Abstract
The analysis of lunar laser ranging data requires very accurate calculations of the lunar physical librations. Libration terms are given which arise from the additive and planetary terms in the lunar theory. The large size of the recently discovered terms due to third degree gravitational harmonics will allow some of these harmonics to be measured, in addition toβ andγ, by laser ranging to the Moon. Combining the laser ranging determinations ofβ = 630.6 ± 0.5 × 10−6 andγ = 226.4 ± 3.0 × 10−6 with lunar orbiter measurements ofC 20 andC 22 givesC/MR 2=0.395 -0.010 +0.006 . Numerical integration promises to be an effective method of calculating librations. Comparison of numerical integrations with analytic series indicates that the calculation of the series due to third and fourth degree harmonics is not yet as accurate as the more extensively developed second degree terms.
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