Advanced techniques: the gravitational slingshot

[Horus Lupercal]

I do the same thing with Saturn. Moons don't give as much of an assist though...

Compared to planets, no. But in the standard system, the only objects that have a better gravity than Ganymede is Earth and Venus. And expanded system, that fact only changes to include the other gas giants. Next time you're headed that way, try it. I wasn't kidding about the Uranus part.

 

[Lt. Snakestrike]

Compared to planets, no. But in the standard system, the only objects that have a better gravity than Ganymede is Earth and Venus. And expanded system, that fact only changes to include the other gas giants. Next time you're headed that way, try it. I wasn't kidding about the Uranus part.

Yeah, I know, I've accidently flung one of my supersolids out of the system with Jupiter, and Saturn's had similar trajectories as well (including a failure with Unbound's injection which was on the wrong side of the planet).

 

[Horus Lupercal]

Yeah, I know, I've accidently flung one of my supersolids out of the system with Jupiter, and Saturn's had similar trajectories as well (including a failure with Unbound's injection which was on the wrong side of the planet).

Ha, screaming at it 'where's the brakes on this damned thing!' whilst you're outbound at solar escape velocity...

 

[Lt. Snakestrike]

Ha, screaming at it 'where's the brakes on this damned thing!' whilst you're outbound at solar escape velocity...

That's what saves are for... My phone always starts to run a little slower on these trips due to the number of saves I make.

 

[Altaïr]

@Altaïr could you make a guide about how to perform gravity assistances with Jupiter's moons to help achieve an Europa Orbit with less fuel??
Also If its possible, what's the most efficient way to get in and about of the Jovian System?

Hi, and welcome to the forum
@Horus Lupercal is right indeed, to get to Jupiter, the most efficient way is the VEEGA path, as you literally get Jupiter for the price of Venus.
Then once in the jovian system, the first thing to be aware of is that, without considering gravity assist, the most efficient way to satellize around a moon is by performing a bi-elliptic transfer.
Here is an example with Europa:

First I enter the jovian system, and I burn at the periapsis to satellize, but I let my ship on a very elliptical orbit.
Then, when I reach the apoapsis, I burn to raise the periapsis at Europa level:

Now I just have to adjust the trajectory to encounter Europa. You'll only need a very small burn at the periapsis:

Then the insertion itself:

You still need a big burn to satellize, but it's still better than a direct transfer.

Now with the gravity assist maneuver:

The beginning is similar, but instead of aiming for Europa, it's better to encounter Ganymede first. That's because Ganymede is the heaviest moon, and thus the most effective to brake. Europa is the lightest on the contrary. This would also work with Europa, but you'll need more fly-bys.

Then get an encounter with Ganymede, and make a retrograde fly-by like this:

After the fly-by here is my trajectory:

It's much better now.
At that point you can either perform a direct insertion into Europa orbit, or perform a few fly-bys above Europa to slow down even more. That's basically the same technique as for Mercury.

 

[Altaïr]

In and out I tried to say

Oh, you also asked how to get out of Jupiter.
I haven't much fuel left (I didn't take into account the return part), but I could still make it.

To get out of Jupiter once in Europa's orbit, the most direct method (injection burn from Europa, directly onto a transfer trajectory to Earth) is also the most inefficient
It will literally cost you tons of fuel if you do that.

A more subtle way is by using the Oberth effect from Jupiter. First I set Jupiter as a target, and burn so that I'm on such a trajectory:

Then, once I reach the periapsis above Jupiter, I burn enough to quit the Jovian system:

The problem is that you have to anticipate, as your trajectory must be correctly oriented in the end.
That maneuver is more efficient, but from Europa it still costs a lot (I had to use infinite fuel to be honest).

There's an even more efficient trajectory, but that also requires more anticipation: the bi-elliptic transfer.
From Europa orbit, put your ship on a highly elliptical trajectory:

To know when you should burn, you can select Jupiter as a target, and burn prograde when your ship is at the opposite of the transfer window.
Then once you reach the apoapsis, lower your periapsis to Jupiter level:

And once you're at the periapsis, burn to quit the jovian system, until you cross the Earth's trajectory:

That last burn is very cheap.
Globally, it's significantly more efficient: I didn't have to use infinite fuel this time, and I even have a reserve left.

 

[Blazer Ayanami]

Oh, you also asked how to get out of Jupiter.
I haven't much fuel left (I didn't take into account the return part), but I could still make it.

To get out of Jupiter once in Europa's orbit, the most direct method (injection burn from Europa, directly onto a transfer trajectory to Earth) is also the most inefficient
It will literally cost you tons of fuel if you do that.

A more subtle way is by using the Oberth effect from Jupiter. First I set Jupiter as a target, and burn so that I'm on such a trajectory:
View attachment 14104
Then, once I reach the periapsis above Jupiter, I burn enough to quit the Jovian system:
View attachment 14106 View attachment 14107
The problem is that you have to anticipate, as your trajectory must be correctly oriented in the end.
That maneuver is more efficient, but from Europa it still costs a lot (I had to use infinite fuel to be honest).

There's an even more efficient trajectory, but that also requires more anticipation: the bi-elliptic transfer.
From Europa orbit, put your ship on a highly elliptical trajectory:
View attachment 14109
To know when you should burn, you can select Jupiter as a target, and burn prograde when your ship is at the opposite of the transfer window.
Then once you reach the apoapsis, lower your periapsis to Jupiter level:
View attachment 14111 View attachment 14112
And once you're at the periapsis, burn to quit the jovian system, until you cross the Earth's trajectory:
View attachment 14113 View attachment 14114
That last burn is very cheap.
Globally, it's significantly more efficient: I didn't have to use infinite fuel this time, and I even have a reserve left.

Thanks a lot for your explanation @Altaïr! Now I can perform my Europa Rover Mission more easily! I plan to make it full Reusable so I need a lot of optimization...

 

[Blazer Ayanami]

Yeah, my path looks more like a game of Jupiter moons pinball than an organised flight plan. I've not done Europa yet either, Io and Ganymede mostly so mine will be different to yours and I still had to do a furious amount of burning to make an orbit once I'd done all I could with assists. And landing shouldn't be so bad, Europa ground speed is half that of Ganymede.

I know what you mean The same happened to me the first time I went to Europa.

 

[Lt. Snakestrike]

@Altaïr do you think it'd be feasible to use a martian or jovian gravity assist for a return from Saturn to Earth?

 

[Horus Lupercal]

@Altaïr do you think it'd be feasible to use a martian or jovian gravity assist for a return from Saturn to Earth?

Not to answer for the Stig, but I do it a lot heading back this way from the Gas Giant side of the system. Even if you take one that kicks you further spinward, it's then easier to raise your periapsis to Earth and dive in for some aerobraking

 

[Altaïr]

@Altaïr do you think it'd be feasible to use a martian or jovian gravity assist for a return from Saturn to Earth?

I never tried but what's sure is that you won't get much of Mars. That planet is light, I never use it for gravity assist (I already tried but it's really not worth it).
On the contrary you may have a really big kick from Jupiter, probably too much. That's the opposite problem, that planet is massive. Which @Horus Lupercal seems to confirm
I don't play that much with Saturn, but a simple Oberth maneuver should give quite a cheap result, I wouldn't bother with gravity assist to be honest. The greatest effort is still escaping Saturn in this case.

 

[SPQRALAN]

The angle comparisons are in reality vector addition simplified. In Altaïr 's examples, he is using the same planet and the magnitude of the spacecraft's velocity remain the same from entry to exit, so it is safe to compare the angles. But if:

• You do a powered slingshot
• You have a planet whose velocity changes during its elliptical orbit(not in SFS)

the magnitude of the vectors will change, so comparing the angles is not the best way. Vector addition is.

You can see the velocity vectors and trajectory of the powered slingshot below.
Vi= Initial velocity of spacecraft
Vf= Final velocity of Spacecraft(after powered slingshot)
Vp= Velocity of planet


You can add Vi and Vp together to get resultant velocity(VR) at entry by using the Law of Cosines:


Note: When adding vectors, add them from head to tail to get theta(θ). This is different than comparing angles in Altaïr 's example.

Similarly, you can also add Vf and Vp together to get resultant velocity(VR) at exit by using the Law of Cosines.


Then you can compare the speeds to see how much gain the gravitational assist gave you.

 

[Altaïr]

Thanks SPQRALAN
As you said I simplified a lot so that most people understand, but that's a nice addition for those who want to explore further the logic behind.

 

[The Dark in the Light]

This is a bit of a request, but could you make a video on how to do this? I cant really get it from reading the stuff, even thought it's really well written.

 

[Altaïr]

I'll try to find some time to do it, but I'm not really used to make video tutorials, so this may not be immediate.

 

[8BitCosmonaut]

I never really got into the mathematics or mechanics of how slingshots work, neither do I have the schedule for it.

Maybe after I have completed the engine, I'll take a look. However I see no equations, unless I am blind, it would be interesting to see the "gears" of your machine. How exactly does a planet's gravitational constant or force re-direct the path of any passing object?

 

[Dodo]

That feeling when you mastered the Gravity maneuvers perfectly without any lessons, but simply playing debt in the SFS and constantly trying to save fuel
Very good and cool Lesson!

 

[8BitCosmonaut]

yeah its like forging, they'll eventually know work the steel right, but how the metal behaves on the molecular level, they don't know.

I wanna know its "molecular behavior", I wanna know the equations.

 

[TtTOtW]

Here's a simple attempt to explain the "why".

If you take any point in space, you'll have a net gravity vector you could assign to it. The closer to the assisting body, the larger the scale of the vector at that point. It creates a field of sorts, and at each point of the spacecraft's trajectory, it will be influenced exactly to the degree of the scale and direction of the vector at that point.

A simple demonstration.
So as you can see, the net amount of gravitational force applied to the rocket before periapsis must necessarily equal the amount of gravitational force after it. This means you split the total force in half across an axis drawn through the periapsis and the gravitational centre of the assisting body. The difference is that the approach half of the trajectory adds the force to the current momentum of the rocket. Thus it accelerates to periapsis. This exact same effect is mirrored on the other side as deceleration. Thus the deceleration curve will match the acceleration curve exactly. They perfectly cancel one another out. The speed upon exiting the SOI will match the initial entry speed.

So why the slingshot effect, "free energy"?

The force of gravity will have a net effect with regards to direction. It will be greater than zero, no matter what you do. And since the magnitude of gravitational force on the spacecraft increases exponentially as the distance to the surface drops, that means the great bulk of force applied will occur in close proximity to the assisting body.

While the forces cancel out perpendicular to the body across the axis, the components at each point that are parallel to the axis converge to form a net acceleration vector toward the body's centre from the periapsis. That net energy may then be drawn up against the initial energy vector of the rocket upon entry of the SOI to determine the amount of directional deflection. The change in direction will have a different interaction with the gravitational field of the dominant body outside the SOI due to the vector changing direction compared to before the assist. This equation will have an increase or decrease in energy. That corresponds to accelerating or decelerating. Direction before and after the time in the assisting body's SOI willl also be different.

I do hope this helps, Cosmo. I may not have Altaïr's education, but I do understand this much.

 

[Space pilot]

Mission to Pluto.
slingshot by Jupiter.
Speed increased +20%

 

[Pink]

View attachment 35672
Mission to Pluto.
slingshot by Jupiter.
Speed increased +20%

Jupiter's not in the right place there.

 

[Horus Lupercal]

Jupiter's not in the right place there.

...?
It won't be in the same place as when the slingshot was conducted as time will have passed, the spacecraft has moved a fair distance and so will Jupiter.
May not be as far away, but that depends on the time lapse

 

[Pink]

...?
It won't be in the same place as when the slingshot was conducted as time will have passed, the spacecraft has moved a fair distance and so will Jupiter.
May not be as far away, but that depends on the time elapse

True, I just thought that Jupiter moved too far considering the probe has only gone past Saturn's orbit. I'm probably over-estimating how much zoom a Jupiter assist gives!

 

[Horus Lupercal]

True, I just thought that Jupiter moved too far considering the probe has only gone past Saturn's orbit. I'm probably over-estimating how much zoom a Jupiter assist gives!

You're right though. It took Voyager One 18 months to get to Saturn from Jupiter, and it looks like Jupiter has done a quarter of an orbit since the flypast (about 3 years)

 

[Jryeem]

I always use a slingshot around the moon to use as little fuel as possible to venus