M.Sc Thesis

M.Sc StudentBelyanin Sofia
SubjectSemi-Analytical Study of the Effect of Earth's Precession
on Geosynchronous Satellites
DepartmentDepartment of Aerospace Engineering
Supervisor PROF. Pinchas Gurfil
Full Thesis textFull thesis text - English Version


This work studies the long-periodic effects of equinoctial precession (EP) on geosynchronous satellites moving in the gravitational field of the Earth, the Moon and the Sun. The model of the perturbing potential includes the Earth's zonal and tesseral harmonics of the 2nd order and the lunisolar perturbations, inducing long-periodic and secular variations. The motion in  a reference frame co-precessing with the Earth is considered, assuming that the obliquity of the Earth and the precession angular velocity remain constant during the satellite's mission.

We investigate how north-south station-keeping of geostationary satellites is affected by the EP and show that time of staying within the allowed geosynchronous

window is shorter in the presence of the EP.

Our study is focused on near-equatorial circular orbits. The variational equations in non-singular orbital elements are derived to avoid singularities at zero inclination and eccentricity. Thus, the differential equations governing the out-of-plane motion are decoupled from the in-plane variational equations. Perturbation theory based on Lie transforms is used to obtain a second-order long-periodic solution for the inclination and the right ascension of the ascending node. This solution is used to determine initial orbit orientation for which the inclination constraint is satisfied during the longest possible period.

We found that for missions with inclination constraints of several degrees,  this period may be about 2 weeks shorter if EP is taken into account.  We also conclude that in cases of more strict inclination constraints (tenths of a degree), when the station-keeping maneuvers are necessary to maintain the inclination inside the allowed window for a long time (more than 10 years), an additional fuel consumption of up to 1% may be required.