A method for determination of elliptical Kepler orbits from two position vectors

Details A method for determination of elliptical Kepler orbits from two position vectors A method for determination of elliptical Kepler orbits from two position vectors

Oct 1976

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1976stin...7726046p&link_type=abstract

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Mathematics

Elliptical Orbits, Kepler Laws, Orbit Calculation, Position (Location), Eccentricity, Satellite Orbits, Transcendental Functions, Vectors (Mathematics)

Scientific paper

As a starting approximation for determining earth satellite orbits from observation values, the Kepler orbit corresponding to the measured values is normally used. The Gaussian method of determining a Kepler orbit using two position vectors diverges if the angle between the two vectors is larger than 70 deg (for orbits with an eccentricity which is not too large). A transcendental equation is presented for the difference of the eccentric anomalies, in the form Delta E = f(Delta E) in which a solution exists for every angle size. An estimation of the differential quotient for the function f is derived.

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