Rendezvous with a vessel in an inclined Munar/Minmus orbit

[dlrk]

I'm attempting to launch from Kerbin and rendezvous with a vessel in an inclined Munar orbit. I'm looking for a more precise way to do this than just fiddling with maneuver nodes and hoping for the best. Is there a way to time the launch such as a direct or same orbit Mun injection will work?

[Specialist290]

Alexmun's Launch Window Planner also works for finding launch windows between moons in the same planetary system, the same way it does for planets. It might come in handy here.

EDIT: Bah, misread the question.

Edited October 10, 2015 by Specialist290

[Guest]

Depends on scenario. Is mission time a critical factor? If not, overall mission efficiency is not going to be affected appreciably by doing a direct injection style launch. The biggest savings occur through leveraging oberth effects. I would aim to make my an/dn be as close to the target ap/pe also, allowing you to match planes as far away in munar orbit as possible.

[OhioBob]

When you arrive at Mun you want the plane of your incoming trajectory to be as close as possible to the plane of the munar orbit that you're trying to match. Fiddling with the maneuver node is part of the answer, but you also have to wait for the axis of the munar orbit to be properly aligned relative to Kerbin. If you arrive at the wrong time, you may not be able to get anywhere close to the same plane. However, waiting a day for Mun to advance further along in its orbit can dramatically change the situation. For instance, if the axis of the munar orbit is pointed in the direction of Kerbin then, 10 hours later after Mun has completed a quarter revolution, the axis will no be pointed to the left as seen from Kerbin. You just have to figure out when the timing is right so you arrive with the least amount of costly adjustments to make.

You might also be able improve your approach by making a mid-course correction after your initial trans-munar injection. This is particularly true if you need a normal/anti-normal component to your trajectory. In that case, I usually like to make my initial injection just a prograde burn. After that I place a second maneuver node at the first AN/DN, perform whatever plane change is necessary, and refine the targeting.

[MKI]

Depends on scenario. Is mission time a critical factor? If not, overall mission efficiency is not going to be affected appreciably by doing a direct injection style launch. The biggest savings occur through leveraging oberth effects. I would aim to make my an/dn be as close to the target ap/pe also, allowing you to match planes as far away in munar orbit as possible.

This

Unless you want point point accuracy, which is extremely time consuming for almost no gain. The main focus should be getting your intercept angles to line up as far and as long away as possible.

A launch to LKO should be in the plane of the moon you are trying to reach. So an equatorial orbit for the Mun, and a slightly titled orbit for Minimus. Or you can be lazy like me and just change your AN/DN once in orbit. (burn roughly 250 delta-V).

Then when you do your transfer to the said moon try to line up your AN/DE as soon as possible. I generally do this once I enter the sphere of influence, changing the AN/DE should only take a little Delta-V. Doing it in Kerbin SOI means you risk getting it wrong since the nodes could be off by a little or a lot.

[ajburges]

When you arrive at Mun you want the plane of your incoming trajectory to be as close as possible to the plane of the munar orbit that you're trying to match. Fiddling with the maneuver node is part of the answer, but you also have to wait for the axis of the munar orbit to be properly aligned relative to Kerbin. If you arrive at the wrong time, you may not be able to get anywhere close to the same plane. However, waiting a day for Mun to advance further along in its orbit can dramatically change the situation. For instance, if the axis of the munar orbit is pointed in the direction of Kerbin then, 10 hours later after Mun has completed a quarter revolution, the axis will no be pointed to the left as seen from Kerbin. You just have to figure out when the timing is right so you arrive with the least amount of costly adjustments to make.

You might also be able improve your approach by making a mid-course correction after your initial trans-munar injection. This is particularly true if you need a normal/anti-normal component to your trajectory. In that case, I usually like to make my initial injection just a prograde burn. After that I place a second maneuver node at the first AN/DN, perform whatever plane change is necessary, and refine the targeting.

I follow a different line of thought. This gives way more launch windows with minimal dV cost.

Establish and execute transfer orbit that will intercept target orbit

> Plot intercept trajectory

> Correct encounter for prograde, retrograde, or polar flyby

> align the Pe with an intercept of target orbit (you want Pe to touch target orbit)

During capture burn, you can easily get 10+ degrees of inclination change for (essentially) free due to trigonometric ratios. Doing this at intercept allows you match orbit quickly.

If you need a lot of inclination change, do an elliptical capture (with 10+ degrees of inclination change) and finish all but 5 degrees of inclination change at Ap. Remember, small orthogonal thrust is nearly free during a large burn.

This approach also allows for a 1 orbit rendezvous every time!

This approach works due to the non-linear ratio of trigonometric functions sin(x)+cos(x) (the sum of the component trust vectors) is greater than 1 for angles (0,90) (degrees). At 10 degrees AoA, you still realise 98.5% prograde efficiency, but also get 17.3% orthogonal thrust. For about an extra 1.54% burn time, you get a 11x return. That's better than the Oberth effect! However, remember that the returns are based on AoA: smaller AoA yields higher returns for the increased burn time.

[Laie]

I'm attempting to launch from Kerbin and rendezvous with a vessel in an inclined Munar orbit. I'm looking for a more precise way to do this than just fiddling with maneuver nodes and hoping for the best.

I'm not aware of any tools that will help you. However, a well-calibrated eyeball may save you some fiddling.

What you want to do (from how you ask I guess you figured it out, but I lay it out it nonetheless):

a) have you Munar periapsis below the target vessel's orbit. This will make for comparatively cheap plane change maneuvers, either during the capture burn or at a high apoapsis after capture or any combination of both.

have you incoming trajectory close to the target orbit, so you don't need much of a plane change.

If you do a energy-efficient transfer to the Mun, you hang out at your high apoapsis around Kerbin until the Mun catches up with you, so seen from the Mun's perspective, you will come in from ahead of it's trajectory. Seen from Kerbin, you will enter the Munar SOI from the side.

In order to have a chance of closely matching the target trajectory at the time you reach the Mun, you have to do the transfer burn when the target orbit is nearly at a right angle relative to the Mun's trajectory.

Slight problem: it's not exactly a right angle, more 110°. I suggest you plan a transfer burn, look by how many degrees your projected orbit deviates from the target's, then discard the maneuver and fast-forward while the Mun moves that many degrees along it's path around Kerbin. Then plan another maneuver and do it for real.

Trying to get it perfectly right will not be worth the hassle. You can do a small inclination change (~5°) almost for free during your capture burn. So once you get it that close, you can just go ahead -- any further node fiddling will only save you 5-10m/s.

[OhioBob]

I follow a different line of thought. This gives way more launch windows with minimal dV cost.

Establish and execute transfer orbit that will intercept target orbit

> Plot intercept trajectory

> Correct encounter for prograde, retrograde, or polar flyby

> align the Pe with an intercept of target orbit (you want Pe to touch target orbit)

During capture burn, you can easily get 10+ degrees of inclination change for (essentially) free due to trigonometric ratios. Doing this at intercept allows you match orbit quickly.

If you need a lot of inclination change, do an elliptical capture (with 10+ degrees of inclination change) and finish all but 5 degrees of inclination change at Ap. Remember, small orthogonal thrust is nearly free during a large burn.

That's what I do too, except I still try to time my launch so that the plane change is reduced as much as possible. A mistimed launch and we could have a plane change of 30-, 45-, or even 60-degrees or more, depending on the inclination of the munar orbit. By properly timing the departure, it might be possible to get that plane change down to 10-degrees, maybe less. When confronted with a large plane change, I think it comes down to a choice of (1) elliptical capture, or (2) waiting for a better launch window. I've done it both ways, though I usually find it easier just to warp ahead until I see a geometry that's more to my liking. I then like to perform a single capture burn that includes the plane change.

Edited October 10, 2015 by OhioBob

[Guest]

This is a good question and something that I wanted to expand on a little more with some screenshots. Hopefully, someone will set up a challenge for this type of scenario to get the community involved to see just which way is the best.

First, I launched this simple little 2 stage rocket and got it into 45x45 polar orbit around the Mun

I then launched another rocket, exactly the same as the first, to rendezvous and dock with the first. 3458 m/s to 70x70 orbit around Kerbin.

Next, I created a node for the Kerbin-Mun transfer. I want the PE of the Mun flyby to intersect with the orbit of ship 1. Not quite there at this particular time so I will have to time warp.

So, after eyeballing the angle that I needed for my rendezvous point, I upped the time warp. I got it kinda close.

After executing the burn and time warping to the Mun close approach, I"m at 4318 m/s.

Next, I burned retrograde at the close approach until my ship was just barely captured in Mun orbit. Notice, if everything is perfectly executed, the DN and the AP should line up. I'm a little off here, but should be close enough. Mission dv is at 4396 m/s.

Next, time warp out to the DN and burn either normal or anti-normal, whichever is closer, until planes match. dv now at 4509m/s.

Time warp back to the PE again and burn retrograde until a close approach with ship 1 is achieved. dv = 4510 m/s

Finally, time warp around again to the rendezvous point with ship 1, burn anti-target until target velocity = zero, and perform docking maneuvers. Total dv = 4717 m/s.

[OhioBob]

Good example, Otis. I see nothing wrong with your technique, though there is something that I would have likely done differently. Referencing the following image,

You have the orbit of the target ship oriented in such a way that the plane change is as big as it can possibly get, about 90 degrees. I would have warped ahead until Mun's orbital path is approximately normal to the plane of the target orbit (i.e. until the target orbit is aligned roughly 10 o'clock to 4 o'clock as the image is currently oriented). I then would have adjusted my approach trajectory so that I came in flying over one of Mun's poles (which pole depends on the direction of the orbit). In this way the plane of my incoming trajectory would be approximately the same as the plane of the target orbit. It should be possible to get the planes close enough that only a small change is necessary, which can easily be accomplished in combination with the capture burn for very little ÃŽâ€v.

Both methods are valid. My method requires a very small plane change while near Kerbin to adjust the trajectory so it comes in over one of Mun's pole. I usually do this as a separate course correction shortly after the initial trans-munar injection burn. Your method requires a plane change in munar orbit and an additional burn to lower the apoapsis. My method might require more time at Kerbin waiting for the proper alignment*, but your method takes more time after arriving at Mun. It might be six of one half dozen of the other in terms of efficiency. What's best is probably what each individual feels most comfortable with.

(ETA) *On second thought, you have to wait for a proper alignment as well, so you get no advantage there.

(ETA #2)

I've studied this situation some more and ran a test to compare the methods. Both methods should use the same ÃŽâ€v for trans-munar injection and orbit insertion. What we need to compare is the large plane change in Otis' method, versus the course correction + small plane change in my method. According to the images posted by Otis, the spacecraft's velocity at munar apoapsis is 79.4 m/s, which means a burn of about 112 m/s is needed to complete a 90 degree plane change. According to the test I just ran, the course correction needed to get into a polar trajectory was 87 m/s. This gives me 25 m/s to work with, which will buy an 11 degree plane change when included with the orbit insertion burn. Therefore is comes down to how accurately the planes can be matched when using my method. If better than 11^o then my method is more ÃŽâ€v efficient, if worse than 11^o then Otis' method is better. I think that in the end the difference is so small that it's just a matter of preference.

By the way, below is a screenshot from the test I ran showing the trajectory of my spacecraft passing over Mun's north pole. Although I didn't bother to put a target vehicle in orbit, you can see from the image how it would be possible to insert directly into a matching orbit.

Edited October 11, 2015 by OhioBob