How to eject into a resonant orbit?

[WarpPrime]

Playing RSS (no RO/RP-1) on a 1.11.2 save. I've mastered the stock system and have moved on to RSS but it's schooling me, especially with maneuver planning so I have Mechjeb and KER to work with.

However, I'm struggling to create gravity assist chains, as Mechjeb doesn't support that. I've got an interplanetary spacecraft with about 5km/s of dV, so I can't really get that far without gravity assists. I'm planning to do multiple assists off of Earth by ejecting into a 2:3 resonant orbit. How can I launch into a resonant orbit which sends me into other resonant orbits? Is there a delta-v formula to calculate this? I've seen Stratenblitz and Bradley Whistance do these kinds of gravity assists and would like to know how they do it. Is there a plugin that I am missing that they use?

[The Aziz]

There's a useful tool:

 

I think it supports RSS.

[Arrowstar]

6 hours ago, The Aziz said:

There's a useful tool:

 

I think it supports RSS.

KSPTOT author here.  Thanks for the shoutout!  Yes, KSPTOT can handle RSS solar systems if you feed it the celestial body information it needs to understand the RSS solar system.  After that, it's just a matter of designing your tour using the Multi-flyby Maneuver Sequencer tool.

Let me know if you have any questions, OP.  You can post them over on the KSPTOT forum thread.

[king of nowhere]

On 11/8/2021 at 7:02 PM, WarpPrime said:

Playing RSS (no RO/RP-1) on a 1.11.2 save. I've mastered the stock system and have moved on to RSS but it's schooling me, especially with maneuver planning so I have Mechjeb and KER to work with.

However, I'm struggling to create gravity assist chains, as Mechjeb doesn't support that. I've got an interplanetary spacecraft with about 5km/s of dV, so I can't really get that far without gravity assists. I'm planning to do multiple assists off of Earth by ejecting into a 2:3 resonant orbit. How can I launch into a resonant orbit which sends me into other resonant orbits? Is there a delta-v formula to calculate this? I've seen Stratenblitz and Bradley Whistance do these kinds of gravity assists and would like to know how they do it. Is there a plugin that I am missing that they use?

No, no real formula that I know of - maybe one, but later about this. You just have to calculate, manually, your orbital time.

The good news is, it's easier than it looks like; i recently learned it, and it worked immediately.

I made a very simple datasheet to calculate this

As you can see on the red circle, the two lines of numbers are just iterations, where the same numer is added over and over. In this case the upper line is the orbital period of Eve, and the lower line is the orbital period of my spaceship. So, the first line is just telling me that eve will return to the same position after 261.9 days, and then after 523.8 days, and then after 785.7.... while my spaceship will return to the intercept in 174.6 days, and then the next time in 349, and so on.

And i just manually look if some of those numbers check. In this case, the datasheet shows that in 523.8 days eve will pass again through the intercept having made 2 orbits, while my spaceship will pass in the same spot at the same time having made 3 orbits, so a 2:3 resonance. But i used a 9:10 on kerbin earlier, and it's not any different.

If the numbers don't check, i look where the numbers are closer, and I try to refine it. For example, in this case maybe i started with 180 days of orbital period, saw i would be late for a 2:3 resonance, and tried to adjust for a faster orbit. if that was not possible, i could have tried for a 3:4 resonance, and so on. there are more refined ways and more accurate tools, but this one suffices.

Manuever-node wise, the way to do it is to set up a manuever node (without any actual deltaV used) after the gravity assist. it will tell you the new orbital period. so you try to adjust your flyby so that the new orbital period, shown in the second manuever node, will match what you calculated. You can't see your new orbital time when you adjust the flyby, you have to tinker with the correction manuever blindly and then select the second manuever node and see if the orbital time is right. however, with a bit of trial and error you can do it. and if your new orbit is a few hours shorter or longer than it should be, a correction manuever to fix that is cheap - so long as it's just a few hours.

This image shows one such manuever planned. You can see the new orbital period, 385 days, in the bottom left corner of the image; it's the 9:10 resonance with kerbin i calculated. you can see the manuever node selected.

 

Now, i said that there was some formula in addition to all this. Namely, there are 2 other mathematical boundaries.

The first, and most important, is that you leave your planet after the flyby at the same speed you arrived, only in a different direction. example of why this is important: after my third kerbin flyby, i reached an intercept to eve. i was aiming for moho, and from eve to moho a transfer takes roughly 1000 m/s excess speed (in addition to eve escape). but my trajectory from kerbin had a 600 m/s intercept speed over eve. Guess what? No matter how much i tinkered with the trajectories, i could never intercept moho the way i wanted. I had to provide the additional 400 m/s with a burn at eve periapsis.

So, if you've ejected from earth at the minimum excess speed, you won't ever be able to reach jupiter with any amount of flybys. you need two planets to bounce against each other, gaining energy at every step. on kerbin you can also use mun, if you include a mun flyby you can leave kerbin at a different speed than you had coming in. but the real moon has too much of an orbital inclination and too slow an orbital time for this to be practical. On the plus side, if you left earth on an inclined orbit, you can use the flyby to change your orbital inclination for free.

 

second boundary, every planet can give you an assist for a limited amount of deltaV - the closer the pass, the higher the deltaV. if that deltaV is not enough, you have to make multiple passages. For example, kerbin can give you roughly 500 m/s kick, maybe 700. if you are coming from jool, excess speed of 1000 m/s, and you want to go to eve, you can do it - convert your excess speed of 1000 m/s going away from the sun to 1000 m/s going towards the sun.

But you won't be able to do it in one passage. not even in 2. you have to first lower solar apoapsis, ejecting into a resonant orbit to meet kerbin again, lower apoapsis again, into another resonant orbit, and finally you can leave kerbin with kerbin as your solar apoapsis. because you had to change your speed by 2000 m/s, and kerbin can give at most 700 m/s, so you needed no less than 3 flybys. I can't give you hard numbers, unfortunately. especially not for rss.

 

I hope I was clear. In addition, I can link you to the mission report where i describe how i went from ike to moho with resonant gravity assists. It took very long, but it was surprisingly cheap, and very rewarding. and my mothership didn't have enough deltaV to do it any other way. It is described in detail, so you may get some additional information.