Why were Apollo missions limited to 2.5 earth orbits?

[Peter47]

Just a minor query that I have, which someone with knowledge may be able to answer.

I understand that Apollo missions were schedules to have one and a half orbits of Earth to check things out before TLI and could do a further one of necessary to resolve any unexpected issues after which the the mission would have to be scrapped. I have come across two reasons for this. The first was that cryogenic hydrogen leaked out the third stage of the Saturn V and the second was limited battery capacity, presumably for the instrument unit. Does anyone know which?

I suppose that there could have been a third reason, missing the launch window but I have never seen this mentioned.

[wiggy]

I'm going to have to give this some thought but my gut feeling is once you've launched into what is effectively an inertially referenced earth orbit I'm not sure a "TLI window", driven by celestial mechanics comes into it, at least not for a few hours - every orbit you should come back around to the roughly same fixed point in space where TLI needs to start but of course that's not fixed relative to the ground.....(and I'll stop digging a hole for myself at that point). I've seen reference somewhere (I'll have to look it out) to early work on the S-IVB and a TLI as late as six hours/three orbits plus was investigated - as I recall, and I'm hazy on this, it that was possible from a guidance /S-IVB consumables standpoint but was suboptimal in other areas, including the possibility it would have placed a definite requirement for a larger than ideal initial course correction using the Service Propulsion System.

As you say LH2 loss and battery life will have been the bigger player, the early declared spec for the S-IVB ended up being four to five hours in orbit prior to TLI, which fits with the usual plan of TLI after e.g. 2 hours 45 min GET (Apollo 11), and for them the second and final option at 4 hrs 15min...

Have you had a dig around techy sites using google such as e.g. the Apollo experience reports?

FWIW

NASA stuff (https://history.nasa.gov/SP-4206/ch6.htm)

[MechEngr]

If the Moon was in a very elliptical orbit or if the plane of the Apollo orbit around Earth was not in the same plane as the orbit of the Moon, then I could see where the periodic windows might be grouped with long intervals, but the orbit seems rather circular (0.055 eccentricity) and NASA would be likely to keep the inclination of the spacecraft orbit in alignment with the Moon's.

Don't look at the Apollo 8 experience reports. This is a head's up.

[tdracer]

I wouldn't dismiss the TLI 'window' too quickly. Earth launch times were set to get the moon in the desired position (with not a lot of leeway, although I don't remember specifics). Further, earth launch windows were limited to a few days each month in order to have the moon in the necessary position - they couldn't launch except for those days.
I took a class back as an undergrad on orbital mechanics - but I didn't do very well at it (the guy in our class that did ended up with a job working orbital mechanics - apparently if you 'got it', companies that did that sort of thing found you highly desirable).

[wiggy]

Yes you're correct td, I shouldn't have written it off sooner.

The issue of the TLI window gets covered in some depth in the following..

NASA discussion (https://history.nasa.gov/afj/launchwindow/lw1.html#TLI)

Fundamentally if you miss the optimum injection opportunity (i.e. TLI) you will need to perform a plane change as part of the next one, which costs propellant, further away from the optimum slot you get the bigger the plane change/propellant requirement.

The essay actually goes as far as discussing how to generate three TLI windows but ultimately it appears NASA made a decision to go with the "up to three orbits/two injection opportunities" option.

Best guess would then be that decision then drove the requirement for the stage to be capable of orbital cruise of 4.5 hours, for example:

." The [Hydrogen Continuous Vent System] remains in operation for the duration of orbital coast until restart preparations begin. Average duration of coast has been approximately 2.5 hours on Apollo lunar flights although the original design conditions specified 4.5 hours."

University paper (https://commons.erau.edu/cgi/viewcontent.cgi?article=2883&context=space-congress-proceedings)

From a battery POV there was certainly enough amps available for several hours post TLI to provide control throughout LM extraction and the subsequent S-IVB slingshot maneuver.

Hope that helps the OP.