Zero initial partial derivatives of satellite orbits with respect to force parameters violate the physics of motion of celestial bodies

摘要

Satellite orbits have been routinely used to produce models of the Earth’s gravity field. In connection with such productions, the partial derivatives of a satellite orbit with respect to the force parameters to be determined, namely, the unknown harmonic coefficients of the gravitational model, have been first computed by setting the initial values of partial derivatives to zero. In this note, we first design some simple mathematical examples to show that setting the initial values of partial derivatives to zero is generally erroneous mathematically. We then prove that it is prohibited physically. In other words, set-ting the initial values of partial derivatives to zero violates the physics of motion of celestial bodies.