How do you calculate closest ground track point to TGT

[cyberKerb]

I'm trying to learn how I would calculate when a craft in orbit would have a ground track that flies over/close to a Target that is on the ground.

I know you can use the stock map for this, but if you're in IVA, that information is not available. (ignoring Scansat and other such mods for this query) It's all so easy with the visual representation that scansat gives... Providing you're not brute forcing it, just need to wait until the orbit looks close to passing over the landed vessel. Then perform an orbit adjustment burn so that ground track line goes right over the lander.

I've seen the "closest approach distance" and "time to closest approach" calculations in IVA mods MAS and RPM. I'm hoping there was someone who knew the funky maths involved for this calculation, who might be able to modify that calc so it works for a the target on the ground? ie the closest approach would be the from the ground track path, not the distance from the orbiting vessel to the ground vessel.

I know @Arrowstar, has got their awesome trajectories tool with all it's wonderful visualisations, but what I'm after is a calculation that can be used to find the future orbit when I should perform that orbit adjustment so the ground track gets very close to the point where the landed vessel is at.

 

 

[Arrowstar]

4 hours ago, cyberKerb said:

I know @Arrowstar, has got their awesome trajectories tool with all it's wonderful visualisations, but what I'm after is a calculation that can be used to find the future orbit when I should perform that orbit adjustment so the ground track gets very close to the point where the landed vessel is at.

You could do this in KSPTOT's Launch Vehicle Designer with some ease I think:

1. Create a ground object at the point you want to overfly;
2. Set up your initial state, an initial coast, an impulsive delta-v maneuver, and another post-delta-v coast;
3. Set up a maximum "extrema" for ground object elevation to the point in (1);
4. Set up a constraint that that extrema needs to be 90 degrees at the end of the second coast;
5. Run the optimizer.

I can't think of an analytical way to do what you're asking, I think it might need to be optimized out in all but the simplest cases.

That's just my thought, let me know if you have any questions.

EDIT: Yup, just tried it.  This is very easy in KSPTOT LVD.

Red line is the pre-burn orbit and the grey line is the post-burn orbit.  The trajectory is viewed in the body-fixed frame, meaning that the surface of Kerbin is stationary and the orbit is plotted against that. You see the grey line passing over the red marker, which is the ground object I randomly put down on the surface (this could be your landing site or whatever).

Let me know if you have any questions.

Edited July 24, 2020 by Arrowstar

[cyberKerb]

21 hours ago, Arrowstar said:

You could do this in KSPTOT's Launch Vehicle Designer with some ease I think:

I can't think of an analytical way to do what you're asking, I think it might need to be optimized out in all but the simplest cases.

That's just my thought, let me know if you have any questions.

Thanks @Arrowstar - I was pretty confident that you'd work it out with your tool. However, maybe I set up the question with too many restrictions that made you think I was after a solution finder. I've added some context below to help.

 

I'm after a value that can be used by the player to find their own solution for landing close to a ground target from orbit. This is preferred rather than give them the complete solution. Currently there is not enough information in an IVA for this, even with mods, provided you don't look at any map screens of console that show ScanSat.

The proposed calculation/function would be added to a variant of the RPM mod. RPM has a small CRT screen in the older technology controls (no glass cockpit here), hence the no map restriction. It would only be able to calculate the closest distance from ground track information. eg: Closest TGT distance to ground track: 1345Km.

Calculating the required burn is not required and it would only look at the current orbital period and not multiple orbits. 'How' to use this information would be something for the player to work out. I'm hoping that helps simplify the parameters?

 

The information would in theory allow an IVA player to plan and execute a landing burn for a ground target so it's close to desired landing point. I'd implement a small UI in the CRT display of the IVA mod RPM so the distance in KM could be visible. Depending on how intense that function is to run, it might be click-to-run and not something that is constantly refreshed. There would be only one parameter the user could modify, with the rest nabbed from the API to get current state. 

For parameters, i figure the function could require at least the body, craft orbit, lat/long of target and a variable of UT (Universal Time) for starting condition. Ideally, it would only calculate this on for 1 orbit period from the UT given and result in how close the ground track is to the target location. ie Example result could be '214353m'.

 

Thinking over it more, I could re-word the problem as:
What would I need to do to workout the LatLon position for when the ground track crosses the targets Latitude or Longitude?

If I could get that, I think all that's required then is to do a 'great circle' calc (old forum post for reference) for the two position to find the distances across a sphere surface and select the lowest value to get the minimum distance?

 

All of this would let me run the calc for this orbit, or if I change the starting UT, I would get the next orbit. That information would be enough (I think) for me to know which way to make an Normal / Anti-Normal burn. Specifically when my Orbit is 1/4 of the Orbit period prior to the closest AN/DN node. (90 degrees prior to the next AN/DN in the Orbit) Running the calc a third time after a guesstimate of the burn duration would tell me if I got close by checking if the distance reduced significantly.

 

Otherwise, if there was a way to use Vector3d for this, I'd love to learn how.

Edited July 25, 2020 by cyberKerb
removed bad idea

[Gargamel]

Moved to C# Support upon request.

[cyberKerb]

1 minute ago, Gargamel said:

Moved to C# Support upon request.

Thanks - figured I was starting to lean the conversation into API references and though it would be better there.

[cyberKerb]

Oh boy - I've been digging and found this maths area fun to dig into, but I think I've worked out what I need to do.

I think I have to iteratively calculate (~7-8 loops) to get a close approx of distance to the ideal flyover point. Anyone know of a way to do that with Vector3d?

 

 

 

Edited July 26, 2020 by cyberKerb