Advanced Question Calculating Launch Windows

[Nemoricus]

I've been trying to find materials that talk about how to calculate launch windows, and come up rather empty so far, so I thought I'd ask if anyone here knows how to do so.

I'm well aware of Launch MFD and similar, but these provide an answer to the question without giving any information on the method behind it.

So, given a target with a given equatorial inclination, semi-major axis, argument of periapsis, LAN, and true anomaly, how would one go about calculating when the orbit passes over a given site on the surface?

If my reasoning is correct, if you know the longitude the LAN is currently over, you can calculate when the orbit will cross over the launch site. However, correctly determining where the LAN is seems to be a problem.

Once the longitude of LAN is known, adding asin(launch latitude/inclination) should give you the longitude at which the orbit is currently passing over the target latitude. Then you can take the difference between that longitude and the launch site's longitude, divide that by the planet's angular velocity, and get the time to that orbital crossing.

Similar reasoning applies to finding the time to the other intersection, since the longitude of the descending node is 180 from that of the ascending node, and you should just be able to subtract asin(launch latitude/inclination).

Accounting for signs and wrap-around has been glossed over in this. Given that, is my reasoning correct? And how does one find the longitude the LAN is over?

Also, is there a better way to do this?

 

[orbekler]

We've been discussing this in the italian forum some time ago, how to get to ANY satellite/planet in an easy way and having the best NEXT window and get the minumum possible RInc, from ANY earth site, even out of crossing:

http://orbiteritalia.forumotion.com/t1765-niubbi-su-marte

Basically, Launch MFD doesn't (or at least didn't) find windows for objects NOT crossing the launch site.

I can assure you it works!

Let me some time to translate.

---------- Post added at 18:21 ---------- Previous post was at 13:59 ----------

Case 1:
launch site crosses the destination orbital plane, northern or southern emisphere.

In the example the Moon was chosen because its orbit is visible in Map MFD (but it's not mandatory to have it).

Starting at Wideawake, wait for the first node, in this case ascending, so heading is 90°+~22°=112° (in case of descending node, RInc would be subtracted)

http://orbiteritalia.forumotion.com.../i43.servimg.com/u/f43/16/03/26/19/orb112.jpg

After take-off, RInc decreases, and with the help of RCS correction, it would get near 0°.

http://orbiteritalia.forumotion.com...i43.servimg.com/u/f43/16/03/26/19/orb2b11.jpg

Of course, for crossed objects, Launch MFD is the best solution.

In Case 2, where there is no crossing (and we cannot use Launch MFD), it's just a bit more complicated, but at the end, it works.

Translating.

 

[Zachstar]

For Case 2 you are referring to an off plane transfer right?

Those have always annoyed me. Yes you can use transX to find when a surrogate can do an off-plane than launch into it's orbit but TransX wasnt made for that kind of work and it is clunky.

This is one of the reasons I wish Orbiter Navigator would have been completed. With solver tools.

 

[orbekler]

For Case 2 you are referring to an off plane transfer right?

No. I'm trying to get the minimum deviation possible with the launch heading, but of course you're out of plane.

Read below.

Case 2:
1) launch site not crossing destination orbit plane;
2) launche site in northern emisphere (example KSC) - in southern emisphere the rule changes.

For planets Map MFD doesn't visualize orbit, so we olny use Align MFD.

For the Moon it's easy to understand the concept because we can see easily when we reach the minimum deviation from its orbit plane:

- Radius Vector (P) oscillates between ascending and descending nodes NEVER touching them, in opposition to case 1 where it crossed them;
- RInc oscillates between a max and min value, example ~51.5° to ~5.6.

http://orbiteritalia.forumotion.com...43.servimg.com/u/f43/16/03/26/19/orb1_c10.jpg

Obviously the best launch time will be when RInc is at minimum, that is, for the northern emisphere, when we get near the descending node (anticipating a bit, for Earth rotation).

Heading will be of 90°, then again, RCS correction to mantain RInc to the minimum value.

http://orbiteritalia.forumotion.com...43.servimg.com/u/f43/16/03/26/19/orb2_c10.jpg

Destination planet orbits are not visible to Map MFD, so we got to rely only to Align MFD (but of course it works also for satellites).

For sites in northern emisphere (like KSC): Radius Vector gets near to descending node, when it changes direction to reach ascending node, we have to wait until DN gets near 90°, that will be the minimum deviation from the destination plane. After launching with heading of 90°, again RCS to make corrections to RInc, that should stay at minimum as possible.

For sites on southern emisphere: same thing as above, but the node of interest will be the ascending one (AN), so after Radius Vector gets near it, it changes direction, and again must reach 90°. That will be launch time. ALWAYS 90° heading.

http://orbiteritalia.forumotion.com...43.servimg.com/u/f43/16/03/26/19/orb3_c10.jpg

RInc improved a bit as seen.

This is just a rule of thumb, but works well enough.

Of course, beyond a certain value of latitude outsid crossing, it is convenient to perform an Off-plane transfer.

 

[Zachstar]

Well yes for launch sites is Russia or China it is better to launch for best orbital advantage and then do the off-plane transfer. I am just mentioning how annoying it is to do this at this point in time.

 

[Nemoricus]

I am afraid that, while these responses are informative, none of them answer the question I'm actually trying to work on.

That is, I'd like to be able to *calculate* when the launch windows are. Assuming that the target orbit is reachable from the launch site and that you have the orbital parameters of the target in the source body's equatorial frame of reference, how would you go about calculating the times when the orbital plane crosses over your launch site?

 

[orbekler]

You're right, I cannot say "right time will be in x minutes", just "now it's the right time".
I saw unanswered this thread for a while, so I thought that this explanation was better than nothing.

If the target orbit is reachable from the launch site, then Launch MFD is perfect for the purpose, and at least the programmer of this add-on should know the calculation behind it.