On a transformation of the differential equation of the lunar theory.

Details On a transformation of the differential equation of the lunar theory. On a transformation of the differential equation of the lunar theory.

Sep 1971

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1971cemec...3..289m&link_type=abstract

Celestial Mechanics, Volume 3, Issue 3, pp.289-311

Statistics

Computation

3

Scientific paper

This work contains a transformation of Hill-Brown differential equations for the coordinates of the satellite to a type which can be integrated in a literal form using an analytical programming language. The differential equation for the parallax of the satellite is also established. Its use facilitates the computation of Hill's periodic intermediary orbit of the satellite and provides a good check for the expansion of the coordinates and frequencies. The knowledge of the expansion of the parallax facilitates the formation of differential equations for terms with a given characteristic. These differential equations are put into a form which favors the solution by means of iteration on the computer. As in the classical theory we obtain the expansions of the coordinates and of the parallax in the form of trigonometric series in four arguments and in powers of the constants of integration. We expand the differential operators into series in squares of the constants of integration. Only the terms of order zero in these expansions are employed in the integration of the differential equations. The remaining terms are responsible for producing the cross-effects between the perturbations of different order. By applying the averaging operator to the right sides of the differential equations we deduce the expansion of the frequencies in powers of squares of the constants of integration.

Affiliated with

Also associated with

No associations

Rating

On a transformation of the differential equation of the lunar theory. does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On a transformation of the differential equation of the lunar theory., we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On a transformation of the differential equation of the lunar theory. will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-1377280