Lunar tidal acceleration obtained from satellite‐derived ocean tide parameters

Analysis of 100 sets of mean elements of Geos 3 computed at 2‐day intervals has yielded observation equations for the M 2 ocean tide from the long periodic variations of the inclination and node of the orbit. If the second‐degree Love number is given the value k 2 = 0.30 and the solid tide phase angle is taken to be 0°, the values are (3.99″ ± 0.4) × 10 −2 sin [σ(τ) + 327° ± 4°] = 1.26″/cm × 10 −2 C 22 + sin [σ(τ) + ε 22 + ] ‐ 0.32″/cm × 10 −2 C 42 + sin [σ(τ) + ε 42 + ] + … for the inclination and (2.73″ ± 0.7) × 10 −2 cos [σ(τ) + 291° ± 13°] = −0.24″/cm × 10 −2 C 22 + cos [σ(τ) + ε 22 + ] − 3.38″/cm × 10 −2 C 42 + cos [σ(τ) + ε 42 + ] + … for the node, where σ(τ) = 2Ω − 2 M * − 2ω* − 2Ω*; M *, ω*, and Ω* are the lunar mean anomaly, argument of perigee, and right ascension of the ascending node, respectively; and Ω is the Geos 3 right ascension of the ascending node. Combining these equations with the result obtained by Goad and Douglas (1977) for the satellite 1967‐92A gives the M 2 ocean tide parameter values C 22 + = 3.23 ± 0.25 cm, ε 22 + = 331° ± 6°, C 42 + = 0.87 ± 0.19 cm, and ε 42 + = 113° ± 6°. Under the assumption of zero solid tide phase lag the lunar tidal acceleration is mostly (85%) due to the C 22 + term in the expansion of the M 2 tide with additional small contributions from the O 1 and N 2 tides. Using Lambeck's (1975) estimates for the latter, we obtain for the tidal acceleration in lunar longitude the value = −27.4 ± 3 arc sec/(100 yr) 2 , in excellent agreement with the most recent determinations from ancient and modern astronomical data. The mean elements of Geos 3 are also presented in tabular form.