Astronomy and Astrophysics – Astronomy
Scientific paper
Feb 1982
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982azh....59..142s&link_type=abstract
(Astronomicheskii Zhurnal, vol. 59, Jan.-Feb. 1982, p. 142-146.) Soviet Astronomy, vol. 26, Jan.-Feb. 1982, p. 87-89. Translati
Astronomy and Astrophysics
Astronomy
Artificial Satellites, Equations Of Motion, Orbit Calculation, Orbital Mechanics, Satellite Orbits, Shadows, Conics, Half Spaces, Roots Of Equations
Scientific paper
The equation determining the points of intersection of a satellite orbit with the conical shadow of a planet (the shadow equation) is reduced to the fourth-degree algebraic equation for the tangent of half the longitude of the satellite measured from the point of the terminator at which the satellite enters the shadow half-space. With such a choice of longitude the roots of the equation, corresponding to the points of intersection of the orbit with the shadow, are always positive and bounded. The condition of the loss of two sign changes in the Sturm series for the left side of the shadow equation as the values of the above-mentioned tangent go from 0 to + infinity is used as the criterion of existence of these roots.
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