Orbital mechanics question (oberth related)

[jab136]

Just wondering, if I want to go from the surface of the mun (or minimus) to a transfer orbit to say duna is it more efficient to do a burn in such a way as to

1) go straight from the starting velocity of 0 to an escape trajectory from kerbin

or

2) would it be more efficient to make a burn to put myself in an orbit with ap at the radius of the mun, pe at ~70km and then make a burn at pe to put myself on the transfer orbit.

I was thinking the calculation would be for

1)dV= transfer dV from kerbin to destination + (dV required to get from stationary on mun to escape from mun + orbital velocity of mun + dV required to get from escape from mun to escape from kerbin)

2)dV= transfer dV from kerbin to destination + (dV required to get from stationary on mun to escape from mun trajectory that would give pe of 70 km + dV required to get from eliptical orbit to escape from kerbin

I just attempted the calculation using my equations and it gave me the solution that a prograde escape burn from the mun would put me on an escape trajectory from kerbal (the orbit equation is giving me a negative semi major axis when I use the sum of the orbital velocity of the mun and the escape velocity of the mun with the radius of the mun) which is not true, and that a retrograde burn would put me in a retrograde orbit around kerbin. what am I doing wrong? My issue is probably with relative velocities, as I have always found those to be confusing.

Dr. Melton, if you are reading this, sorry, I should have been paying more attention in Orbital Mechanics instead of playing KSP, but you probably are not on this forum so I think I am safe

+1 jebs if you aren't Dr. Melton and you know where I go to school without the help of google

+2 jebs if you know who I am from this post

thank you to everyone who posted, it appears that my question was answered

Edited July 22, 2014 by jab136

[Cerberus738]

I would say it's more efficient to burn straight from the surface to an escape. you wouldn't be wasting any deltaV circularizing your orbit. If you wait until the mun is in the right position you could launch straight off the surface into an escape and have your resultant solar orbit fairly close to an intercept. I expect that would take some significant planning though and i cannot help you with that.

[jab136]

I wasn't planning on circularizing my orbit, the whole maneuver would be three burns, takeoff to escape from mun/elliptical trajectory around kerbin, burn at pe of kerbin, burn at duna

[Aethon]

If you're already fully fueled on the mun, wait 'till the mun lines up with Kerbin pro/retro grade and swing by Kerbin for the Oberth effect. It can be tricky to line it up for a short (say moho bro) transfer window but the dv savings will be worth it!

Nija'd sorta

[jab136]

yah I thought so, but I kinda want to know the actual dV savings, and my equation is obviously off, can anyone troubleshoot the equations I posted?

[Eric S]

I used to do this a lot when I was using Kethane, but with Minmus instead of the Mun, since it took less fuel to land and take off from Minmus.

I don't remember how much it saved, but it definitely took less delta-v to depart Minmus with a low Kerbin periapsis and then burn at the periapsis while swinging past Kerbin. The timing was tricky, but could be done. I suspect that the same holds true for the Mun, but I'm not certain.

[Red Iron Crown]

The transfer to Duna is so small a burn that the drop to low Kerbin altitude will likely only save you a handful of dV overall, probably not worth the effort and complication.

Now, if you were doing a much bigger burn, like to Jool or Moho, the savings would be greater and likely worthwhile.

[r_rolo1]

Whille Duna might not be the best example, it is always better to burn near the bottom of the parent gravity well, both for efficiency and to change inclination ( it is far cheaper to use the parent body gravity to do that work for you ).

Actually I remember a Scott Manley video from 0.16 ( just before planets were put into the game ), that dealt with that issue exactly:

P.S. Full disclosure: I do remember this video because it was pretty much the only time I taught something to Scott Manley on KSP ( the person he mentions in the beginning of the video is me ). Most of the times it is the other way around

Edited July 22, 2014 by r_rolo1

[jab136]

I had some time to think about this, and I think I realized what my issues with calculation were, re-doing now will post again later if I don't get it right

[Yasmy]

Here's a table of the approximate costs of going from a low orbit (~10 km above ground or atmosphere) to around a moon to a planet other than the moon's parent, ignoring inclination and eccentricity. The table compares three methods:

1) Dropping down to the parent planet (~ 50km if no atmosphere, atmosphere + 10k otherwise) for the interplanetary transfer burn.

2) Going interplanetary from the moon directly.

3) For comparison, the cost of going from the parent, not starting at the moon.

Nephew ->  Uncle:  Moon->Parent->Uncle  Moon->Uncle  Parent->Uncle
 Gilly ->   Moho:          776.2           1366.6        1643.4
 Gilly -> Kerbin:          506.7            497.3        1373.4
 Gilly ->   Duna:          775.1           1363.7        1642.3
 Gilly ->   Dres:         1308.3           2475.7        2176.5
 Gilly ->   Jool:         1647.9           3047.7        2516.7
 Gilly ->  Eeloo:         1785.8           3263.9        2654.7
   Mun ->   Moho:         1135.4           1509.0        1698.5
   Mun ->    Eve:          462.1            348.0        1024.1
   Mun ->   Duna:          497.6            414.1        1059.7
   Mun ->   Dres:          987.4           1278.5        1550.3
   Mun ->   Jool:         1360.5           1840.5        1923.9
   Mun ->  Eeloo:         1520.3           2064.9        2083.8
Minmus ->   Moho:          943.4           1957.7        1698.5
Minmus ->    Eve:          270.1            439.7        1024.1
Minmus ->   Duna:          305.6            566.8        1059.7
Minmus ->   Dres:          795.4           1699.9        1550.3
Minmus ->   Jool:         1168.5           2318.7        1923.9
Minmus ->  Eeloo:         1328.2           2558.7        2083.8
   Ike ->   Moho:         1969.9           2158.6        2117.9
   Ike ->    Eve:          907.9            975.0        1055.4
   Ike -> Kerbin:          464.4            421.2         611.4
   Ike ->   Dres:          658.5            671.2         805.7
   Ike ->   Jool:         1158.0           1265.7        1305.7
   Ike ->  Eeloo:         1381.6           1517.6        1529.4
Laythe ->   Moho:         2228.4           1272.9        3134.9
Laythe ->    Eve:         2108.9           1131.3        3015.4
Laythe -> Kerbin:         2048.8           1062.7        2955.2
Laythe ->   Duna:         1979.5            986.3        2885.9
Laythe ->   Dres:         1905.8            908.7        2812.1
Laythe ->  Eeloo:         1892.9            895.6        2799.2
  Vall ->   Moho:         1834.8           1334.3        3134.9
  Vall ->    Eve:         1715.3           1098.9        3015.4
  Vall -> Kerbin:         1655.2            980.1        2955.2
  Vall ->   Duna:         1585.9            844.0        2885.9
  Vall ->   Dres:         1512.2            701.9        2812.1
  Vall ->  Eeloo:         1499.3            677.6        2799.2
  Tylo ->   Moho:         1807.1           1298.3        3134.9
  Tylo ->    Eve:         1687.6           1140.9        3015.4
  Tylo -> Kerbin:         1627.5           1067.0        2955.2
  Tylo ->   Duna:         1558.2            987.7        2885.9
  Tylo ->   Dres:         1484.5            912.6        2812.1
  Tylo ->  Eeloo:         1471.6            900.7        2799.2
   Bop ->   Moho:         1451.6           1652.4        3134.9
   Bop ->    Eve:         1332.1           1275.0        3015.4
   Bop -> Kerbin:         1272.0           1068.1        2955.2
   Bop ->   Duna:         1202.7            810.9        2885.9
   Bop ->   Dres:         1129.0            510.4        2812.1
   Bop ->  Eeloo:         1116.1            454.9        2799.2
   Pol ->   Moho:         1335.3           1739.4        3134.9
   Pol ->    Eve:         1215.8           1332.0        3015.4
   Pol -> Kerbin:         1155.7           1104.1        2955.2
   Pol ->   Duna:         1086.4            814.5        2885.9
   Pol ->   Dres:         1012.7            461.6        2812.1
   Pol ->  Eeloo:          999.8            394.0        2799.2

Like Red Iron Crown suggested, going directly to Eve or Duna from the Mun is cheaper than dropping down and performing the interplanetary burn at Kerbin, but going to any other planet directly from the Mun is more expensive. Also note that dropping down to the parent planet can be used to perform a cheap inclination change for some transfers.

I don't have time to type up the equations at the moment. It's just a series of applications of the vis-viva equation, and taking into account the orbital velocity of a body when you cross its SOI.

Edited July 22, 2014 by Yasmy

[LethalDose]

I think someone has shown that an Oberth maneuver from Minmus tends to be dV saving, but from the Mun, it tends to be more costly (I didn't dig in to check the numbers on the table above). This tends to be caused by the Larger dV cost to escape the Mun, and the smaller benefit of the Muns lower orbit.

It works great from Minmus, though.

[Xavven]

Nice one, Yasmy! Your table demonstrates that it's not always the best to drop down to the parent planet. If you're already orbiting a massive body and it's in a low orbit (like Tylo, for example) then your combined orbital velocity with respect to the Sun (Kerbol) is already very high.

If you're orbiting a small moon in high orbit, it makes sense to drop down to the parent planet only if your destination is far away. With neighboring planets, the Oberth effect doesn't make up for the dV you spend lowering your periapsis.

[Jimbimbibble]

Also, keep in mind that you have a good chance of missing your launch window if you're trying to hit Duna via Mun or Minimus. I would do whatever is easiest to pilot because we're only talking about less than 200m/s here. Your best bet is just to go strait from LKO rather than potentially miss the window by days and have the burn cost a lot more dV.

[metaphor]

Very nice chart Yasmy.

Also here's a visual guide from reddit.

The relevant Kerbin system:

[jab136]

Here's a table of the approximate costs of going from a low orbit (~10 km above ground or atmosphere) to around a moon to a planet other than the moon's parent, ignoring inclination and eccentricity. The table compares three methods:

1) Dropping down to the parent planet (~ 50km if no atmosphere, atmosphere + 10k otherwise) for the interplanetary transfer burn.

2) Going interplanetary from the moon directly.

3) For comparison, the cost of going from the parent, not starting at the moon.

Nephew ->  Uncle:  Moon->Parent->Uncle  Moon->Uncle  Parent->Uncle
 Gilly ->   Moho:          776.2           1366.6        1643.4
 Gilly -> Kerbin:          506.7            497.3        1373.4
 Gilly ->   Duna:          775.1           1363.7        1642.3
 Gilly ->   Dres:         1308.3           2475.7        2176.5
 Gilly ->   Jool:         1647.9           3047.7        2516.7
 Gilly ->  Eeloo:         1785.8           3263.9        2654.7
   Mun ->   Moho:         1135.4           1509.0        1698.5
   Mun ->    Eve:          462.1            348.0        1024.1
   Mun ->   Duna:          497.6            414.1        1059.7
   Mun ->   Dres:          987.4           1278.5        1550.3
   Mun ->   Jool:         1360.5           1840.5        1923.9
   Mun ->  Eeloo:         1520.3           2064.9        2083.8
Minmus ->   Moho:          943.4           1957.7        1698.5
Minmus ->    Eve:          270.1            439.7        1024.1
Minmus ->   Duna:          305.6            566.8        1059.7
Minmus ->   Dres:          795.4           1699.9        1550.3
Minmus ->   Jool:         1168.5           2318.7        1923.9
Minmus ->  Eeloo:         1328.2           2558.7        2083.8
   Ike ->   Moho:         1969.9           2158.6        2117.9
   Ike ->    Eve:          907.9            975.0        1055.4
   Ike -> Kerbin:          464.4            421.2         611.4
   Ike ->   Dres:          658.5            671.2         805.7
   Ike ->   Jool:         1158.0           1265.7        1305.7
   Ike ->  Eeloo:         1381.6           1517.6        1529.4
Laythe ->   Moho:         2228.4           1272.9        3134.9
Laythe ->    Eve:         2108.9           1131.3        3015.4
Laythe -> Kerbin:         2048.8           1062.7        2955.2
Laythe ->   Duna:         1979.5            986.3        2885.9
Laythe ->   Dres:         1905.8            908.7        2812.1
Laythe ->  Eeloo:         1892.9            895.6        2799.2
  Vall ->   Moho:         1834.8           1334.3        3134.9
  Vall ->    Eve:         1715.3           1098.9        3015.4
  Vall -> Kerbin:         1655.2            980.1        2955.2
  Vall ->   Duna:         1585.9            844.0        2885.9
  Vall ->   Dres:         1512.2            701.9        2812.1
  Vall ->  Eeloo:         1499.3            677.6        2799.2
  Tylo ->   Moho:         1807.1           1298.3        3134.9
  Tylo ->    Eve:         1687.6           1140.9        3015.4
  Tylo -> Kerbin:         1627.5           1067.0        2955.2
  Tylo ->   Duna:         1558.2            987.7        2885.9
  Tylo ->   Dres:         1484.5            912.6        2812.1
  Tylo ->  Eeloo:         1471.6            900.7        2799.2
   Bop ->   Moho:         1451.6           1652.4        3134.9
   Bop ->    Eve:         1332.1           1275.0        3015.4
   Bop -> Kerbin:         1272.0           1068.1        2955.2
   Bop ->   Duna:         1202.7            810.9        2885.9
   Bop ->   Dres:         1129.0            510.4        2812.1
   Bop ->  Eeloo:         1116.1            454.9        2799.2
   Pol ->   Moho:         1335.3           1739.4        3134.9
   Pol ->    Eve:         1215.8           1332.0        3015.4
   Pol -> Kerbin:         1155.7           1104.1        2955.2
   Pol ->   Duna:         1086.4            814.5        2885.9
   Pol ->   Dres:         1012.7            461.6        2812.1
   Pol ->  Eeloo:          999.8            394.0        2799.2

Like Red Iron Crown suggested, going directly to Eve or Duna from the Mun is cheaper than dropping down and performing the interplanetary burn at Kerbin, but going to any other planet directly from the Mun is more expensive. Also note that dropping down to the parent planet can be used to perform a cheap inclination change for some transfers.

I don't have time to type up the equations at the moment. It's just a series of applications of the vis-viva equation, and taking into account the orbital velocity of a body when you cross its SOI.

Thank you, I figured it was just the orbit equation, and vis-viva equation applied a bunch of times, I think I also failed to take into account that the magnitude of the exit velocity does not equal the velocity after the burn, even if you burn purely tangentially to the parent body, so my initial problem was a mistake on my part

[LethalDose]

The transfer to Duna is so small a burn that the drop to low Kerbin altitude will likely only save you a handful of dV overall, probably not worth the effort and complication.

Now, if you were doing a much bigger burn, like to Jool or Moho, the savings would be greater and likely worthwhile.

I was thinking about this... and I don't think the bolded part of this statement is correct: The savings is not destination dependent. Dropping down from orbit of a satellite in the same way is going to give you the same speed at Kerbin Pe, so the additional amount needed to reach escape velocity is always going to be the same, and then the dV to make the transfer is always going to the same static value. This is actually demonstrated on the table above, as the differences between the "Moon-parent-uncle" and "Parent uncle" entries are constant within 1-2 m/s.

Using the "Duna only saves you a handful of dV" vs Jool and Moho, If you crunch the numbers:

Minmus -> Duna saves 1059.7 - 305.6 = 754.1

Minmus -> Moho saves 1698.5 - 943.4 = 755.1

Minmus -> Jool saves 1923.9 - 1168.5 = 755.4

You can see it's ~ .75 km/s of dV savings across the board in absolute value, and therefore the proportionate savings is actually better for the smaller burns.

However, I won't debate that refueling around a moon prior to an Oberth maneuver is more worthwhile as the burns become longer because you can engineer an overall lower dV craft (can free up some mass for payload) and your ejection maneuver burn is shorter.

Unless by "savings" you mean overall craft mass savings instead of dV savings. You don't get dV savings, but if you're hauling less fuel, the fuel you do have is more efficient (more dV/ton), due to the "Tyranny of the rocket equation".

Edited July 22, 2014 by LethalDose
added example

[Red Iron Crown]

I was thinking about this... and I don't think the bolded part of this statement is correct: The savings is not destination dependent. Dropping down from orbit of a satellite in the same way is going to give you the same speed at Kerbin Pe, so the additional amount needed to reach escape velocity is always going to be the same, and then the dV to make the transfer is always going to the same static value. This is actually demonstrated on the table above, as the differences between the "Moon-parent-uncle" and "Parent uncle" entries are constant within 1-2 m/s

You're burning beyond escape velocity. The greater the difference between your destination's orbit and Kerbin's orbit, the more dV you will save by harnessing Oberth by dropping to low Kerbin altitude. Have a closer look at Yasmy's chart (which is excellent Yasmy, thanks for sharing):

 Nephew ->  Uncle:  Moon->Parent->Uncle  Moon->Uncle  
   Mun ->   Moho:         1135.4           1509.0        
   Mun ->    Eve:          462.1            348.0        
   Mun ->   Duna:          497.6            414.1        
   Mun ->   Dres:          987.4           1278.5        
   Mun ->   Jool:         1360.5           1840.5        
   Mun ->  Eeloo:         1520.3           2064.9        

You can see that dropping to low Kerbin altitude costs 214m/s extra for Eve, 83m/s extra for Duna, 374m/s less for Moho, 291m/s less for Dres, 480m/s less for Jool, and 544m/s less for Eeloo. It should be clear from this that the savings are not a fixed amount.

Edit: You edited your reply while I was replying. No offense, but you're reading the chart wrong. The values you're using are nephew->destination vs parent->destination; all that does is compute the dV required to transfer from Minmus' orbit to LKO which will not change. It is Nephew->Uncle vs. Nephew->Parent->Uncle that we're talking about, since we won't be circularizing at LKO. Basically, ignore the third column of the chart for the OP's example since we're not considering burning directly from LKO.

Edited July 22, 2014 by Red Iron Crown
Fixed some minor errors.

[LethalDose]

You're burning beyond escape velocity. The greater the difference between your destination's orbit and Kerbin's orbit, the more dV you will save by harnessing Oberth by dropping to low Kerbin altitude. Have a closer look at Yasmy's chart (which is excellent Yasmy, thanks for sharing):

 Nephew ->  Uncle:  Moon->Parent->Uncle  Moon->Uncle  
   Mun ->   Moho:         1135.4           1509.0        
   Mun ->    Eve:          462.1            348.0        
   Mun ->   Duna:          497.6            414.1        
   Mun ->   Dres:          987.4           1278.5        
   Mun ->   Jool:         1360.5           1840.5        
   Mun ->  Eeloo:         1520.3           2064.9        

You can see that dropping to low Kerbin altitude costs 214m/s extra for Eve, 83m/s extra for Duna, 374m/s less for Moho, 291m/s less for Dres, 480m/s less for Jool, and 544m/s less for Eeloo. It should be clear from this that the savings are not a fixed amount.

Edit: You edited your reply while I was replying. No offense, but you're reading the chart wrong. The values you're using are nephew->destination vs parent->destination; all that does is compute the dV required to transfer from Minmus' orbit to LKO which will not change. It is Nephew->Uncle vs. Nephew->Parent->Uncle that we're talking about, since we won't be circularizing at LKO. Basically, ignore the third column of the chart for the OP's example since we're not considering burning directly from LKO.

Okay, yeah we're talking about different things. I read the chart correctly, but I misunderstood the OP's question.

I'm comparing the cost of escape using Oberth Maneuver after escaping the satellite (which appears to be the Nephew-> Parent -> Uncle column) to the cost of leaving directly from low kerbin orbit (the Parent -> Uncle column).

You're comparing the cost of using an Oberth maneuver after escaping the satellite (again, nephew -> parent -> Uncle column) to the cost of escaping without an Oberth maneuver (the Nephew -> Uncle line). And from the look of it, that is OP's question: To Oberth, or not to Oberth?

But honestly, something strikes me as... "hinkey" about destination affecting the savings of the burn. If the following values are constant:

• initial altitude
  
• initial velocity
  
• target escape velocity

and Pe over parent is consistent (either just above the atmosphere for Oberth, or at the moon's altitude for not oberth), then the velocity at Pe (when you're perfoming the ejection maneuver) should be consistent.

And if your velocity at Pe is consistent, then Vtarget - VPe (the savings) should also be consistent...

Anyway, it doesn't really matter, because in all cases, Minmus should be a better place to start/refuel when using an Oberth maneuver to leave the Kerbin system than the Mun, and using an Oberth maneuver is always superior to not using an Oberth maneuver from Minmus. I get that the Mun was given in the OP's question as an example, but IMO it's a mediocre starting point, at best, for interplanetary travel.

In defense of my gaffe above, I will point out that this kind of question is almost always asked in terms of a Minmus refueling station.

[Yasmy]

There's nothing wrong with my math, to within the stated approximations.

Vtarget - VPe is consistent, but it is not the savings. It is merely the Vtarget minus the low-planetary-orbit to moon transfer delta-v, (if what you mean by Vtarget is the delta-v from LKO to enter another planet's SOI.)

The savings (or loss) is something like (dv to reach hyperbolic excess velocity V at the parent's SOI from the moon's orbit) - (dv to reach the same hyperbolic excess velocity V at the parent's SOI from parent on a return orbit from moon, ie, Vtarget) - (dv to drop the periapsis down from the moon to the parent).

That's not going to give a nice simple value for the savings as a function of the hyperbolic excess velocity V, or as a function of Vtarget.

Edited July 23, 2014 by Yasmy

[Red Iron Crown]

The amount of dV saved varying by destination is because the amount of orbital energy removed to drop to low Kerbin altitude is the same no matter the destination, but the amount of energy that must be added to eject varies greatly, and is larger the further the destination's orbit is from Kerbin. The more energy that needs to be added to the orbit, the more beneficial the Oberth effect becomes, because Oberth is multiplicative rather than additive. Think of it in terms of money: Say you can buy a 10% discount coupon for $10. You wouldn't buy it for a $50 item. It's only worthwhile to buy for items >$100, and the more expensive the item, the more savings the coupon is worth.