Classical mechanics teaches us that the orbital plane of a point mass orbiting a spherical planet remains fixed relative to distant stars. For Earth, the rotation-induced equatorial bulge adds a quadrupole term to the gravitational potential and exerts a torque on satellites that makes their orbital angular momentum precess. We show how choosing a satellite’s orbit makes this precession match Earth’s annual motion about the Sun, yielding Sun-synchronous orbits and, as a special case, dawn--dusk orbits with nearly constant illumination. We also explain why perfect synchronicity with the Sun is impossible: a satellite on a circular orbit keeps mean solar time, whereas sundials follow apparent solar time. The equation of time involves the angle between Earth’s perihelion and the vernal equinox. We estimate its secular drift from Earth’s spin-axis precession and from planetary perturbations of the perihelion, using a simple ring-averaged approach.
Khanna et al. (Thu,) studied this question.