Lunar tidal acceleration obtained from satellite‐derived ocean tide parameters

Abstract

Analysis of 100 sets of mean elements of Geos 3 computed at 2‐day intervals has yielded observation equations for the M2 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 k2 = 0.30 and the solid tide phase angle is taken to be 0°, the values are (3.99″ ± 0.4) × 10−2sin [σ(τ) + 327° ± 4°] = 1.26″/cm × 10−2C22+ sin [σ(τ) + ε22+] ‐ 0.32″/cm × 10−2C42+ sin [σ(τ) + ε42+] + … for the inclination and (2.73″ ± 0.7) × 10−2 cos [σ(τ) + 291° ± 13°] = −0.24″/cm × 10−2C22 + cos [σ(τ) + ε22+] − 3.38″/cm × 10−2C42+ cos [σ(τ) + ε42+] + … for the node, where σ(τ) = 2Ω − 2M* − 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 M2 ocean tide parameter values C22+ = 3.23 ± 0.25 cm, ε22+ = 331° ± 6°, C42+ = 0.87 ± 0.19 cm, and ε42+ = 113° ± 6°. Under the assumption of zero solid tide phase lag the lunar tidal acceleration is mostly (85%) due to the C22+ term in the expansion of the M2 tide with additional small contributions from the O1 and N2 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.