Tidal evolution of the Keplerian elements

Understand

We address the expressions for the rates of the Keplerian orbital elements within a two-body problem perturbed by the tides in both partners.

• The formulae for these rates have appeared in the literature in various forms, at times with errors.
• We reconsider, from scratch, the derivation of these rates and arrive at the Lagrange-type equations which, in some details, differ from the corresponding equations obtained previously by Kaula (1964).
• We also write down detailed expressions for $da/dt$, $de/dt$ and $di/dt$, to order $e^4$.