Orbital Maneuver Question

[Spricigo]

39 minutes ago, Abastro said:

This is contradiction

Ahh! My suspicion was right then.  Actually the problem is we all didn't notice the limits of the equation also we didn't correctly accounted for some symmetric situations. We actually  didn't proved opposite arguments but argued s lot about the same thing. 

39 minutes ago, Abastro said:

What do you mean? Multiply u and v? Why?

If you multiply u by -1 you revert the planet's path. 

If you multiply v by - 1 you revert the ship path. 

Again a case of symmetry. The results you get in those reverted paths must be equivalent to the base case. 

So if with v and - u we find that change in velocity is -2(u+v) that is equivalent to - 2(u-v) we obtain if we take - v and - u.  

If we take 0 and -u the change of velocity will be  2u. If we take -v and 0 change in velocity will be 2v.

2v is equivalent to 2u, most of our discussion is moot. 

[Reusables]

20 minutes ago, Spricigo said:

If you multiply u by -1 you revert the planet's path. 

If you multiply v by - 1 you revert the ship path. 

Again a case of symmetry. The results you get in those reverted paths must be equivalent to the base case. 

So if with v and - u we find that change in velocity is -2(u+v) that is equivalent to - 2(u-v) we obtain if we take - v and - u.  

If we take 0 and -u the change of velocity will be  2u. If we take -v and 0 change in velocity will be 2v.

2v is equivalent to 2u, most of our discussion is moot. 

Right! Gosh, I should be bad at communication. I'm sorry.

(Besides, I was confused because you mentioned numbers; A number can be either scalar or 1-dimension vector)

[Cpt Kerbalkrunch]

I had the first reply in this thread, read through the next few that came in, then was off the forum for a few days. I come back, and I can't believe there are over 50 replies now. And I really can't believe I read through every one of them without the top of my head blowing off.

I see @SYDWAD is following the thread, but I wonder if he's following the conversation. I know I wasn't. I understand stand what you're saying in a general sense because I've played the game a lot (I pretty much know what can and can't be done at this point), but I'm not going to spend a second trying to contemplate the math you guys are throwing out. I'll just take your word for it.

The OP had asked: can it be done (yes, but not quite like the diagram), and for low fuel (no, depending what you'd call "low fuel"). In my reply I had said that Jool/Tylo was a good bet, but that I thought Eeloo was the way to go.

I neglected to ask SYDWAD if he intended to play it straight; i.e. no cheats, no mods, launch from Kerbin and go. If so, I would do this:

Launch from Kerbin to Jool to take advantage of the free capture. I have now instantly raised my Pe to the height of Jool, and it cost me nothing. I would time the encounter to occur while Jool is still behind Eeloo. I take the next window to Eeloo, and ride it to the top of the roller coaster (I don't know Eeloo's Ap off hand, but I know it's way up there). At this point, nothing fancy, just get down low and burn away from the sun. For a looong time.

I also neglected to ask what the end game was. What next? Playing planetary pinball to raise your solar Pe (while orbiting retrograde) would be a lot of fun, I think. I'd love to see the way each planet's gravity would effect your orbit.

Anyway, that's my thinking. And, though I won't really understand it, I'm curious if the math would back that up. Or is the one-two punch of Jool/Tylo the way to go? Though I play career, I may just do it for fun to find out. I've got tons of cash anyway, and it'll make a good post in "what did you do in KSP today". Curios to see if you guys would go Plan A (Eeloo), or Plan B (Jool/Tylo).

[Kryxal]

Definitely either Jool/Tylo or Jool/Laythe directly into retrograde as best as possible.

[Spricigo]

3 hours ago, Cpt Kerbalkrunch said:

 you guys would go Plan A (Eeloo), or Plan B (Jool/Tylo).

Assuming no time constraints?  With the objective of minimal fuel consumption? 

Plan C: multiply slingshots around Eve and/or Kerbin. 

Plan B,  If plan C is not an option. 

 

Edit: Throwing a bit of aerobraking in the mix for bonus kerbal points

Edited April 26, 2017 by Spricigo

[Cpt Kerbalkrunch]

19 minutes ago, Kryxal said:

Definitely either Jool/Tylo or Jool/Laythe directly into retrograde as best as possible.

 

16 minutes ago, Spricigo said:

Assuming no time constraints?  With the objective of minimal fuel consumption? 

Plan C: multiply slingshots around Eve and/or Kerbin. 

Plan B,  If plan C is not an option. 

I just want to clarify: you're saying Jool/Tylo because of their combined power, correct? Otherwise, the standard move of being high and slow would be the proper way to flip your orbit, wouldn't it? It works well at planets and moons. I've even done it at Jool for a rescue, but I've never tried a solar flip, though.

As an aside; I know the proper way IRL would be multiple-assists (did you see that crazy trip the Europeans are taking to get to Jupiter?). However, I don't use mods, so any more than two encounters would probably be beyond me.

[Spricigo]

2 hours ago, Cpt Kerbalkrunch said:

 

I just want to clarify: you're saying Jool/Tylo because of their combined power, correct? Otherwise, the standard move of being high and slow would be the proper way to flip your orbit, wouldn't it? It works well at planets and moons. I've even done it at Jool for a rescue, but I've never tried a solar flip, though.

 

 

If we decide to change the orbit using only gravity slingshot how high we are(relative to the central body) become irrelevant. Yes, the deltaV required will be proportional to the inverse of the distance, however the deltaV available will be proportional to the distance. In fact the only thing that actualy matter its the proportion between mass of the ship and mass of the planet, thus, for a given ship the only important factor its the mass of planet. (ok, there is some slight inaccuracies in that explanation, but the general idea is there)

So appart from the mass of the planet, the only other consideration is how much deltaV it takes to get to the planet. That is why I personally choose Eve/Kerbin, less deltaV to reach (also assuming infinity time/patience available)

Quote

(did you see that crazy trip the Europeans are taking to get to Jupiter?).

 

pretty much standard practicy IRL e.g.

 

Edited April 26, 2017 by Spricigo

[Human Person]

I have developed a technique to get into a retrosolar orbit using a gravity assist from Jool.

It has to be Jool because it's orbital velocity is small and it's high mass let's you do very effective gravity assists. Don't bother with EVE, it's way too close to the sun.

you have to do a powered gravity assist in such a way that you leave Jools SOI parallel to it's orbit. That means, you have to enter Jool's SOI at quite some velocity. You can do this by doing an inefficient jool transfer (ideally some time after the perfect transfer window).

The biggest burn is yet to come: Circularizing your retro-solar orbit (if you want a low retrosolar orbit, this is going to be painful).

And now what? How to get home? Forget about gravity assists from Eve or Kerbin, you are now moving way too fast for them to help you. 

You can still do boosted assists, as the obearth effect still works, so getting an near Eve-flyby and performing a burn at periapsis might be your best bet to get your aphelion back to jool, where you could slingshot yourself back into a counter-clockwise orbit (again I doubt this to be possible without another burn at Jool PE).

 

 

[Human Person]

Look At my tutorial here: 

and participate in the challenge!