocity change vector for a man will point backward at an angle. This is easier the faster the man is running and the longer are the arms edit2:not sure about arms.

Edited May 11, 2013 by Nao

[Temstar]

Oh wait, when you say " in front" do you mean "from below the target's orbital altitude" or "from the leading edge side"?

Either way you slice it though, you can get an encounter (and thus a gravitational assist) from either direction regardless of weather the target is a superior or inferior planet. Here's I'll show you both types of encounter using the Mun as an analogy:

Here we have a Mun encounter from below the Mun's orbital altitude, that is at the moment my craft will enter Mun SOI it will be somewhere between the Mun and Kerbin. In this case Mun's gravity will serve to slow my craft down relative to Kerbin, although since the phase angle of this encounter is not very good I won't get the nice figure 8 free return trajectory back to Kerbin. If I were to coast on this trajectory to the Mun and then perform a Mun orbit insertion I will insert this craft into a retrograde Munar orbit.

Here I've executed a tiny prograde burn, so small the fuel usage was less than 1L. By arriving at the encounter point 1 minute and 18 seconds earlier I will intercept the Mun and smash right onto its surface.

Here I've excuted a further tiny prograde burn, you can see that the oxidiser and fuel gauges have gone down by 1L each. This burn allows me to arrive at the encounter point before the Mun reaches the same area, thus what happens is my spacecraft crosses Mun orbit in front of the Mun, then the Mun catches up to me from below and drags the spacecraft forward with its gravity, resulting in that huge Kerbin orbit that will send the spacecraft to near Kerbin escape velocity. If I were to perform a Mun orbit insertion following this trajectory I will insert this spacecraft into a prograde Munar orbit.

[Nao]

@Temstar

But, but in every example you are arriving in front of the Mun, it's only at what (Kerbin) altitude you enter Mun SOI that changes with those burns.

In both 1st and 3rd example you accelerate the (Kerbin) orbit by slingshoting on the Mun. The only difference being that 1st example does this by going around Mun counter-clockwise it and 3rd goes clockwise.

What made me understand this was hovering the cursor over "Mun encounter" while still in transfer (LKO -> Mun). In every possible setup it showed Mun's expected position behind that of ship's position at encounter.

Cheers!