The cae2ho.m script uses a Runge-Kutta-Fehlberg 7(8) numerical method to numerically integrate the first-order form of the orbital equations of motion. This is a variable step size method of order 7 with an 8th order error estimate which is used to dynamically change the integration step size during the simulation. This software also uses a one-dimensional minimization algorithm due to Richard Brent to solve the close approach problem. Additional information about this numerical method can be found in the book, Algorithms for Minimization Without Derivatives, R. Brent, Prentice-Hall, 1972. As the title indicates, this algorithm does not require derivatives of the objective function. This feature is important because the analytic first derivative of many objective functions may be difficult to derive. The objective function for this program is the scalar geocentric distance of the celestial body or spacecraft.
The lunar and planetary ephemeris used in this computer program is based on JPL DE421. A Windows compatible DE421 binary ephemeris file is available at www.cdeagle.com.
David Eagle (2020). Closest Approach Between the Earth and Heliocentric Objects (https://www.mathworks.com/matlabcentral/fileexchange/39270-closest-approach-between-the-earth-and-heliocentric-objects), MATLAB Central File Exchange. Retrieved .
Updated fundamental transformation matrix. Also updated PDF user's manual to reflect this modification.