Effects of motion of the equatorial plane on equatorial elements of an Earth satellite

As the reference system an intermediate, quasi-inertial reference frame is adopted. In this system the inclination and the argument of perigee are referred to the instantaneous equator of date, and the longitude of the node is measured from the mean equinox of 1950.0 along the mean equator of 1950.0 and then along the instantaneous equator of date. The Earth is rotating uniformly in this system, thus giving a particularly simple expression for the sidereal angle. The Lagrange's planetary equations in their usual form which hold for the orbital elements referred to the nonrotating axial system defined at 1950.0 are used. Then the equations are modified to include the effects of motion of the reference system and transformed into Gaussian form. Because of this motion partial derivatives of orbital elements with respect to time are introduced in the equations. The partial derivatives are derived from the expressions including the terms up to the third order of precession. The equations are solved by the method of linear perturbations and the perturbations to satellite equatorial orbital elements by the motion of the equatorial plane are obtained.