The influence of the Earth’s oblateness on the image motion velocity during the electro-optical survey of the planet’s surface

Abstract

In this paper we derive the formulas describing velocity of the planet’s surface orbital survey image in the focal plane, obtained via on-board electro-optical equipment in the nadir-viewing geometry, with consideration for the Earth’s oblateness. The Earth is modeled as a perfectly rigid spheroid uniformly rotating about its axis of symmetry. The orbit of the satellite’s mass center is perturbed because of the Earth’s oblateness in the direction of its rotation axis. The orbital camera’s prime focus is located in the satellite’s mass center. We present the graphs of image motion velocity vector coordinates in the focal plane depending on time (true anomaly) and the graphs of the velocity fields. The obtained results are compared to the results in case of a spherical Earth. In the latter case the satellite’s mass center moves along a Keplerian elliptic orbit. Key words: image motion velocity, focal plane, Earth’s satellite.