How to make Body Closest Approach nodes behave

[natsirt721]

This fine morning I was attempting to send a mission to Moho. I fired up AlexMoon's transfer calculator and found a dandy transfer the mercurial planet. Plugging the escape velocity into my maneuver node I looked at the closest approach indicator to Moho. 12e9 km?? That's not right? I fiddled with the time and burn vector a bit but I couldn't manage to make it anything less than 1.9e9 km. "Something's not right here" I said to myself, "AlexMoon's a smart dude, he wouldn't lie to me like that".

So I started thinking, why would my closest approach indicator be incorrect? The conclusion that I arrived at was that the indicator finds the first local minimum distance from the maneuver rather than the global minimum distance.  "Gee, that's pretty annoying, the indicator should probably search one full orbital period and show the minimum for that time, not just search until a local min is found," I said,  "In general, the method works fine, but once you start using non-hohmann transfers where the relative geometry of your spacecraft and the body becomes more complicated, it completely breaks down."

Then the epiphany hit. The indicator always shows the local minimum after the last node on the plan, the same way that the node line indicators do. Could I trick the game into searching further in time by placing another maneuver node with no dV later along my path?

As it turns out, I could.  By placing an empty node past the reported time of closest approach and sliding it along my planned trajectory towards where I expected the encounter to be, the closest approach indicator jumped to the new node and followed it all the way to the encounter.  By setting the time of the dummy node directly when I expected to arrive at Moho, it was a trivial matter to tweak the burn vector and time to achieve an encounter.  I suspect that this tactic will also work for vessel-vessel transfers, but I have yet to implement it there.

Note: This was achieved with an old game, and may not even be applicable for new versions.

[Superfluous J]

I've done this before to find actual encounters in the future. Never tried it to find a tricky encounter with another world. I'll have to give it a try.

[Geschosskopf]

I've said it before and I'll say it again....

All the transfer window calculators go by ejection angle based on the 2-dimensional angle between the starting and target planets.  This is totally the wrong thing to do with Moho.  If this is all you care about, you'll get a Moho encounter just fine, but you'll find that you're crossing its orbit at a steep angle, meaning you have a lot of velocity relative to Moho.  Which means your capture burn will be in the range of 4000-6000m/s despite the relatively cheap transfer burn.

So, the whole trick to getting to Moho is minimizing the capture burn, putting it down in the region you expect (and as shown on the dV map) for a planet of comparable size.  To do this, you need to make your velocity vector as close to parallel (as seen from above in 2D) with Moho's orbit at intercept as possible, so your velocity relative to Moho in its SOI is as small as possible.  This can only be done from an orbit inside of Eve.

Thus, what you do is leave Kerbin when Kerbin is on Moho's AN/DN line.  Pay no attention AT ALL to where Moho is at that time, only Kerbin's position matters.  Your transfer burn is aimed to put your Ap (while still in Kerbin's SOI) at whichever of Moho's AN or DN is on the opposite side of the sun.  Once you're in solar orbit, that point becomes your Pe and your Ap is up at Kerbin's orbit.  It is highly unlikely that Moho will be anywhere near your solar Pe when you get there.  Hope it isn't.  If it its, don't try to capture but gravity brake off it to lower your solar Ap down below Eve's altitude.

Regardless, your next step is to pull your solar Ap down to somewhere between Moho and Eve, so you're fairly close to the sun (for a "relatively" fast orbital period) but have a different orbital period than Moho.  After a few solar orbits, eventually you and Moho will sync up at your solar Pe and you'll get an encounter.    And then your capture burn will only be a few hundred m/s, as shown on the dV map.  And because you're hitting Moho at its AN or DN, you don't need any plane change to get there from Kerbin, so the total transfer burn (although done in 2 steps) is also about what the dV maps shows.  Going back home is kinda the reverse of this process.  Leave Moho at its AN or DN with Kerbin, then coast between  Kerbin and Eve until you sync up.  The trip can take several years overall but isn't that expensive on fuel.  As usual in KSP, you have a choice of fuel or time.

As an alternative to the above, you can leave Kerbin at a transfer window for Eve.  Aim for an Eve intercept but cut inside it so you gravity brake and get your solar Pe down about to Moho's altitude.  Then you'll have to adjust your solar Pe to either Moho's AN or DN, usually involving some radial as well as retrograde.  Then wait 1 or more solar orbits to sync up.  This method is not quite as fuel efficient as the bi-elliptic transfer but it's not that much worse, so can be used on the rare occasions when you need to start before Kebin is lined up on Moho's AN/DN line, if Eve happens to be lined up for a transfer just then.

Edited June 15, 2019 by Geschosskopf

[Xavven]

@Geschosskopf Good writeup.  I also have in my personal notes that AN/DN node is more important than phase for Moho.

 

@natsirt721 I've also found this to be the case in detecting intercepts for orbital rendezvous with other spacecraft. It's a good trick to know for KSP.

[natsirt721]

@Geschosskopf While your tactic might make it technically easier to execute, I don't see that it actually saves you any dV.  The launch planner I used correctly gave the the transfer and injection burn vectors, which I agree were significantly higher than the dV map said, but that's why I used the planner instead of the map. I would expect that the intermediate burn to bring your aphelion down to phase with Moho makes up for the injection dV.  Although, there are probably some savings from staying coplanar with Kerbin.  I'll have to try it next time I need to go there.

[Snark]

On 6/14/2019 at 6:02 PM, natsirt721 said:

By placing an empty node past the reported time of closest approach and sliding it along my planned trajectory towards where I expected the encounter to be, the closest approach indicator jumped to the new node and followed it all the way to the encounter.  By setting the time of the dummy node directly when I expected to arrive at Moho, it was a trivial matter to tweak the burn vector and time to achieve an encounter.

Yup.  Actually, it's even better than that:  you can use this little trick to plan an intercept multiple orbits into the future.  (Pretty similar to what @Geschosskopf describes above, except that you can plan the encounter from the get-go without having to actually time-warp through multiple orbits to see where you're going.)

Let's say I want to go to Moho, and I want to simplify the problem caused by the fact that its orbit has a fair bit of inclination to it.  The easiest way to do that is to launch from Kerbin when I'm at its AN / DN relative to Moho's orbit.  But of course that won't be the "correct" launch window to Moho.  So here's what I can do:

1. Wait until Kerbin is at the AN / DN relative to Moho's orbit, and launch solar with enough dV that my Pe precisely kisses (i.e. is tangent to) Moho's orbit at the opposite node.
2. Place a node right at solar Pe (i.e. at the place where my orbit touches Moho's) but don't give it any dV yet.
3. The "closest approach" marker now shows where Moho will be after that.
4. I could do one big huge burn to lower my Ap until I get a Moho encounter at my second Pe... but suppose I don't want to do that (for example, it gives up a lot of Oberth benefit due to not doing my braking burn low over Moho).
5. So I then place a "dummy" node out at Ap (after my first Pe, where I dropped the first node in step 2 above).
6. Now I click the + button on the dummy node.  Note that the "closest approach" marker for Moho jumps to a new location.  That's because it's now showing the closest approach an extra orbit into the future.
7. Is this new approach pretty close?  Yes?  Then great.  No?  Okay, click + again to jump ahead another orbit into the future.
8. When I'm reasonably satisfied with the approach... go back to my initial node at Pe (the one I created at step 2) and start giving it some dV in the solar direction.
9. Note how quickly the closest approach marker moves, with just a little bit of dV!  That's because it's "amplified" N times, where N is the number of orbits ahead I've gone.

This allows getting an encounter with the target with a smaller burn, as long as one is willing to wait more orbits for the encounter to happen.

I've also used this technique to good effect for rescuing kerbals in LKO when I want to use one mission to rescue multiple kerbals.  Using the multi-orbit rendezvous lets me sweep up extra kerbals with very tiny amounts of dV expenditure. 

[natsirt721]

Wow. That is...brilliant. I'm going to use that extensively for my OPM orbiters.

[Geschosskopf]

11 hours ago, natsirt721 said:

@Geschosskopf While your tactic might make it technically easier to execute, I don't see that it actually saves you any dV.  The launch planner I used correctly gave the the transfer and injection burn vectors, which I agree were significantly higher than the dV map said, but that's why I used the planner instead of the map. I would expect that the intermediate burn to bring your aphelion down to phase with Moho makes up for the injection dV.  Although, there are probably some savings from staying coplanar with Kerbin.  I'll have to try it next time I need to go there.

As I said, the killer at Moho is the CAPTURE burn, NOT the transfer burn.  If you go to Moho directly from Kerbin, you cannot help but enter Moho's SOI at something approximating a right angle to Moho's motion.  This makes the capture burn be in the range of 4000-6000 m/s.  First, you have huge velocity transverse to Moho's orbit due to your steep dive from Kerbin, which you have to kill off completely.  Then you have to create a huge velocity in the same direction Moho is going, and it's going quite fast across your bow because it's so close to the sun.

To avoid this problem, you have to approach Moho at a much shallower angle.  This requires getting there from a much more circular orbit.  And to create such an orbit that intersect's Moho's, your Ap has to be inside of Eve's orbit.  This is why you do a bi-elliptic transfer.  The 1st ellipse is the initial burn out from Kerbin, which puts your solar Pe at Moho's orbit.  The 2nd ellipse is the one that pulls your solar Ap down inside of Eve.

So yeah, the 2nd transfer burn adds to what you already burned for the direction trip.  HOWEVER, it reduces the capture burn down to a few hundred m/s, so like a 90% savings.  THAT's where you save the dV.  And if you don't think saving several thousand dV is significant, you probably have UFO technology and don't bother with orbital mechanics anyway

And as I said, by aiming for the the AN or DN, you totally skip spending even more dV on plane changes.

[natsirt721]

I understand the concept of a three-burn phasing intercept, but in cases where the semi-axis ratio is less that about 12, (starting to destination) the bi-elliptic transfer has at best equal performance to a direct transfer, and inferior performance to a pure hohmann.  From wikipedia:

Quote

One sees that the Hohmann transfer is always more efficient if the ratio of radii  is smaller than 11.94. On the other hand, if the radius of the final orbit is more than 15.58 times larger than the radius of the initial orbit, then any bi-elliptic transfer, regardless of its apoapsis radius (as long as it's larger than the radius of the final orbit), requires less  than a Hohmann transfer. Between the ratios of 11.94 and 15.58, which transfer is best depends on the apoapsis distance . For any given in this range, there is a value of  above which the bi-elliptic transfer is superior and below which the Hohmann transfer is better.

Now yes, if you're trying to do a pure hohmann from Kerbin to Moho, you're going to have a bad time because hohmann transfers assume the destination is coplanar with your origin, and you're going to pay dearly for a 7 degree inc change in heliocentric space. But that's just a lack of understanding of when to use a hohmann transfer - you should be using a Lambert solution for complex transfers like this.

I tested this in sandbox, executing the kerbin escape burn and using nodes to SWAG the rest of the flightplan. Starting from a 6,000km circular Kerbin orbit and resulting in an inclined 30km circular Moho orbit, the three-burn approach took about 320 days and cost this much:

Burn	dV
Kerbin Escape	1517
Course Correction	53
Perihelion Phasing Burn	1162
Moho Insertion	2583
Total	5315

The perihelion burn was the lowest dV cost to achieve a one-period Moho intercept. I could have reduced my aphelion further to reduce my insertion burn, but I'm not going to save thousands of m/s by burning at perihelion rather than at Moho.  Like my previous post postulated, this method was technically very easy to execute and required little to no fiddling with nodes to achieve intercept.

The direct lambert transfer took about 95 days and cost this much:

Burn	dV
Kerbin Escape	2493
Course Correction	55
Moho Insertion	2805
Total	5353

The planner I used put my transfer ellipse at a 5.5 degree inc w.r.t. Moho and about 8.7 degree inc w.r.t. Kerbin. It estimated the total dV cost at 5316, which - allowing for course correction and steering losses - is pretty much exactly what the nodes give.

Energy is energy, and in a two-body environment there isn't a lot you can do other than pray to lord Oberth and burn at your maximum velocity.  Adding the phasing burn makes the other two more mild, but at the end of the day, you still need to affect a total change in energy to capture at Moho.  You're not going to oberth your way out of 40% of your energy costs, at least not for this transfer.

I think we can both agree on one thing though, and that is you shouldn't use a hohmann transfer to get to Moho.

Edited June 16, 2019 by natsirt721
reorder some paragraphs

[Xavven]

All good points. My 2 cents:

1. You still have to do an inclination change one way or another. The question is whether you end up doing that in solar orbit, or in Moho's SOI to take advantage of its gravity.
2. You save some dV by using Moho's gravity. Moho's gravity isn't strong, so the Oberth effect is small, but it's not insignificant either.
3. If you do most of your dV burn in one place (such as while in Moho orbit) then you're going to need a good TWR or else you'll incur steering losses, or worse yet, fail to capture in time and leave Moho's SOI. Higher TWR comes at the cost of a bigger, heavier engine, and more weight on an upper stage like this has profound effects all the way down to your first stage.
4. In my personal experience, one of the worst things you can do when trying to get to Moho is haphazardly fiddle with the maneuver node until you get any old intercept. Most likely you're going to have a huge radial component to the capture burn. You need your solar PE to gracefully kiss the edge of Moho's orbit, which minimizes the radial component, and if you do it at an AN/DN then you can use the Oberth effect, however small, from Moho to help with the inclination change.

[Geschosskopf]

28 minutes ago, Xavven said:

All good points. My 2 cents:

1. You still have to do an inclination change one way or another. The question is whether you end up doing that in solar orbit, or in Moho's SOI to take advantage of its gravity.

Unless you're planning on docking with a pre-existing station in Moho orbit, there's no need for an inclination change upon arrival there.  Being in an inclined orbit gives you more choices of landing sites.  If you're worried about your inclination for the return trip, don't be.  30^ inclination at Moho equates to far, far less once back in solar orbit.  But if it does bug you, build the lander so it can make at least 1 surface hop (so you can hit 2 biomes).  Land anywhere the 1st time, then hop to the equator.  And of course, then leave when Moho is at its AN or DN with Kerbin.

 

28 minutes ago, Xavven said:

1. If you do most of your dV burn in one place (such as while in Moho orbit) then you're going to need a good TWR or else you'll incur steering losses, or worse yet, fail to capture in time and leave Moho's SOI. Higher TWR comes at the cost of a bigger, heavier engine, and more weight on an upper stage like this has profound effects all the way down to your first stage.

This only happens with a poor intercept, as in crossing Moho's orbit at a steep angle.  If you do a bi-elliptic transfer, you can get the capture burn down to a few hundred m/s, for which you have plenty of time even with a weak engine.

 

28 minutes ago, Xavven said:

1. In my personal experience, one of the worst things you can do when trying to get to Moho is haphazardly fiddle with the maneuver node until you get any old intercept. Most likely you're going to have a huge radial component to the capture burn. You need your solar PE to gracefully kiss the edge of Moho's orbit, which minimizes the radial component, and if you do it at an AN/DN then you can use the Oberth effect, however small, from Moho to help with the inclination change.

That only solves half the problem.  Even if careful node tinkering irons out your radial velocity relative to Moho, it does so at the expense of increasing your velocity parallel to Moho.  Having just done a steep dive down to Moho from Kerbin, your ship is hauling ass with respect to Moho, even if going the same direction.  Thus, the capture burn is still huge, usually in the 2000-3000m/s range.  But by lowering your solar Ap with the bi-elliptic method, you greatly reduce your relative velocity to Moho at the intercept, so the capture burn is in the hundreds instead of thousands.

[Xavven]

20 minutes ago, Geschosskopf said:

Unless you're planning on docking with a pre-existing station in Moho orbit, there's no need for an inclination change upon arrival there.  Being in an inclined orbit gives you more choices of landing sites.  If you're worried about your inclination for the return trip, don't be.  30^ inclination at Moho equates to far, far less once back in solar orbit.  But if it does bug you, build the lander so it can make at least 1 surface hop (so you can hit 2 biomes).  Land anywhere the 1st time, then hop to the equator.  And of course, then leave when Moho is at its AN or DN with Kerbin.

 

This only happens with a poor intercept, as in crossing Moho's orbit at a steep angle.  If you do a bi-elliptic transfer, you can get the capture burn down to a few hundred m/s, for which you have plenty of time even with a weak engine.

 

That only solves half the problem.  Even if careful node tinkering irons out your radial velocity relative to Moho, it does so at the expense of increasing your velocity parallel to Moho.  Having just done a steep dive down to Moho from Kerbin, your ship is hauling ass with respect to Moho, even if going the same direction.  Thus, the capture burn is still huge, usually in the 2000-3000m/s range.  But by lowering your solar Ap with the bi-elliptic method, you greatly reduce your relative velocity to Moho at the intercept, so the capture burn is in the hundreds instead of thousands.

I'm meaning to refer to the inclination of Moho vs. Kerbin, with respect to the sun. I think of transferring to Moho as an orbital rendezvous, but where your target has a gravity well you can exploit for gravity assistance. Basically, even if you capture at an AN/DN of Moho, you inherited a 7 degree inclination difference from Kerbin that you have to work off one way or another. You can do that in solar orbit, or you can do that as part of your capture burn at Moho, but either way, your orbit with respect to the sun has to change inclination by 7 degrees. Doing it in Moho's SOI just uses Moho's gravity to assist, reducing your dV expenditure.

I'm not sure what you mean by bi-elliptic transfer in this case. My understanding of it is wikipedia-level: https://en.wikipedia.org/wiki/Bi-elliptic_transfer. I thought a bi-elliptic meant raising your Ap far beyond the new orbit you wish to transfer to, raising/lowering your Pe at the extreme Ap, then finally lowering your extreme Ap. What you're describing is (I think) lowering your Ap with respect to the sun twice (not raising it above Kerbin first), splitting up the burn in two places -- one in solar orbit and one while in Moho's SOI, so that you don't have one big burn. It doesn't decrease your total dV required though. If anything, it increases your dV requirement because part of your burn is in solar orbit where you're not making use of Moho's gravity well.

Lastly, radial-in/radial-out burns are the least efficient way to change your orbital energy. Prograde/Retrograde are generally the most efficient. So your increase your dV requirements in total by crossing Moho's orbit in such a way that you need a radial component to your burn with respect to the sun.

I think we'd be more on the same page if you totaled the dV required on all of your burns starting from LKO, not just your final capture burn.

[natsirt721]

Bi-elliptic, using the procedure he outlined here (or scroll up).

I find that putting my Moho periapse high up helps to mitigate steering losses, as Moho's gravity doesn't buy you a lot of help from Oberth, and the lower your periapse the worse your steering losses are, for a given TWR.  Current mission has a maximum acceleration of ~2 m/s^2, so I put the periapse around 2500 km. That high, you're moving basically straight through Moho's SOI so your steering losses are negligible, even for the 15-20 minute burn. I usually end up with my apoapsis in the 2400-2500 km range and my periapse grazing the surface, and I don't care about inclination, but 30-50 deg is good for surface coverage.  Then when you have to leave, your velocity at apoapsis is pretty small, and you can just burn like hell in the direction you need to go in order to escape.  You just need to make sure the lander has a few hundred m/s extra to land from the highly elliptical orbit.

[Nicky21]

Thank you for this post. It saved many of my still brown hairs from turning white.