How to read the delta V map if you travel to moons

[Jackissimus]

Hi, a newbie, I'm just trying to wrap my head around this. Consider this map:

Say I want to visit Gilly. Do I have to lower my orbit all the way to low Eve orbit, then raise the orbit again to intercept Gilly? Or can I save the deltaV by intercepting Gilly directly? Generally, how do I read this map if I want to skip over the planets to go directly to their moons (Jool is a nice example)? Also, how about travelling back to Kerbin then?

[stupid_chris]

Well with a proper aerobrake maneuver you could save a bunch of delta V. By aerobraking and leaving your periapsis a bit further than Gilly's orbit, your capture burn is virtually costless. you can simply raise your periapsis above Eve's atmosphere and wait for the right window do do a Hohmann transfer to Gilly. If you bring enough delta V for the intercept, you should be fine usually.

Delta V maps are far from being the optimal paths, they're just a good header. And to come back, the delta V is different and can't be read from that map

Basically, once in LKO, you could get in a low Gilly orbit for 3030m/s easily

[Jackissimus]

Delta V maps are far from being the optimal paths, they're just a good header. And to come back, the delta V is different and can't be read from that map

Basically, once in LKO, you could get in a low Gilly orbit for 3030m/s easily

Let's not consider aerobraking for now. You gave me a deltaV of 3030m/s to get in low Gilly orbit. That's just about what I get when I add the 1290 and 1650 m/s on the map. Well I was wondering whether I could skip going to Eve and thus avoid later raising the orbit to Gilly with the 1650 m/s. Intuitively it seems logical to me, but I think I may be missing some physics.

Also, how is the deltaV different for the trip back?

[stupid_chris]

Let's not consider aerobraking for now. You gave me a deltaV of 3030m/s to get in low Gilly orbit. That's just about what I get when I add the 1290 and 1650 m/s on the map. Well I was wondering whether I could skip going to Eve and thus avoid later raising the orbit to Gilly with the 1650 m/s. Intuitively it seems logical to me, but I think I may be missing some physics.

Also, how is the deltaV different for the trip back?

Well the 3030m/s was assuming an aerobrake maneuver. And well to have an intercept with Gilly without stabilizing your orbit first, you'd have to be insanely precise, I don't think it would be easy to do. It's hard to predict how you would come in to Eve ans where Gilly would be at that time. There's also the fact that Gilly's SOI is ridiculously small. It's better to get an orbit around Eve first. That's why I proposed the aerobrake maneuver. It's not hard really, just setting your periapsis at the right height and enjoying the light show. But you know, you don't need to raise the orbit to Gilly if you don't lower it under it's orbit first. Then you just need to wait for the right phase angle and transfer then.

And the delta V to come back will mostly be affected by the fact you will probably simply want to come right back to land on Kerbin. For example the transfer burn to the Mun is ~800m/s, but then coming back is only roughly ~250m/s because you're not circularizing around Kerbin You can Backtrack but you have to take the same exact paths as on the map to come back, and it's not always the most efficient way.

Edited July 17, 2013 by stupid_chris

[Ralathon]

Let's not consider aerobraking for now. You gave me a deltaV of 3030m/s to get in low Gilly orbit. That's just about what I get when I add the 1290 and 1650 m/s on the map. Well I was wondering whether I could skip going to Eve and thus avoid later raising the orbit to Gilly with the 1650 m/s. Intuitively it seems logical to me, but I think I may be missing some physics.

Also, how is the deltaV different for the trip back?

The main reason you want to get close to eve is aerocapture to lose velocity. You're in an elliptic orbit with periapsis at Eve's orbit and Apoapsis at Kerbins orbit. This means that you're going faster than Eve when you encounter it. If you dip into the atmosphere for a moment to bleed off your velocity you can get into an elliptical orbit around Eve. At that point it's just a matter of waiting for Gilly to get close. So you only need a few dV (to raise periapsis out of the atmosphere after your capture) to get from Kerbol orbit to Gilly.

If for whatever reason you don't want to aerocapture it is certainly possible to go straight from Kerbol orbit to Gilly orbit. But you'll need a lot of dV and you need to be lucky on Gilly's position.

Let's drag out some equations shall we.

I'm going to assume our spacecraft starts out in a 100km Kerbin orbit. First order of business is to get into an elliptical orbit around Kerbol. Such an orbit would have a velocity at apoapsis of:

V(ap) = sqrt((1-e)GM(sun)/((1+e)*a)) = 8530 m/s relative to the sun.

Kerbin itself already has an orbital velocity of 9284 m/s, so we only need to escape Kerbin's SoI with a relative velocity of 754 m/s

V(exit)^2 = (V(burn)+V(init))^2 - V(esc)^2, the V(esc) for a 100km orbit on kerbin is about 3177 m/s. Our initial circular orbit at 100km has an orbital velocity of 2246 m/s

V(burn) = sqrt(V(exit)^2 + V(esc)^2) - V(init) = 1019 m/s to get an Eve encounter.

Velocity at periapsis for an elliptical orbit with r(per)=r(eve) and r(ap)=r(kerbin) is:

V(per) = sqrt((1+e)GM(sun)/((1-e)*a)) (formula for orbital velocity at periapsis)

If I plug in the relevant numbers from the wiki I conclude your spacecraft will be going 11681 m/s relative to the sun. This is assuming an optimal orbit where Eve is located at its apoapsis when you encounter her.

Eve moves at 10811 m/s relative to the sun at that point. So your velocity relative to eve is 870 m/s before entering the SoI.

When falling into eve's SoI we gain a bit of velocity.

V(ini)^2 = V(max)^2-V(esc)^2. (formula for hyperbolic excess velocity)

V(max) = sqrt (V(ini)^2 + V(esc)^2)

V(esc) = sqrt(2GM/r) where r is Gilly's apoapsis (this would be the optimal scenario)

Plugging in the numbers we come to the conclusion that our spacecraft will be moving at 1045 m/s relative to Eve at Gilly Apoapsis.

Let's say we're lucky and Gilly happens to be in that exact position when we show up. Gilly moves 274 m/s relative to eve at apoapsis. So our velocity relative to Gilly is 771 m/s.

So if everything lines up perfectly you need a braking burn of at least 771 m/s if we ignore the trivial amount for Gilly orbit. In practice it'll almost always be much more.

So in total we need 1790 m/s to get from a 100km Kerbin orbit to a Gilly orbit in the absolute best case scenario. If you were to use aerobraking you could almost completely negate the 771 m/s braking burn at Eve, saving almost half your fuel.

I'm not going to bother calculating the dV for the trip back. But you can just use the same maths I just used. If correct it should be slightly less due to the Oberth effect. So don't be surprised if you end up with different values.

[Jackissimus]

So that means that I can go from here to here ...

... with significantly less deltaV than the map suggests, right?

You see I am also really interested in this because of Jool's moons. It's not that difficult to aim for those moons when approaching. And I don't like aerocapture - it has never been done in RL. Even iterative aerobraking with an orbit insertion burn has been done only on Mars and Earth but never on the bigger planets. Galileo didn't do it on Jupiter, Cassini didn't do it on Saturn. That's because it's really difficult to predict how it will turn out.

[Ralathon]

So that means that I can go from here to here ...

... with significantly less deltaV than the map suggests, right?

You see I am also really interested in this because of Jool's moons. It's not that difficult to aim for those moons when approaching. And I don't like aerocapture - it has never been done in RL. Even iterative aerobraking with an orbit insertion burn has been done only on Mars and Earth but never on the bigger planets. Galileo didn't do it on Jupiter, Cassini didn't do it on Saturn. That's because it's really difficult to predict how it will turn out.

Yep, The map assumes that you slow down to a low circular orbit and go back up to Gilly from there. It's like going from the 5th floor to the 4th via the basement. It can be done way cheaper.

If you want to play around inside the Joolian system I suggest against aiming for your moon and suicide burning till capture. You'll be moving at Joolian escape velocities at that point, so it'll be ridiculously expensive.

If you want to avoid aerocapture maneuvers I suggest aiming for either Tylo or Laythe. Both are excellent targets for gravity assists to slow yourself down. That should save you a lot of dV.

[stupid_chris]

You see I am also really interested in this because of Jool's moons. It's not that difficult to aim for those moons when approaching. And I don't like aerocapture - it has never been done in RL. Even iterative aerobraking with an orbit insertion burn has been done only on Mars and Earth but never on the bigger planets. Galileo didn't do it on Jupiter, Cassini didn't do it on Saturn. That's because it's really difficult to predict how it will turn out.

Actually, not so much. The real reason aerocapture has never been attempted is because carrying a heavy heatshield to protect the craft during the atmosphere skimming makes it not worth it. Aerocapture is not extremely precise, but it is precise enough. But an ablative heatshield capable of protecting Galileo or Cassini would've been way too heavy.

Anyway, if we we're preventing ourselves from doing things because we never did it in real live, we shouldn't be using nuclear engines as they have never been launched and we shouldn't be sending people further than the Moon's orbit. It' a game, you'll save a really big amount of delta V by aerobraking.

[Mr Shifty]

- You can't get to Gilly without entering Eve's SOI, so you're going to be aiming for Eve intercept.

- If you do a Hohmann transfer from Kerbin to Eve, you'll be going about 850 m/s (relative to Eve) when you enter Eve's SOI.

- Gilly's orbit is highly eccentric, but say you manage to catch it when it's furthest out, at an altitude of 48,125Mm above Eve. When you reach this point, you'll be going about 925 m/s Eve relative.

- Making the wild assumption that you enter Gilly's SOI at the ideal angle (i.e. from its retrograde around Eve), your Gilly-relative velocity at Gilly's SOI would be about 650 m/s.

- Since Gilly has barely any gravity, you're going to still be going about 650 m/s at 10 km. To circularize there, you need to be going about 19 m/s, so your burn would be about 630 m/s.

- Worst case, however has you meeting Gilly head-on at its periapsis, which would take about 2200 m/s to slow down from.

- And, like sc pointed out, you're going to have to be pretty lucky to hit it on the way in. You might be able to do it by slowing down at Eve periapsis just enough to close your orbit (about 70 m/s), then waiting however many orbits on that long ellipse (120 hours per orbit) for intercept with Gilly.

[Frederf]

Advisable or not, direct-to-moon transfers are best approximated as the transfer to the planetary body with a capture that is sum of the capture speeds of the two bodies.

For example:

Kerbin - Eve

Transfer 1030

Capture 1310

Eve - Gilly

Transfer 1650

Capture 210

Kerbin - Gilly

Transfer ~1030

Capture ~ 1520

[Jackissimus]

... It' a game ...

Exactly. A sandbox game. I used to play with aerocapture, it's boring and unrealistic. Capturing a shaky interplanetary vessel in Jool's atmo? No thank you. I believe I am actually getting more out of the game by not playing it like everybody else.

[stupid_chris]

Exactly. A sandbox game. I used to play with aerocapture, it's boring and unrealistic. Capturing a shaky interplanetary vessel in Jool's atmo? No thank you. I believe I am actually getting more out of the game by not playing it like everybody else.

Bah it's up to you ^^ Whatever wags your dolphin, if you're having fun I'm not gonna stop you

[Jackissimus]

- You can't get to Gilly without entering Eve's SOI, so you're going to be aiming for Eve intercept.

- If you do a Hohmann transfer from Kerbin to Eve, you'll be going about 850 m/s (relative to Eve) when you enter Eve's SOI.

- Gilly's orbit is highly eccentric, but say you manage to catch it when it's furthest out, at an altitude of 48,125Mm above Eve. When you reach this point, you'll be going about 925 m/s Eve relative.

- Making the wild assumption that you enter Gilly's SOI at the ideal angle (i.e. from its retrograde around Eve), your Gilly-relative velocity at Gilly's SOI would be about 650 m/s.

- Since Gilly has barely any gravity, you're going to still be going about 650 m/s at 10 km. To circularize there, you need to be going about 19 m/s, so your burn would be about 630 m/s.

- Worst case, however has you meeting Gilly head-on at its periapsis, which would take about 2200 m/s to slow down from.

- And, like sc pointed out, you're going to have to be pretty lucky to hit it on the way in. You might be able to do it by slowing down at Eve periapsis just enough to close your orbit (about 70 m/s), then waiting however many orbits on that long ellipse (120 hours per orbit) for intercept with Gilly.

Great summary! Thanks, you gave me an idea of how to think about this. I could maybe also tweak my Eve incoming angle a bit just after entering SOI, that way I might not need to wait too many orbits for Gilly ...

[Jackissimus]

Advisable or not, direct-to-moon transfers are best approximated as the transfer to the planetary body with a capture that is sum of the capture speeds of the two bodies.

Why is this?

[Frederf]

I'm confident that the transfer dV is practically identical for another planet and it's moon. It's like the gasoline used driving to another country and being concerned about which house you arrive at.

The capture dV... I made that up. I tried to think through it logically and I made a guess. I think if you encountered the planet body and did a sling through its gravity to aim you for its moon you would travel a path very similar to the piecewise path the dV map indicates except you could cancel the planet capture and planet-moon dV's against each other. What I don't understand is why the capture dV for Eve is less than the Eve-Gilly transfer dV.

[stupid_chris]

What I don't understand is why the capture dV for Eve is less than the Eve-Gilly transfer dV.

Because Gilly sits on an inclined and eccentric orbit.

[Frederf]

Perhaps that's a bad example then. Can you take the Kerbin-Duna and Duna-Ike figures and though any simple math express Kerbin-Ike as a result of that?

[Sathurn]

edit my fail.

Edited July 19, 2013 by Sathurn

[metaphor]

Yes these maps are misleading. You wouldn't go to a low orbit around a planet and then burn back up to reach its moons since that's very inefficient. The more efficient way to do it is to get an intercept with the planet, and then burn retrograde at periapsis until your apoapsis is at the moon's orbit, then burn again at apoapsis to meet the moon.

Here's a more accurate map I just made.

So for example if you wanted to go to Gilly, and you start in a 70 km Kerbin orbit:

Burn 680+180+70+20+90 m/s prograde to get into a Kerbin-Eve transfer orbit.

Plane change as needed and make course corrections so your Eve periapsis is at 100 km.

When you reach Eve periapsis, burn retrograde 80+60 m/s so that your apoapsis is at Gilly's orbit, plane change if needed.

Burn 400+10 m/s at Gilly to get into a low Gilly orbit. (In reality Gilly is not going to be at the exact place you want so you can do something like burn 100 m/s to get a Gilly intercept on the next orbit and then 300+10 m/s to get into low Gilly orbit.)

Edited July 23, 2013 by metaphor

[espm400]

~snip~

You see I am also really interested in this because of Jool's moons. It's not that difficult to aim for those moons when approaching. And I don't like aerocapture - it has never been done in RL. Even iterative aerobraking with an orbit insertion burn has been done only on Mars and Earth but never on the bigger planets. Galileo didn't do it on Jupiter, Cassini didn't do it on Saturn. That's because it's really difficult to predict how it will turn out.

If you think aerobraking is too 'cheaty' or unrealistic, why not get the Deadly Re-Entry mod? I use that one (among others) to bump up the level of realism in my game. Generally speaking, I only use light aerobraking to circularize an eliptical orbit (see: MRO), but when it comes to my Jool moon missions, I tend to scrub off a bit of dV in the upper atmosphere. Combined with a gravity assist whenever possible, can save you a lot dV without creating ship-disintegrating g-forces or heat. Actually, now that I think of it, I don't think I've ever gone from Kerbin directly to a non-Kerbin moon...

Edited July 24, 2013 by espm400

[rpayne88]

Can it be done on theory? Yes. is it practical for a noob (or any KSP player outside of the few who work at JPL) to be doing that? Not unless you want to put a crater in Gilly after several dozen quickloads. What your talking about is basically hitting a moon form LKO that may be on the other side of Kerbol with what, for all intents and purposes, is a bullet. True, you can control your craft by using somewhat inaccurate maneuver nodes. But the thing is, if your off by just a few hundredths of a m/s, you'll miss. That means expending dv to change your trajectory to intercept Gilly once your in it's SOI. And, as said above, you will be moving at a very high velocity. Gilly may have low gravity (so low that some players find it necessary to burn straight down towards it,) but Kerbol doesn't. You will be screaming in with your hair on fire doing a direct injection burn form LKO. That means that even if your trajectory lands on Gilly, you will still need to bleed off copious amounts of velocity to avoid winding up as a smoking crater in the surface. Even then, you may not have enough time if your engines are not powerful enough. My suggestion, like everyone else, would be to go into LEO (low Eve orbit) and then transfer to Gilly. Its easier and allows you to leave your transfer stage in Eve orbit with a much higher velocity making a trans-Kerbin injection all the easier.