(12.145) | ||

(12.146) |

For the Earth-Moon-Sun system, . Given the relatively large size of , we expect the steady-state response to the equilibrium harmonic to be fluid-like (otherwise, the elastic stress within the Earth would exceed the yield stress) (Fitzpatrick 2012). In other words, for the harmonic, which implies from Equations (12.97), (12.98), (12.101), and (12.102) that , , , and . Thus, it follows from the previous two equations that

(12.147) | ||

(12.148) |

We deduce that the Earth's rotation causes a planetary equatorial (i.e., ) bulge of about , and a polar (i.e., ) flattening of , but does not give rise to any spatial variation in ocean depth. The observed equatorial bulge and polar flattening of the Earth are and , respectively (Yoder 1995). Our estimates for these values are too large because, for the sake of simplicity, we are treating the Earth as a uniform body. In reality, the Earth possesses a mass distribution that is strongly concentrated in its core.