(12.29) | ||

(12.30) |

where

(12.31) | ||

(12.32) |

Here, it is assumed that the closest point on the moon's orbit to the center of the planet corresponds to , where is the uniform precession rate of this point. [It is necessary to include such precession in our analysis because the Moon's perigee precesses steadily in such a manner that it completes an orbit about the Earth once every 8.85 years. This effect is caused by the perturbing influence of the Sun (Fitzpatrick 2013).] Suppose that the inclination of the moon's orbit to the planet's equatorial plane, , is relatively small, so that . It follows that

(12.33) | ||

(12.34) |

Thus, Equations (12.22)-(12.24), (12.28), and (12.32)-(12.34) can be combined to give the following expression for the tide generating potential due to a moon in a low-eccentricity, low-inclination orbit:

Here, we have retained a term proportional to in the previous expression, despite the fact that we are formally neglecting terms, because the term in question gives rise to important fortnightly tides on the Earth.