ROTATION OF THE ORBITAL PLANE OF A SATELLITE.

The rotation of the orbital plane of a satellite achieved by a thrust orthogonal to the radius vector and the velocity vector of the satellite is investigated as a function of the propellant mass-to-gross mass ratio, the thrust function and the motor burning time. The problem is treated with a new method which does not presume the knowledge of the powered flight trajectory of the satellite. The investigation is based on two properties of the unit vectors perpendicular to the planes of the osculating ellipses associated with the powered flight trajectory, namely the geodesic curvature and the length of the curve described by this unit vector while the satellite is on its transition course. With these two auxiliary terms the qualitative discussion of the angle between the orbital planes appears to become rather simple. For the quantitative determination of the angle between the orbital planes an ordinary homogeneous differential equation of the third order, which is valid for all types of orbits and thrust functions, is derived. In the special case of a constant acceleration of a satellite in circular orbit, its solution can be written immediately in closed form. Author