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GarrisonChisholm

Solar Skimming for High Speed Interstellar

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Good evening all, I've a simple (I think) question.  I know that if you drop down around Kerbol then your hyperbolic velocity is greater than just burning straight out with the same amount of fuel.  I also know that going faster at Periap produces greater velocity, which means dropping from a higher Apoap.  So the farther out you go before you drop down, the faster you will exit.

However, at a certain point the benefits of dropping down towards Kerbol must be exceeded by the time you've spent traveling out to your Apoap.  In an extreme case, if my target was 1,000,000,000 km out, and I rose to an Apoap of 500,000,000 km, it feels like I may as well have invested that energy in launching directly to the target rather than a sun-skim profile.

Is there an easy way to determine how far out to egress with a sun-skimming plan before it would just make more sense to launch straight out, or am I missing something basic?

 

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Gravity assists. There are tools for that, the most complex I know is KSP-TOT, and believe me, it takes it a while to calculate optional journey, especially when you want to use one planet for gravity assist and go to the other, it has to calculate right time to launch, any potential burns etc.

But you asked a simpler question, and my answer is: you always spend more time on using the gravity assist than going straight forward. You need to go back "down" and "up" again. It all depends on your fuel budget.

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I don't think this is even a gravity assist question, I think it's an Oberth Effect question. By doing "solar skimming" you're borrowing kinetic energy from the star in order to try to raise your apoapsis until it intersects some other body. In effect, solar skimming is identical to using Oberth Effect on Kerbin to help transfer to Duna: the two bodies you are transferring between are stars and the body they are orbiting is the galactic center.

In short, the reason you would do solar skimming is not to save time on a transfer, and in general any time you spend within a solar sphere of influence is going to be insignificant compared to your interstellar transfer time for any realistic transfer system. The reason you would do solar skimming is to save on delta-V and enable an efficient Hohman transfer between the two stars while allowing you to bring less fuel mass.

Edited by dire

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9 hours ago, The Aziz said:

Gravity assists. There are tools for that, the most complex I know is KSP-TOT, and believe me, it takes it a while to calculate optional journey, especially when you want to use one planet for gravity assist and go to the other, it has to calculate right time to launch, any potential burns etc.

But you asked a simpler question, and my answer is: you always spend more time on using the gravity assist than going straight forward. You need to go back "down" and "up" again. It all depends on your fuel budget.

Thank you for KSP-TOT, I will look into that.  I think my rationale was more time than speed, as I just want to make the journey as short as possible.

Burning 40,000 dv in Kerbin orbit to go straight to Valentine (extrasolar planets mod) will take 33,000 years.  Going to Neidon to Kerbol to Jool to Valentine would get me there sooner.  I would sacrifice 5 years travel on the front end as I dove back in but in the end it would pay off.  End (Planet9 mod) is not so far, only ~40 years (i think), so I don't think a super complex trajectory would pay off.  It would be going faster at End, but I doubt it would get there sooner due to the sacrificed out-bound time.  That's really the question I am puzzling over.  At what point does the inbound leg no-longer make sense.  I was trying to find that magic "dividing line."

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I'm only using the stock solar system, but I do have a space station on an extremely long period orbit that goes way into deep space. It has about an 80 year period, I got it there by using what was at the time the largest rocket I had ever built with over 350 meganewtons of thrust at liftoff (it totally wrecked the launch pad). On the way out of Kerbin's SOI it performed the closest flyby of the Mun I've ever done (the altitude was under 2 km ASL at its lowest point when I initiated the escape burn). This gave it enough velocity that when it left Kerbin's SOI it was effective motionless in space and falling toward the sun. Then I refueled with a tanker I had waiting, boosted inward towards the sun with a perigee well below 2000 km over the sun. Then I refueled with another tanker, drifted inward toward the sun, and then did a burn at perigee. This put it on an intercept trajectory with long period asteroid I wanted to build on.

So my answer: Eyeball it and burn huge amounts of fuel.

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21 hours ago, GarrisonChisholm said:

I know that if you drop down around Kerbol then your hyperbolic velocity is greater than just burning straight out with the same amount of fuel.

What you're describing is an Oberth maneuver.  And what you're trying to figure out is "is it worth it", i.e. does it give you more hyperbolic velocity for a given amount of dV on the ship, or less.  And there is no general answer to that question-- it depends on the numbers for a given situation.

21 hours ago, GarrisonChisholm said:

I also know that going faster at Periap produces greater velocity, which means dropping from a higher Apoap.  So the farther out you go before you drop down, the faster you will exit.

Yes, but the "farther out you go, the faster you'll exit" thing is extremely subject to diminishing returns.  Analysis is below, but the short answer is that going way way out into the outer solar system for this is largely pointless.  If you go out to 2x the distance of Jool, for example, you get only about 2% more speed than if you just go out to the distance of Duna.

So an initial pass into the deep solar system isn't necessary.

21 hours ago, GarrisonChisholm said:

Is there an easy way to determine how far out to egress with a sun-skimming plan before it would just make more sense to launch straight out, or am I missing something basic?

Depends what you mean by "easy".  The math is certainly very simple-- it's just applying the vis-viva equation a few times.  Basic algebra.  However, even though it's simple, it's tedious-- you have to do a whole bunch of adding and subtracting of numbers.

I plugged some numbers into a spreadsheet, math details in spoiler:

Spoiler

To be clear, here are the three situations we're comparing:

  • I'm in circular orbit around a body (say, the Sun) that I want to escape.
  • Option 1, a.k.a. "direct burn":  I use all of my dV to do a single big burn in the :prograde: direction, thus effecting my escape.
  • Option 2, a.k.a. "simple Oberth maneuver":  I do two burns.  The first burn is in the :retrograde: direction, using just enough dV to drop my periapsis down as low as it can go, so that I'm skimming the body at low altitude.  Then, when I get down to periapsis, that's where I use all of my remaining dV to burn right there, thus effecting my escape.
  • Option 3, a.k.a. "compound Oberth maneuver":  I do three burns.  First a relatively gentle :prograde: burn that raises my apoapsis fairly high.  Then, at apoapsis, a :retrograde: burn to lower my periapsis down really really low (this is a small burn because my orbital velocity at apoapsis is quite low).  Then, at periapsis, a big :prograde: burn to do my escape.

Which of these will be "best" (in terms of minimizing your transit time to wherever you're going) depends on several things, specifically:

  1. how high is your initial circular orbit
  2. how much extra dV do you have on your ship
  3. how far away is your intended destination

Let's consider the case where my initial orbit is at Kerbin's distance from the Sun; I've got 40 km/s of dV on my ship; and a radius of 500,000 km at solar periapsis (probably don't want to get a lot closer than that, you'd fry) for Oberth maneuvers.  What do the numbers look like?  I plugged these into a spreadsheet and came up with the following.

(Note:  to keep things simple, I've assumed that you're starting in a solar orbit at Kerbin's distance from the Sun, not that you're actually in LKO.  Rationale:  numbers get more complicated, and Kerbin itself is kind of a red herring here.  Yes, it will be significant due to the Oberth benefit of Kerbin, but we're talking aboutthe general attractiveness of direct-versus-Oberth-versus-compound-Oberth, so let's keep it fairly simple for now.)

  • Direct burn:  40 km/s burn :prograde: -> solar excess hyperbolic velocity is 48.4 km/s
  • Oberth maneuver:  First burn, 6.81 km/s :retrograde:. Second burn, 33.19 km/s :prograde: .  -> solar excess hyperbolic velocity is 88.0 km/s
  • Compound Oberth maneuver, going out to Duna's orbit:  First burn, 0.92 km/s :prograde:.  Second burn, 5.06 km/s :retrograde:.  Third burn, 34.02 km/s :prograde:.  -> solar excess hyperbolic velocity is 101.7 km/s
  • Compound Oberth maneuver, going out to Dres' orbit:  First burn, 2.09 km/s :prograde:.  Second burn, 2.95 km/s :retrograde:.  Third burn, 34.96 km/s :prograde:.  -> solar excess hyperbolic velocity is 103.0 km/s
  • Compound Oberth maneuver, going out to Jool's orbit:  First burn, 2.71 km/s :prograde:.  Second burn, 1.88 km/s :retrograde:.  Third burn, 35.41 km/s :prograde:.  -> solar excess hyperbolic velocity is 103.6 km/s
  • Compound Oberth maneuver, going out to 2x Jool's orbit:  First burn, 3.24 km/s :prograde:.  Second burn, 0.99 km/s :retrograde:.  Third burn, 35.77 km/s :prograde:.  -> solar excess hyperbolic velocity is 104.1 km/s

 

So what's the bottom line?  It comes down to this:

  • Don't do a direct burn.  It's a lot less effective than an Oberth maneuver.  Even a "simple" Oberth maneuver that just drops from Kerbin straight down to the Sun will get you a much higher solar excess hyperbolic velocity than a direct burn will.
  • Doing a compound Oberth maneuver is better than a simple one... but not by all that much.  In the above analysis, you only get (at most) about 18% more speed from a compound Oberth maneuver than from a simple one.
  • If you do a compound Oberth maneuver, don't bother going way far out on the initial pass.  It's really subject to diminishing returns.  In the above example, a compound Oberth that goes out to 2x the distance of Jool will only get you slightly more than 2% more speed than if you just go out to Duna.

 

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One issue here is how high speed are you aiming for?
For an real life realistic interstellar probe you have to get into the 2-5% of c, here it simply don't matter at all. You might want to drop close to the sun so the laser array get some more time to lock on you. 
In KSP distances are scaled down and it might well be practical. 
Note that one benefit is accuracy, you will not go much closer than 1/5 of Moho orbit (might be to close) still it give an long time to do your burn the drop burn is not relevant here but adds to your initial speed. 
Currently doing high dV intercept with various bodies in KSP and the 1km/s you get from an Minmus drop helps accuracy a lot over an low orbit burn as you have an km/s head start. 
Yes this is irrelevant in real life but very relevant in KSP if you want an high speed run. 
Solar panels is another issue, you get more power out of them in KSP, this will help an fly by probe a lot. 

Edited by magnemoe

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This is why I love this community.  Thank you @Snark and All.  That was the insight I was hoping for.  My plans will now be simpler and more attuned.  :]  

If I don't screw it up I will post it in the results.  If i do screw it up, it will appear in my mission report.  :D

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