Principia/RSS lunar launch windows

[IncongruousGoat]

I'm currently playing with RSS, RO, RP-0, and Principia installed, and I'm considering the problem of launching to the Moon from Cape Canaveral. Now, as most RSS players should know, in regular (non-Principia) RSS, the minimum relative inclination between the Moon and Cape Canaveral is a constant .23 degrees, which makes it easy to launch from the Cape to the Moon. However, Principia simulates lunar nodal precession, which means that the minimum relative inclination between the Cape and the orbit of the Moon varies between .15 degrees and around 9 degrees over an 18-year cycle. The question then becomes, is there a way to compute lunar launch windows from the Cape, taking into account both the nodal and apsidal precession of the Moon, as simulated by Principia?

[Weywot8]

Just curious, doesn't that mean we'd have to re-define 'transfer window'? Otherwise, you'd only launch every 18.6 years or 18.6*8.85 years at the minimum inclination+minimum PE.

 

[IncongruousGoat]

9 hours ago, Weywot8 said:

Just curious, doesn't that mean we'd have to re-define 'transfer window'? Otherwise, you'd only launch every 18.6 years or 18.6*8.85 years at the minimum inclination+minimum PE.

 

No, since you can always do a Baikonur-style transfer, where you launch such that your TLI trajectory intersects the Moon's at the Moon's ascending or descending node. The question is how to figure out when those transfers are available.

[DrLicor]

What I do is select a target with KER, wait untill the relative inclination is near 0.23, mostly around the 0.30, and launch. It in the rendavouz menu of KER

[IncongruousGoat]

14 minutes ago, DrLicor said:

What I do is select a target with KER, wait untill the relative inclination is near 0.23, mostly around the 0.30, and launch. It in the rendavouz menu of KER

That's what I normally do as well. The problem is, as I said, that Principia simulates the Moon's nodal precession, which causes the relative inclination of the Moon and the Cape to vary over an 18-year cycle, over the majority of which you have to launch to the Moon similarly to how you would if you were launching from Baikonur.

[Weywot8]

Not understanding what you are looking for then -  technically, the moon is never "in plane" over the Cape but the inclination minimises over a period of 18.6 years, as you've said.. The optimum for that 'lunar month" would be the day around when the moon will pass the correct 'node' as everyone has described - "Baikonur-style" with two potential launch windows for that day - one generally much better than the other. which is reserved for "oops, missed the first one".

 Astronomers already measure the time it takes the moon to complete a node-node orbit, incorporating the precision of nodes - the draconic/draconitic month = 27.2122 days. So your 'optimum' launch window comes every draconitic month since the last one +/- planets rotation to best launch angle for that day.

If you are simply looking for the month/year of minimum inclination, then it's just 18.61 years after the last minima. Oddly enough Apollo 11 launched in the year of maximum inclination - 1969.  Maybe it was to get the best coverage of potential landing spots instead of being stuck at the equator (just speculating)

The last minima was October 2015 - so it was nearly in plane then and we could launch 'whenever' during the later half of 2015 which is another version of 'optimum' launch window.

 

More generally,the inclination is minimised when N = 180

N(T) = 259.16 - 1934.14T + 0.0021T², 

where T = the number of Julian centuries that have passed since midnight on 1 January 1900 at the Greenwich meridian.

Hope that answers your question.

 

 

Edited June 19, 2017 by Weywot8
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[IncongruousGoat]

@Weywot8 Thank you. I'll have to recalibrate things to fit with RSS, which wouldn't appear to be properly set up (for example, 1969 in-game is an optimal launch window), but this should help greatly.

 

[Jaeleth]

My two cents... Apollo launch in 1969 had more to do with winning the space race  and fulfilling Kennedy's promise than any specific optimal launch window  or for having a nice choice of landing sites. Besides, the Saturn had enough Dv to go the distance anyway

Edited June 20, 2017 by Jaeleth
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