Can meaningful work on inclination happen far from the nodes?

[Laie]

I've launched a very low-TWR vessel from KSC (28 degrees and a bit) and want to spiral it out to equtorial GEO.

Basic approach: point prograde and apply my minuscule thrust until apoapsis is high enough. Then look and fix as necessary.

My question now is, what can I do about inclination during the long burn?I expect to go around the world several times until AP touches GEO, which means I'll also cross the equator several times. While I don't expect to reach zero inclination during the long burn, I do think I should be able to shave off a few degrees. But how? Should I:

• thrust parallel to the equator at all times?
• point +-30° from prograde whenever I go down/up?
• only deviate from prograde when I'm "near" an AN/DN? If so, how near and by what measure?
• something else I didn't think of?

Please don't suggest a higher TWR or periapsis kicking. Both are out, because of reasons.

Edited May 29, 2020 by Laie

[bewing]

Is wasting dV an issue with this craft/mission?

If it is, wait until after you have achieved your Ap. The dV savings will be very significant.

If you don't care about dV, then it partially depends on just exactly how bad your TWR is. You want to do inclination changes just before your An/Dn, because the burn will push your node away from you (it won't move much at first). If you're willing to spend 10% of your dV changing your inclination inefficiently, then burn normal/anti-normal each time you reach 15 degrees in front of your Dn/An.

[Laie]

13 hours ago, bewing said:

Is wasting dV an issue with this craft/mission?

Well, I'm spiraling outward - that alone is already pretty inefficient, dV-wise. This doesn't mean I'm willing to blow dV for no gain, though.

13 hours ago, bewing said:

If it is, wait until after you have achieved your Ap. The dV savings will be very significant.

Even for a standard two-impulse transfer to GEO, it is worthwhile to add some normal to the first burn in LEO: the savings on the second burn are larger than the additional cost for the first.

GTO+GEO maneuvering

normal m/s at PE	dv PE	dv AP	total
0	2480	1830	4310
500	2510	1720	4230
1000	2620	1725	4340

These were arrived at "experimentally", dialling in maneuvers: 1) PE kick to 35,786 km at DN, 2) circularize and fix inclination in one maneuver at AN/AP. I think it's interesting that dv at AP appears to increase again despite the inclination being lower... anyway, this gave me the idea of working on the inclination on the way up.

Due to the spiraling-out approach, I will also have a rather high PE by the time my AP touches on GEO.That is, I will also have contributed quite a bit to circularisation already, leaving less prograde work to be done at AP, and generally a lower-magnitude burn to hide the normal component in. I think this makes it even more important to already work on inclination before I get to AP. Then again, orbital mechanics is weird.

[AHHans]

Hmmm....
If you burn at a small angle to prograde then you can get some gain for negligible cost. In my "experience" the main reason not to include some plane correction in a PE burn is that it might shift the node to a worse position for the correction during the AP burn (for a Hohmann transfer and apart from convenience). So I think if you burn at a node anyhow then some angle is always positive, but that the optimal angle to prograde probably depends on the specifics of the orbit.
If you only thrust parallel to the equator (== in the plane of your target orbit) then you won't cancel the velocity perpendicular to the equator / distance to the equator that you already have. So I don't think that this is the optimal strategy.
The main reason plane-change burns or circular orbits are done at the nodes is mostly that only there a short (== high thrust) burn can actually get you onto your target plane. Another reason might be that it is most efficient there because your difference to your target plane is velocity not position and thus Oberth. Also if you burn radial at nearly a 90 deg phase angle to the nodes then it is easy to overdo it and increase the angle of your plane again.

So my guess is that burning at an angle to prograde during most of the spiral is probably a good idea. How much of the region around the "anti-nodes" (== 90 deg away from the nodes) you want to exclude is up to you.
[Edit:] This assumes that your thrust is low! I.e. that you'll have to burn with a large radial component for multiple orbits to match your planes.

How do you plan to control the maneuver anyhow? This doesn't seem to be a maneuver that would be fun to fly manually.

1 hour ago, Laie said:

I think it's interesting that dv at AP appears to increase again despite the inclination being lower...

Hmmm.... That sounds wrong. My guess is that this is more a "measurement error" than an actual effect. (E.g. that the PE and AP after the burn at PE weren't 100% identical.) What I do expect is that the dV at AP doesn't change much when you are already close-ish to your target plane after the burn at PE.

Edited May 30, 2020 by AHHans