Statistics – Computation
Scientific paper
Aug 1991
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1991ads..confq....v&link_type=abstract
AAS and AIAA, Astrodynamics Specialist Conference, Durango, CO, Aug. 19-22, 1991. 19 p.
Statistics
Computation
Celestial Mechanics, Orbital Elements, Trigonometric Functions, Angles (Geometry), Angular Momentum, Bessel Functions, Conservation Laws, Lagrange Multipliers
Scientific paper
Kepler's equation: M = E-e Sin E, is frequently solved for E(M) in order to determine v (where M is the mean anomaly, E the eccentric anomaly, e the eccentricity, and v the true anomaly). By introducing a new auxiliary angle F at the second focus of the ellipse, computations can be reduced. If E is near 0 or 180 deg, this method will always be more accurate than the conventional technique. The new solution is calculated and presented to the 5th order in e, and the resulting residuals are presented. In addition a new companion equation, using the 3 point, or H angle method is also presented, for values of E near 90 deg. These techniques are frequently faster and more accurate.
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