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Right approach for interplanetary rendezvous with a polar orbit


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last week i tried to get a ship to interplanetary rendezvous (from Vall) with another ship that was in a polar orbit around Laythe. 

i wanted to make the encounter that way i only had to adjust only one parameter to get the right inclination.  but how hard i tried i couldn't find the right time or angle to get the correct burn.

i tried many different positions in the planets' orbit to get an encounter but that didn't work. even with a lot of prograde, radial and normal adjustments.

i eventually had to pick a very inefficient encounter with laythe and had to make an adjustment burn of 17 degrees to get a proper encounter with the designated ship.  

my question is:

how do i get a ship efficiently aligned with a ship that is already in an certain polar orbit around another planet. 

I'm sorry if it all sounds a bit vague but I'm currently not available to make a proper screenshots.  

i could make some sketches in paint if that would be helpful. 

Edited by xendelaar
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Short answer would be to watch my video on encounters, as I do that exactly in it I believe: you can watch it here.

Longer text version: during interplanetary transfer, probably around your apoapsis if you're transferring from Kerbin, you should make a correction burn. (EDIT: basically, you don't want to be too close to the planet, but doing the adjustment burn too close to Kerbin is impractically efficient.) Put down a maneuver node and make sure the icon are showing, that will make the next step easier.

Next, you want to find the celestial body you want to encounter on the map and click on it. Hit focus view or whatever that message to center your camera on it is. Scroll and wiggle until you can both see your maneuver node and the planet. Look for your trajectory from the original encounter you set up. Use the maneuver node to move that line around until it is at the desired height and inclination. Be very mindful of the direction you're coming in, you don't want to be on the right orbit in the wrong direction.

That's it about it.

Edited by Ohm is Futile
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You will always to be able to get a polar orbit (by following @Ohm is Futile's instructions), but not necessarily the one you want for a rendezvous. It depends on each ship's direction of travel when it approaches Laythe. The ship waiting at Laythe is in an orientation determined by how Kerbin, Jool, and Laythe were aligned when you flew the first mission, and when you launch the second mission, they will have moved around and out of alignment with that initial polar orbit, so the second ship will approach from a different direction. A remote station in a polar orbit can be expensive in terms of delta V as compared to a station in an equatorial orbit, since you're guaranteed a cheap encounter for the latter.

One way to deal with that would be to capture yourself into a Jool orbit first, then try various encounters with Laythe from several angles, possibly waiting multiple orbits, until you find a good one. This allows your ship to approach Laythe from a variety of directions instead of just the one you happen to get by chance from the initial transfer.

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1 hour ago, xendelaar said:

how do i get a ship efficiently aligned with a ship that is already in an certain polar orbit around another planet. 

Short answer: you can't, but there's workarounds.

 

Long answer: orbits are not bound to anything except the position of their focus point (which is the gravity well being orbited). Thus, as the focus travels, the orbit follows the focus and remains with it. However, that is all. The orbit does not follow anything other than the position. If the focus rotates, the orbit ignores it. If the focus itself orbits something else and thus takes a curved path, the orbit ignores the attitude change. It always* stays exactly, perfectly fixed in the same orientation it was when it was first established.

That means that any orbit, but especially polar orbits, will appear to "drift" from the point of view of their focus. If you are on the Mun, and there is something in a polar orbit of it, you will notice that sometimes, this polar orbit is orientated so that the north pole pass will go in the prograde direction of the Mun's own path. But at another time, the north pole pass may be radial in, radial out, or even retrograde to the Mun's own path... or anything in between. That is because the Mun travels in a circle around Kerbin, but the polar orbit only follows the position. It does not turn with the circle to always face the same direction with respect to the Mun's path of travel**. So from Kerbin's point of view, the polar orbit is sometimes edge-on towards the observer, and sometimes shows its broad side.

Which also works for Laythe, or course. Sometimes, a thing in a polar orbit of Laythe will be edge-on towards Jool. And sometimes it will be broad side on. And not only towards Jool... it can also be any position with respect to your arriving spacecraft. It can be aligned for rendezvous, it can be perpendicular, it can be anything in between. When exactly each phase happens depends solely on how and when the orbit was intially set up. If the orbit is not aligned for rendezvous when you arrive... well, tough luck. There's absolutely nothing whatsoever you can do. Go perform a plane change to align yourself after capture.

Two workarounds can mitigate the issue.
- One, if you arrive at the wrong time, that means that you left at the wrong time, resulting in intercepting Laythe at the wrong position in its orbit. Leave later, or leave sooner, or try wasting time or accelerating while already en route. Perhaps that way you can hit Laythe when the position is better.
- Two, if you're forced into a large plane change, try to employ your usual bag of tricks to make plane changes cheaper, especially the "highly elliptical orbit" trick. First, circularize equatorial, then line yourself up under your target orbit, push the apoapsis waaaay out there, and once at apoapsis, flip your orbit polar. It will still be costly, but this method usually saves at least some dV.

 

(* in a 2-body approximation like the one KSP uses, anyway)

(** this is why a single polar satellites can scan an entire celestial body - regardless of whether or not the body itself rotates. The travels of the body around its own parent is enough to make sure the polar orbit passes over every single bit of surface eventually.)

Edited by Streetwind
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6 minutes ago, HebaruSan said:

[snip]

Right, good point, Laythe is a satellite. Getting into a polar orbit is simple enough, but getting into the same polar orbit is not quite as easy. Yup, I would definitely recommend shooting for Jool first, doesn't even need to be a polar orbit of Jool (in fact, it probably shouldn't be) and wait for a good opportunity to transfer from Jool to Laythe with both matching orbits and inclinations and such.

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3 minutes ago, Ohm is Futile said:

doesn't even need to be a polar orbit of Jool (in fact, it probably shouldn't be)

Good point of clarification; I was definitely imagining an equatorial Jool parking orbit for the encounter-hunting phase.

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@Streetwind thanks for the thorough advice.

i was in an equatorial orbit around Jool in this case (near Vall). and i tried to sit around and wait until i finally got a aligned encounter but after an hour fiddling with nodes i eventually gave up. 

i guess that wasn't a bad approach at all after all. maybe i should have waited longer. :)

thanks again for the explanation

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A economical way without a lot of maths and guesswork is to plot a node so that you will get a polar orbit, any polar orbit but with a low pe.

Get to pe and close the orbit but only just so that the ap is as high as possible.

Do a plane change from as close to ap as possible while raising your pe to that of the target.

Plot your intercept.

 

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If you are going for a non-equatorial orbit in your destination SOI, then the plane of that orbit is determined by the timing of the moment when you arrive in that SOI. If you want to change the plane, you have to change the timing. Which you do by either slowing down (relative to your target CB) before you hit the SOI (so that it takes longer to get there), or speeding up to hit the SOI faster. So it takes a couple burns. You can't seriously do it by just setting one maneuver node.

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This is partly exacerbated by the fact that Vall and Laythe are in the same orbital plane; having some relative inclination between your initial and destination bodies offers you a chance to get at least a little help in setting up an encounter.  Since you don't have that, you have to provide all of the inclination yourself.

This is even more exacerbated by the fact that you're trying to get the correct polar orbit--the problem here is not the inclination but the longitude of ascending node, and the quirks of the Joolian system make it either exceptionally easy or exceptionally difficult to get encounters with the right longitude of ascending node, but without much in between those extremes.

To illustrate:  I will assume that you are starting in a Vall equatorial orbit.  You burn to transfer and put a little normal thrust into the burn so you leave Vall's sphere of influence at an inclined angle.  Let's assume that you can get an encounter with Laythe that is close to polar.  The periapsis of this encounter is going to be near the equator--but to efficiently change the longitude of ascending node, you really want the apsides to be over the poles.  However, you can't do that with an efficient transfer.

This happens because while you orbit Vall, your motion relative to Jool is going to follow Vall's orbit.  There will be some periodic oscillation because you are also moving relative to Vall, but the total motion will average to match Vall's orbit (as it should, because otherwise you wouldn't stay in Vall's orbit).  Even if you begin in a polar orbit of Vall and leave its sphere of influence directly over the north pole, you'll still move mostly in the same speed and direction as Vall--your total inclination relative to Vall's orbit about Jool would be about three degrees.  You can deflect the speed and direction but you can't ignore them.  Any efficient transfer from Vall to Laythe is going to take advantage of the fact that they're moving in the same direction and plane around Jool (taking that advantage is what makes such a transfer efficient), and that in turn will cause you to enter Laythe's sphere of influence from the side relative to its poles.  This will always put your periapsis at or near the equator whether your orbital path is equatorial, polar, or anything in between.

As others have said, timing is important, but that will only work well if the craft you want to intercept also transferred in from Vall.  If it had, then you wouldn't be asking here how to do it, so instead I will tell you why you cannot do it:  orbital resonance.  Vall and Laythe are in a 1 : 2 orbital resonance (meaning that Laythe orbits Jool twice for each time Vall orbits once), and while this makes transfer windows regular, repeatable, and fairly common, it also means that that same regularity makes all of those windows identical.  There is room for some variation but if you vary it by too much then you'll miss the window altogether.

This leaves you with a few options.  First, you can try a bad transfer--if you get a Laythe 'encounter' where you just glance through the sphere of influence over one of the poles, then the periapsis will be over the pole. You will be able to close the orbit and adjust the longitude of ascending node fairly easily--in that order, because you'll need to bring big engines and a lot of fuel as you will have a lot of relative speed, not a lot of time to shed it, and no help from the Oberth effect.  Inefficient transfers are inefficient for a reason.

Second, you can try corrective burns after you arrive at Laythe.  If it were me, I'd choose to make an equatorial Laythe orbit and then change the inclination at the correct point so that I can align the longitudes of ascending node at the same time, thus performing two manoeuvres in one burn.

Third, if your interceptor is also a lander, then you can spare yourself a lot of aggravation if you simply land on Laythe's equator, wait until the orbit you want is overhead, and launch to match it, just as you would if it were Kerbin.  If landing was part of the mission profile to begin with, then you should be in good shape--unless the craft you want to intercept has the fuel you need to launch from Laythe, in which case ... oops?

Alternatively, you can take a more scenic route.  Tylo is also in orbital resonance with Laythe (and Vall) so there may be something you can work with if you use Tylo as an intermediate.  Pol orbits Jool but is not in orbital resonance with Vall or Laythe, so eventually, you are effectively guaranteed to get a transfer that has the correct orientation.  I leave it to you to determine whether eventually will arrive in anything less than geologic time, and whether going to Pol to get to Laythe offers any fuel savings.

Lastly, you can do something that is in between getting a good encounter from Vall and getting a transfer from somewhere else; you can set up an intermediate orbit between Vall and Laythe and time the transfer from that to arrive at Laythe with the right parameters to easily match your chosen orbit.  Get into your intermediate orbit, make the node, and check the encounter.  If you don't like it, advance the node by an orbit and slide it up the orbital path until you get a new encounter.  Rinse and repeat until you get an encounter that you do like.  Assuming that each new Laythe encounter occurs at a different point on Laythe's orbit (stay away from orbital resonance), then each encounter should also have a different longitude of ascending node.  This is still theoretical--I prefer to correct from equatorial, as I said--so I don't know how well it would work, and there's no easy way to test without doing it, either.

Edited by Zhetaan
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1 hour ago, Zhetaan said:

This is partly exacerbated by the fact that Vall and Laythe are in the same orbital plane; having some relative inclination between your initial and destination bodies offers you a chance to get at least a little help in setting up an encounter.  Since you don't have that, you have to provide all of the inclination yourself.

This is even more exacerbated by the fact that you're trying to get the correct polar orbit--the problem here is not the inclination but the longitude of ascending node, and the quirks of the Joolian system make it either exceptionally easy or exceptionally difficult to get encounters with the right longitude of ascending node, but without much in between those extremes.

To illustrate:  I will assume that you are starting in a Vall equatorial orbit.  You burn to transfer and put a little normal thrust into the burn so you leave Vall's sphere of influence at an inclined angle.  Let's assume that you can get an encounter with Laythe that is close to polar.  The periapsis of this encounter is going to be near the equator--but to efficiently change the longitude of ascending node, you really want the apsides to be over the poles.  However, you can't do that with an efficient transfer.

This happens because while you orbit Vall, your motion relative to Jool is going to follow Vall's orbit.  There will be some periodic oscillation because you are also moving relative to Vall, but the total motion will average to match Vall's orbit (as it should, because otherwise you wouldn't stay in Vall's orbit).  Even if you begin in a polar orbit of Vall and leave its sphere of influence directly over the north pole, you'll still move mostly in the same speed and direction as Vall--your total inclination relative to Vall's orbit about Jool would be about three degrees.  You can deflect the speed and direction but you can't ignore them.  Any efficient transfer from Vall to Laythe is going to take advantage of the fact that they're moving in the same direction and plane around Jool (taking that advantage is what makes such a transfer efficient), and that in turn will cause you to enter Laythe's sphere of influence from the side relative to its poles.  This will always put your periapsis at or near the equator whether your orbital path is equatorial, polar, or anything in between.

As others have said, timing is important, but that will only work well if the craft you want to intercept also transferred in from Vall.  If it had, then you wouldn't be asking here how to do it, so instead I will tell you why you cannot do it:  orbital resonance.  Vall and Laythe are in a 1 : 2 orbital resonance (meaning that Laythe orbits Jool twice for each time Vall orbits once), and while this makes transfer windows regular, repeatable, and fairly common, it also means that that same regularity makes all of those windows identical.  There is room for some variation but if you vary it by too much then you'll miss the window altogether.

This leaves you with a few options.  First, you can try a bad transfer--if you get a Laythe 'encounter' where you just glance through the sphere of influence over one of the poles, then the periapsis will be over the pole. You will be able to close the orbit and adjust the longitude of ascending node fairly easily--in that order, because you'll need to bring big engines and a lot of fuel as you will have a lot of relative speed, not a lot of time to shed it, and no help from the Oberth effect.  Inefficient transfers are inefficient for a reason.

Second, you can try corrective burns after you arrive at Laythe.  If it were me, I'd choose to make an equatorial Laythe orbit and then change the inclination at the correct point so that I can align the longitudes of ascending node at the same time, thus performing two manoeuvres in one burn.

Third, if your interceptor is also a lander, then you can spare yourself a lot of aggravation if you simply land on Laythe's equator, wait until the orbit you want is overhead, and launch to match it, just as you would if it were Kerbin.  If landing was part of the mission profile to begin with, then you should be in good shape--unless the craft you want to intercept has the fuel you need to launch from Laythe, in which case ... oops?

Alternatively, you can take a more scenic route.  Tylo is also in orbital resonance with Laythe (and Vall) so there may be something you can work with if you use Tylo as an intermediate.  Pol orbits Jool but is not in orbital resonance with Vall or Laythe, so eventually, you are effectively guaranteed to get a transfer that has the correct orientation.  I leave it to you to determine whether eventually will arrive in anything less than geologic time, and whether going to Pol to get to Laythe offers any fuel savings.

Lastly, you can do something that is in between getting a good encounter from Vall and getting a transfer from somewhere else; you can set up an intermediate orbit between Vall and Laythe and time the transfer from that to arrive at Laythe with the right parameters to easily match your chosen orbit.  Get into your intermediate orbit, make the node, and check the encounter.  If you don't like it, advance the node by an orbit and slide it up the orbital path until you get a new encounter.  Rinse and repeat until you get an encounter that you do like.  Assuming that each new Laythe encounter occurs at a different point on Laythe's orbit (stay away from orbital resonance), then each encounter should also have a different longitude of ascending node.  This is still theoretical--I prefer to correct from equatorial, as I said--so I don't know how well it would work, and there's no easy way to test without doing it, either.

 wow you took quite some effort to explain why it is so darn difficult to align two crafts into a polar orbit.

you're right that the first vessel came directly from kerbin -》 slowed down at tylo 》 and then stopped at laythe to perform an orbital scan. the other vessel got fuel from vall and went directly to laythe.

i didn't know my question would be this complex. i thought it would be a matter of timing and some node adjustments. 

@Daveroski what you describe sounds like robust method but certainly not an economical method. although changing planes at the ap is off course a good thing to do. thanks for the advice :)

@bewing thanks. i think i tried your method (more or less) and that's how i went from an inclination of 90 degrees to 17 degrees with a lot of fiddling. it's just so frustrating i didn't figure out why i couldn't reduce the inclination to 0 degrees. :) but i guess it's just a bit more complex than i assumed it would be. 

 

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  • 3 weeks later...

I think I found a way to solve the problem for any given polar orbit and starting location. I haven't had time to thoroughly test my theory yet or do any maths on it, so there is still some work that has to be done. I made a small example which I will explain below.  

Let’s say we want to go from Tylo to Vall. Near Vall, a craft is circling the globe in a polar orbit and let’s say we want to rendezvous with this craft! Normally we want to perform a regular hohmann transfer to get to our target. We know that in many cases* we need "the least" amount of delta v when the inclination angle is approximately 0 degrees:

 

*when the inclination between the two orbits is ~0 degrees

00A9q2J.jpg

(HOFFMAN should be HOHMANN... but I'm too lazy to change the pictures ;))

This way, we require the least amount of delta v to get to the target. Unfortunately, this also means that we always approach the target planet from the same angle. In the example above this is means we always have an relative inclination with the target (in the polar orbit) of 90 degrees, which is BAD…

So I figured.. what if we depart from our starting location when the intercept angle is different than 0 degrees, say 30 degrees?! Will this change the angle at which we reach the target planet and the relative inclination with the ship that is in a polar orbit?

wp0p8Us.jpg

(HOFFMAN should be HOHMANN... but I'm too lazy to change the pictures ;))

So I tried this method in my current career and got pretty cool results. As shown in the picture above we can see that for this example, the inclination with the final target is only 6 degrees! THIS IS GOOD!! We spend more energy on the hohmann transfer and  we also reach the planet at a higher relative velocity, but we DO get a better inclination with the final target which is the polar orbit!  

Sorry if my explanation is a bit fuzzy. I just wrote this on my way to work. Please let me know what you think. I will try to produce more quantitative results when I get home. I wonder how efficient this “new” method is.

Edited by xendelaar
hoffman.... DOH!
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Sorry, not gonna work. If your intercept angle is not very very close to zero, then your intercept speed is going to be several km/s -- so your braking maneuver is going to be very expensive. Much more expensive than any plane change at the destination could possibly be.

But you can easily get captured into a polar orbit while using a Hohmann transfer. The only question is whether the solar altitude is right -- so that you go right over one of the poles when you get to your destination.

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1 hour ago, bewing said:

Sorry, not gonna work. If your intercept angle is not very very close to zero, then your intercept speed is going to be several km/s -- so your braking maneuver is going to be very expensive. Much more expensive than any plane change at the destination could possibly be.

But you can easily get captured into a polar orbit while using a Hohmann transfer. The only question is whether the solar altitude is right -- so that you go right over one of the poles when you get to your destination.

Thanks for the feedback! While you’re probably right, I would still like to compare the numbers to give me some closure...Just to get a feeling what the different delta v requirements are for both methods. :) So I will redo the experiment again tonight and I will report back on the forum.  any additional info would be welcome off course :)

Edited by xendelaar
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I don't know why nobody is mentioning argument of periapsis - from my experience, this is the key to matching a target orbit around another body (especially polar orbit). It starts from this - tweak the mid-course correction so that the argument of periapsis lies on the target orbit plane. Visually, it will be the periapsis marker of the maneuver lies on the same plane with the target orbit. Remember, you're not trying to match inclination at this step - you're trying to match argument of periapsis. So if it ended up with a highly inclined capture trajectory, it's fine. Because it's mid-course correction, delta V spent is minimal. Second maneuver, you would capture into an elliptic orbit (this delta V is unavoidable), then third maneuver correct the inclination at apoapsis (this delta V is minimal because we're at apoapsis of elliptic orbit), then you'll be in the same plane as the target orbit, and then it's routine Hohmann transfer or any transfer you'd like to do.

It sounds very efficient to me, since the big boys are the capture burn and the same-plane transfer, which is not avoidable anyway.

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My strategy for getting into any desired orbit from an inter-body transfer is to first adjust my trajectory so that my PE at the target body occurs at the same point where my orbit crosses the desired orbital plane (i.e. at the AN or DN point) and is as low as safely possible. I do this as early as possible so that the adjustments can be done cheaply. When my transfer trajectory is the way I want it I set up a manoeuvre node at PE to capture into an orbit around the desired body, but only barely, with my AP as high as it can go without leaving the target body's SOI. Once I execute my capture burn the opposite AN/DN marker should be at the AP for an extremely elliptical orbit, so I can make whatever inclination changes are needed very cheaply. I do so, then make any other adjustments I need to make to my orbit using standard Hohmann transfers.

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On 2017/05/30 at 0:53 PM, Daveroski said:

A economical way without a lot of maths and guesswork is to plot a node so that you will get a polar orbit, any polar orbit but with a low pe.

Get to pe and close the orbit but only just so that the ap is as high as possible.

Do a plane change from as close to ap as possible while raising your pe to that of the target.

Plot your intercept.

 

I have noticed in videos on Youtube a lot of people get this wrong. When you get to a new SOI, don't circularize immediately. Plane changes use a LOT of dV once circularized. In stead I do a small burn to only just capture orbit. Then do the plane changes at the very high AP. This very large plane changes can be done for very small dV cost. Then once the plane is matched do the circularization burn.

 

The only downside to this is that an orbit with a very high AP takes a long time to complete. So if you have a time constraint for some reason then this might not work properly. In that case you can bring the AP lower, just remember that the lower it is the more costly the Plane Change Burn.

Here is a quick example, say my PE is at 100km above Kerbin and my AP is near Minmus Orbit. To do the 6 degree plane change to match Minmus plane would require 330m/s at PE and only 5m/s at AP for the same plane change.

 

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