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the cheapest moho injection burn

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I am going to Moho and back with limited fuel, and I am using gravity assists to make things cheaper.

Shortly in the future I will have my last Kerbin flyby, which will send me on an Eve flyby, which will give the final correction for moho.

To have the lowest intercept speed, my final orbit must barely touch Moho's orbit; this requires putting the intercept on the opposite side of kerbol respective to my eve flyby. where I place the eve flyby, then, will determine where I can meet moho.

I have two options to reduce intercept speed. first, I can encounter eve when it's at the eve-moho planar change node. this way I can use eve's gravity to reduce orbital inclination compared to moho. reducing speed on the y axis will reduce overall intercept speed, i expect 200-300 m/s less.

Second option is to meet moho at apoapsis. at apoapsis orbital speed is lower, intercept speed is always lower for any rendez-vous when done at apoapsis. On the downside, meeting moho at apoapsis would require the highest plane change, especially coming from eve.

I probably have enough fuel to take a mildly suboptimal trajectory, but I ask anyway. Is it more convenient to use eve's flyby to match orbital plane, and meet moho halfway between apoapsis and periapsis, or is it more convenient to use eve to meet moho at apoapsis, while having the greatest planar difference?

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You're missing some crucial information: why are you going to Moho in the first place?

As in: is this a mission that just needs to orbit, any orbit, to do its job? Or does it need a low orbit? Does it need a polar orbit, or an equatorial one, or does it not matter at all? Is the craft meant to land? Can it land anywhere, or do you want to hit a specific biome, location, or anomaly?

This is relevant because while you can brake into a polar orbit from any direction, getting an equatorial one on the cheap is highly dependant on where you are approaching from. Do the two options you have end up differing in the approach vector they give you, and does that affect your planned mission profile?

Same thing with orbit height: the cheapest way to get a low orbit/surface is to put the periapsis as close to Moho as possible and make a fairly expensive braking burn. But the cheapest way to get any orbit is to put the periapsis at the edge of the SoI and make a fairly cheap braking burn.

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40 minutes ago, Streetwind said:

You're missing some crucial information: why are you going to Moho in the first place?

As in: is this a mission that just needs to orbit, any orbit, to do its job? Or does it need a low orbit? Does it need a polar orbit, or an equatorial one, or does it not matter at all? Is the craft meant to land? Can it land anywhere, or do you want to hit a specific biome, location, or anomaly?

This is relevant because while you can brake into a polar orbit from any direction, getting an equatorial one on the cheap is highly dependant on where you are approaching from. Do the two options you have end up differing in the approach vector they give you, and does that affect your planned mission profile?

Same thing with orbit height: the cheapest way to get a low orbit/surface is to put the periapsis as close to Moho as possible and make a fairly expensive braking burn. But the cheapest way to get any orbit is to put the periapsis at the edge of the SoI and make a fairly cheap braking burn.

i am sending my mothership on moho to drop a lander.

the mothership, for various mod-related reasons (use of kerbalism isru, needs water to make fuel, and there was no water on the more convenient places) must start from Ike and land back on Ike. From Ike I took a Kerbin flyby, which put me in a resonance for a subsequent kerbin flyby. I'm currently there.

When i am in moho orbit, I drop the lander. I don't need to circularize, I have another shuttle that can bring the lander to low orbit.

After moho, I will take a burn to eve, get an eve gravity assist, and use it - with multiple subsequent assists - to return to Duna.

I started at Ike orbit with 5400 m/s. I spent 380 to get the kerbin assist. at moho intercept I estimated 3000 m/s (by the deltaV map it should be less, but I have low thrust from nuclear engines, i factor in some inefficiency). Once it's time to leave moho, it takes 1000 m/s to reach eve. From there I try to get all the way to Duna with just gravity assist, aerobrake at Duna, and get to Ike. I will need some 150-200 m/s to capture and circularize around Ike, and I have 250 m/s high thrust I'll use for landing - but I'll need an additional 200 m/s low thrust too.

So, this gives me an approximate figure of 4500 m/s to perform the mission, and I have 5000 m/s. I have 500 m/s left for course corrections and whatever small manuever I may need.

the best moho approach is to get an equatorial orbit, elliptical to save some fuel when reaching eve. arriving with inclination won't be a huge deal, though; once I am captured in elliptic orbit, I can make a plane change at apoapsis to go equatorial again, for a small cost. ideally, my apoapsis should be directed so that it will make cheaper to leave for eve later, but i have no idea how to calculate that. Though those 500 m/s extra are probably enough to forgive some small mistake here

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3 hours ago, king of nowhere said:

intercept speed is always lower for any rendez-vous when done at apoapsis.

Maybe just a typo, but when coming from above, you meet the target more slowly if you meet at the target's periapsis.

I think you will need to estimate the numbers.  For the relative velocity reaching Moho, it is repeated application of the 'vis-viva equation' (or just doing sums of total energy, gravitation potential and kinetic energy).

Assuming that the gravity-assist at Eve results in a transfer orbit shaped roughly like a Hohmann transfer,
I figure you would leave Eve at 2461m/s (free of fuel cost if the gravity-assist cooperates) and then reach Moho at its periapsis when moving 1466m/s relative to Moho.

So if the deltaV at Eve is free thanks to gravity, and neglecting savings from the Oberth effect at Moho, the choices of where to meet Moho amount to 1400m/s.  That is smaller than the worst-case plane-change, 18km/s sin7°= 2000m/s , but think the nodal line between Eve's and Moho's orbits was not too far from Moho's Ap--Pe line, so you won't have the worst case.

After all that, I think the options are too close in fuel cost to find the best one without using a tool (like KSP with F5 and F9) to compare them in detail.

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8 minutes ago, OHara said:

Maybe just a typo, but when coming from above, you meet the target more slowly if you meet at the target's periapsis.

I think you will need to estimate the numbers.  For the relative velocity reaching Moho, it is repeated application of the 'vis-viva equation' (or just doing sums of total energy, gravitation potential and kinetic energy).

yeah, but those equations only work if there is no inclination to account for. the inclination of moho is a big factor

Quote

I figure you would leave Eve at 2461m/s (free of fuel cost if the gravity-assist cooperates) and then reach Moho at its periapsis when moving 1466m/s relative to Moho.

that's... surprisingly low. I've only been to moho a handful of times - and always starting from eve, which should result in less intercept - but i never got anything less than 2500 m/s intercept.

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4 minutes ago, king of nowhere said:

[vis-viva equations] only work if there is no inclination to account for.

Well, if you do the plane-change where the planes of the two planets' orbits cross, then the burn at each end of the transfer is in the plane of the local planet, so the simple equations hold.  You just add the plane change to the departure and/or arrival burns to get a decent budget for delta-V.

I checked the math, and there is a Hohmann transfer between Eve and Moho with 1500m/s relative velocity at arrival, if you get into Moho's orbital plane before arrival.  Maybe the inclinations made that transfer impractical overall; I'll try next time I start KSP.

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2 minutes ago, OHara said:

Well, if you do the plane-change where the planes of the two planets' orbits cross, then the burn at each end of the transfer is in the plane of the local planet, so the simple equations hold.  You just add the plane change to the departure and/or arrival burns to get a decent budget for delta-V.

yes, but the plane change is generally awfully high, and that way of making transfers is inefficient when the difference in inclination is significant. it's generally much better to meet the planet on the node, so that the injection burn contains also the normal component, and you gain the advantage of pitagora's theorem and of oberth effect.

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Then interpret the vis-viva equation to apply to the plane of your interplanetary transfer.  You know you can reach the Moho's periapsis at 19 726 m/s, while Moho is moving 18 261 m/s, so you need to slow the orbit by 1500m/s.  The angle between those two velocities will be something like 3°, so 19km/s×sin3° =1000m/s error in velocity normal to the orbit.  So combine the components into a 1800m/s burn (ignoring Oberth again).

If you manage to gravity assist from Eve at the point where Eve's and Moho's orbital planes cross, and match Moho's orbital plane there, you will reach Mojo needing to brake by something between 1500m/s (Mojo at Pe) and 2900m/s (Moho at Ap).

Your best choice seems to depend on just how bad the inclination angle is if you try to meet Moho at its Pe, versus just how far from Pe you meet Moho if you leave Eve where the planes cross.   Experiment in the game might be the most rewarding way to go deeper.

Edit: In stock KSP 1.3.1, the crossing points between Eve's and Mojo's orbital planes (AN-DN) look quite close to Mojo's periapsis and apoapsis around the sun.

And orbital velocity in low Moho orbit is 800m/s, so the Oberth effect is significant.  I had to be very careful to meet Moho when my orbit was tangent to Moho's, but then a 950m/s burn got me into low Mojo orbit.

Edit again: Benefits from the Oberth should probably not be included in planning here.  When timing a gravity assist you can maybe choose to meet Eve when it is over Moho's apoapsis, and meet Moho's orbit at its periapsis, but it is very unlikely that Moho will be there at that time.  Probably you will need to make most of your slowing burn while in solar orbit, enough so that you meet Moho a periapsis in the next one or two orbits.

Edited by OHara
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17 hours ago, OHara said:

Then interpret the vis-viva equation to apply to the plane of your interplanetary transfer.  You know you can reach the Moho's periapsis at 19 726 m/s, while Moho is moving 18 261 m/s, so you need to slow the orbit by 1500m/s.  The angle between those two velocities will be something like 3°, so 19km/s×sin3° =1000m/s error in velocity normal to the orbit.  So combine the components into a 1800m/s burn (ignoring Oberth again).

and yet...

I took all the long sequence of gravity assists. Here I got as best as I could with eve. Almost as best; i still have, like, 4° inclination, but I couldn't find a way to get rid of them. I'll try again tomorrow, but it shouldn't make a huge difference.

As you can see, I matched periapsis with Moho's apoapsis almost perfectly. Mohoìs apoapsis is give as 6,315 Gm in the wiki, but the game subtracts the sun's radius of 261 Mm, giving a final figure of 6,064 Gm. My solar periapsis is 6,037, very close - especially considering that I eyeballed eve's insertion point. the orbit is touching moho's very lightly, a great hohmann transfer.

But despite that, I still get 2300 m/s to capture. despite getting a close periapsis to the planet to get oberth effect (in practice, with a 30 minute burn time, I will be much less efficient). when you subtract oberth, it becomes much less efficient than your calculations.

And alexmoon planner keeps telling me of ideal transfers with as little as 1250 m/s capture burn. From a 100 km periapsis. Including circularization. And without matching orbital planes.

I have done all I could conceive to lower intercept speed, and still I get much worse results than what calculations dictate. I am trying to figure out what I'm missing.

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Finding a gravity assist from Eve that is also timed properly to meet Moho is impressive. And 2300 m/s is less than I would have thought.  I figured 2846 m/s, ignoring any benefit from the Oberth effect.

When coming from above, you meet the target more slowly if you meet at the target's periapsis.  You would need a more severe gravity assist from Eve, to bring your craft's periapsis down to 4.2 Gm, but then you need less deceleration at Moho's periapsis.

Edited by OHara
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36 minutes ago, OHara said:

When coming from above, you meet the target more slowly if you meet at the target's periapsis.  You would need a more severe gravity assist from Eve, to bring your craft's periapsis down to 4.2 Gm, but then you need less deceleration at Moho's periapsis.

I thought it would be cheaper to intercept at apoapsis, because normal rendez-vous are. Not sure what changes for a planetary transfer, maybe starting from eve getting to moho's periapsis is cheaper because you get lots of oberth. but I can see, in retrospect, i have to move my orbit much less if I meet eve at periapsis.

Unfortunately, doing so requires reloading back to my last kerbin flyby. perhaps even earlier.

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20 hours ago, king of nowhere said:

I thought it would be cheaper to intercept at apoapsis, because normal rendez-vous are.

This isn't actually true.  A normal rendezvous/transfer has the same properties as this Moho transfer.

When transferring to an elliptical orbit that is bellow your starting orbit, starting from a (mostly) circular orbit, you need to:

Drop your Pe to touch the target orbit.

At your Pe, reduce speed enough to match the rest of the orbit.

When you do this via transferring to target Ap you essentially:

1. Hohmann transfer to target Ap.

2. Circularize at target Ap.

3. Perform the Pe lowering of another Hohmann transfer to lower your pe to match target pe.

When you transfer to target pe you:

1. Perform a Hohmann transfer to target Pe.

2. Abort the circularization burn at Pe partway through, when the Aps match.

Perhaps after work I can work out the math on this to provide a proof.

Edit: another way to think about it, when transferring to an elliptical orbit, you want to match your Pe vs its Pe, or your Ap vs it Ap

Edited by Lt_Duckweed
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49 minutes ago, Lt_Duckweed said:

This isn't actually true.  A normal rendezvous/transfer has the same properties as this Moho transfer.

When transferring to an elliptical orbit that is bellow your starting orbit, starting from a (mostly) circular orbit, you need to:

Drop your Pe to touch the target orbit.

At your Pe, reduce speed enough to match the rest of the orbit.

When you do this via transferring to target Ap you essentially:

1. Hohmann transfer to target Ap.

2. Circularize at target Ap.

3. Perform the Pe lowering of another Hohmann transfer to lower your pe to match target pe.

When you transfer to target pe you:

1. Perform a Hohmann transfer to target Pe.

2. Abort the circularization burn at Pe partway through, when the Aps match.

Perhaps after work I can work out the math on this to provide a proof.

Edit: another way to think about it, when transferring to an elliptical orbit, you want to match your Pe vs its Pe, or your Ap vs it Ap

yeah, ok, but I'm talking about rendez-vous on very elliptical orbits from uncomforable positions. The kind of rendez-vous I'm used to make are between a mothership in a highly elliptical orbit around a planet (it stopped elliptic because it's cheaper to leave afterwards) and a shuttle rejoining it from a different elliptical orbit (it's elliptic because it just got captured). Something like those

Spoiler

And in this case, the angle of the ellipses and the plane will never match exactly, you will need a radial and normal component to the burn, and those are cheaper at apoapsis. Plus, circularizing the shuttle in elliptic orbit and then raising the ellipse again would just be wasteful.

In the last year, I've done nothing but extended grand tours with motherships. Your scenario, where you rendez-vous to an ellipse from below? never encountered it. I suppose it happens when you launch from kerbin towards a space station in elliptic orbit, but I stopped running those kind of missions long ago. My implicit assumption of a "standard" mission differs from most.

And by the way, your scenario is not a good description of how you perform a rendez-vous at apoapsis. Why would I want to circularize in the higher orbit, only to lower periapsis immediately after? You are also ignoring the normal component, assuming the rendez-vous happens from coplanar orbits, which is only the case if you launch from the same planetary body and use mechjeb.

No, the kind of rendez-vous I'm used to make are those with large differences of plane and shape between the orbits. And in those "ugly" transfers, your best bet is generally to start from your apoapsis and find a combination of prograde, normal and radial component that will get you to the target apoapsis at the same time as the target ship. Matching planes and circularizing orbits would be much more expensive.

It's interesting how one makes a certain kind of missions for a long time, and he unthinkingly starts to apply the same kind of solutions that worked for those specific missions also to other missions that would be better done differently. I've done that when i decided to meet moho at apoapsis. It also took me a while, after installing OPM, to realize that each gas giant has a different best way to enter orbit around it, breaking the habit of trying a gravity assist on a moon which only works well for jool. And you've done it in assuming that for a rendez-vous at apoapsis you'd want to circularize first

Edited by king of nowhere
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2 hours ago, king of nowhere said:

yeah, ok, but I'm talking about rendez-vous on very elliptical orbits from uncomforable positions. The kind of rendez-vous I'm used to make are between a mothership in a highly elliptical orbit around a planet (it stopped elliptic because it's cheaper to leave afterwards) and a shuttle rejoining it from a different elliptical orbit (it's elliptic because it just got captured). Something like those

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And in this case, the angle of the ellipses and the plane will never match exactly, you will need a radial and normal component to the burn, and those are cheaper at apoapsis. Plus, circularizing the shuttle in elliptic orbit and then raising the ellipse again would just be wasteful.

In the last year, I've done nothing but extended grand tours with motherships. Your scenario, where you rendez-vous to an ellipse from below? never encountered it. I suppose it happens when you launch from kerbin towards a space station in elliptic orbit, but I stopped running those kind of missions long ago. My implicit assumption of a "standard" mission differs from most.

And by the way, your scenario is not a good description of how you perform a rendez-vous at apoapsis. Why would I want to circularize in the higher orbit, only to lower periapsis immediately after? You are also ignoring the normal component, assuming the rendez-vous happens from coplanar orbits, which is only the case if you launch from the same planetary body and use mechjeb.

No, the kind of rendez-vous I'm used to make are those with large differences of plane and shape between the orbits. And in those "ugly" transfers, your best bet is generally to start from your apoapsis and find a combination of prograde, normal and radial component that will get you to the target apoapsis at the same time as the target ship. Matching planes and circularizing orbits would be much more expensive.

It's interesting how one makes a certain kind of missions for a long time, and he unthinkingly starts to apply the same kind of solutions that worked for those specific missions also to other missions that would be better done differently. I've done that when i decided to meet moho at apoapsis. It also took me a while, after installing OPM, to realize that each gas giant has a different best way to enter orbit around it, breaking the habit of trying a gravity assist on a moon which only works well for jool. And you've done it in assuming that for a rendez-vous at apoapsis you'd want to circularize first

Moho is in an elliptical orbit BELLOW your current solar orbit when coming in from Eve.  The most efficient way to reach it is to lower pe to match near Moho Pe while also matching planes in the same burn.

Since Eve-Moho Dn is quite close to Moho Pe, you want to do your Eve assist at Eve-Moho An.  Off the top of my head, to properly match planes and lower pe takes 2 assists because relative velocity to Eve is too high to do it all at once.

Edited by Lt_Duckweed
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22 minutes ago, Lt_Duckweed said:

oh, my. first i confuse apoapsis and periapsis, and then i confuse above and below. shame on me, i must be tired.

anyway, my general point stands; for the kind of rendez-vous i run usually, which entail ellptic orbits and other elliptic orbits with wildly different orientations, meeting at apoapsis with nonstandard manuevers is the best. i mistakenly  applied this general principle also to this specific rendez-vous, which instead would obey different rules.

by the way, i tried reloading a few saves and trying some more gravity assists, but i can't intercept eve on the correct point. I either reload back 20 years - 20 years where i have to regularly harvest food from greenhouses and inspect the ship against malfunctions - or I keep with the current trajectory of intercepting moho's apoapsis. By all projections I have enough fuel to do it, so I'll take the inefficient transfer. Though it makes me cringe

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