A new approach to the calculation of modified Chapman functions for an ellipsoidal atmosphere of relevance to giant planet ionospheres Original Research Article

We derive a new form of the modified Chapman function for an oblate planet. This new modified Chapman function permits easier implementation of the numerical calculations. We introduce a presentation of the modified Chapman function using a dimensionless parameter that depends on the big semi-major axis for an ellipsoid, the altitude and the scale height. In this manner it is possible to “hide” the atmospheric characteristics of the planet and to formulate the problem in terms of oblateness only. To analytically derive the “classic” Chapman function from the modified Chapman function one only needs to assume that the planetary oblateness is equal to zero and to replace the semi-major axis with the spherical planetary mean radius. An improved and optimized software package for the calculation of the modified Chapman function based on the new theoretical results is developed. The Chapman functions for a spherical planet from this package practically coincide with the results of Wilkes (1954). Tables of modified Chapman functions for Saturn (the most oblate planet) are calculated and electron production rate profiles for the Saturn ionosphere are obtained.