Observed tidal braking in the Earth/Moon/Sun system

Abstract

The low degree and order terms in the spherical harmonic model of the tidal potential have been observed through the perturbations which are induced on near‐Earth satellite orbital motions. This recovery, which is the most complete dynamic model ever obtained, has been achieved through evaluating tracking observations on 17 different, mostly laser, satellites. A new improved GEM‐Tl geopotential model, complete to degree and order 36, was estimated simultaneously with the 66 adjusted tidal coefficients. The gravitational and tidal models were developed using the J2000 Reference System with the adopted nutations of Wahr and the precession model of Lieske. The tidal recovery was made in the presence of an extended oceanographic model containing over 600 long‐wavelength coefficients from 32 major and minor tides. Since solid Earth tides have perturbing frequencies identical to those of the ocean tides, the solid Earth tidal model of Wahr was used as a basis for the recovery of the ocean tidal terms. This provided a complete description of the combined tidal potential sensed by these well‐tracked satellites. This tidal model (for all 32 adjusted and unadjusted tides) has then been used to calculate the secular change in the Moon's mean motion due to tidal dissipation and the tidal braking of the Earth's rotation. The secular change in the Moon's mean motion due to tidal dissipation is found to be −25.27±0.61 arc sec century−2. Our estimate of the lunar acceleration agrees well with that observed from lunar laser ranging techniques, which most recently found −24.9±1.0 arc sec century−2 (Newhall et al., 1986). The corresponding tidal braking of the Earth's rotation is −5.98 ± 0.22 × 10−22 rad s−2. If the nontidal braking of the Earth due to the observed secular change in the Earth's second zonal harmonic (Yoder et al., 1983) is considered, modern satellite techniques yield a total value of the secular change in the Earth's rotation rate of −4.69 ± 0.36 × 10−22rad s−2.