Numerical Determination of the Location of Critical Inclinations for Long Term High Eccentricity Orbits About Mars
Abstract
The purpose of this study is to locate critical inclinations in long term high eccentricity orbits about Mars using numerical methods. A critical inclination is defined as the inclination at orbit insertion which produces a local maximum in the amplitude of the variation of eccentricity or inclination. The perturbation model consists of the first non-zero zonal harmonic of the Mars gravity potential and the Sun as a point mass third body. The search range consists of inclinations from 0.25 to 90.0 degrees, eccentricities from 0.40 to 0.90, periapse radii from 4000 km to 7000 km, and orbit lifetimes of 10 Earth years. The numerical search comprises the following procedure: (1) A time history of eccentricity and inclination is produced for each combination of orbit insertion initial conditions by numerically propagating Lagrange's Planetary Equations. (2) Each time history is fit, in the least squares sense, to a linear function. The standard deviation of the residuals for each fit is employed as the search parameter. (3) A three-dimensional surface plot of the standard deviation in eccentricity and the standard deviation in inclination versus eccentricity and inclination is produced for each value of periapse radius considered. The local maximums in these surfaces identifies the locations of the critical inclinations. (4) The three-dimensional surfaces are then reduced to two dimensions by plotting inclination versus eccentricity for the local maximums in standard deviation.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1989
- Accession Number
- ADA209200
Entities
People
- Denis F. Durand
Organizations
- Air Force Institute of Technology