# Coverage Area Determination for Conical Fields of View Considering an Oblate Earth

## TL;DR

This paper presents an analytical method to accurately determine satellite coverage areas by modeling Earth as an oblate ellipsoid, improving over traditional spherical models, with numerical simulations validating the approach.

## Contribution

Introduces a new analytical technique for coverage area calculation considering Earth's oblate shape, applicable to various satellite pointing configurations.

## Key findings

- The ellipsoidal method provides more accurate coverage area estimates than spherical models.
- Coverage errors depend on orbital parameters and are reduced with the ellipsoidal approach.
- Numerical simulations demonstrate the effectiveness of the new method.

## Abstract

This paper introduces a new analytical method for the determination of the coverage area modeling the Earth as an oblate ellipsoid of rotation. Starting from the knowledge of the satellite's position vector and the direction of the navigation antenna line of sight, the surface generated by the intersection of the oblate ellipsoid and the assumed conical field of view is decomposed in many ellipses, obtained by cutting the Earth's surface with every plane containing the navigation antenna line of sight. The geometrical parameters of each ellipse can be derived analytically together with the points intersection of the conical field of view with the ellipse itself by assuming a proper value of the half-aperture angle or the minimum elevation angle from which the satellite can be considered visible from the Earth's surface. The method can be applied for different types of pointing (geocentric, geodetic and generic) according to the mission requirements. Finally, numerical simulations compare the classical spherical approach with the new ellipsoidal method in the determination of the coverage area, and also show the dependence of the coverage errors on some relevant orbital parameters.