TEI Options

One of the projects I’ve been working on over the past couple of days is trying to figure out exactly how the Apollo CSM TEI burns were done. The official flight plans and flight logs are somewhat ambiguous, for example…

TEI Options

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One of the projects I’ve been working on over the past couple of days is trying to figure out exactly how the Apollo CSM TEI burns were done. The official flight plans and flight logs are somewhat ambiguous, for example when they mention “inclination” I don’t know what plane they are referring to as a reference plane – earth’s equatorial, ecliptic, solar system invariable, lunar equatorial or lunar orbital plane. I’m going on the working assumption that the CSM is coplanar with the lunar orbit (same Ω and i) around the Earth, that the TEI burn is at pericynthion or through pericynthion, argument of pericynthion will place it exactly on the other side of the moon from Earth. I know how long the engine was fired – 137.8 seconds – but I don’t know the propellant velocity or mass of the spacecraft or propellant mass expended during that time so I just use average thrust over that time to make for the known Δv.
The question is: which direction was the spacecraft thrusting? I’ve tried three options – 1: in the direction of the spacecraft velocity relative to the moon, 2: toward a particular point in the sky, and 3: toward the lunar “horizon” (where the horizon is defined as the tangent plane to the position vector relative to the moon at that point). 1 and 3 are very similar to each other (though 1 provides very slightly more C3 than 3), 2 is significantly different and less efficient. I feel like 2 is most likely as the problem is just “aim at the appropriate star and keep it centered” while the other two options require more attitude adjustment through the thrusting.
Note also that in 1 and 3 the spacecraft is technically (in a two body sense) in heliocentric orbit for a few minutes.

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