Astronomy and Astrophysics – Astrophysics
Scientific paper
May 1984
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1984a%26a...134..360b&link_type=abstract
Astronomy and Astrophysics (ISSN 0004-6361), vol. 134, no. 2, May 1984, p. 360-364.
Astronomy and Astrophysics
Astrophysics
29
Celestial Mechanics, Orbit Calculation, Potential Theory, Symmetry, Concentration, Linear Equations, Newton Theory, Partial Differential Equations
Scientific paper
A second order linear partial differential equation is presented, giving the potential functions U = U(x, y), which generate a preassigned family of planar curves f(x, y) = c. In contrast to Szebehely's (1974) first order differential equation, the new equation does not include the total energy E, so that no assumption needs to be made regarding the dependence E = E(f). Using the new equation, a method by means of which it is possible to check whether a given family of orbits in a plane of symmetry may be generated outside a symmetrical finite material concentration above and below that plane is developed. In the case of a positive answer the Newtonian potential of the concentration is found. Depending on the given family f(x, y) = c, this potential may be determined uniquely or not. Examples are offered for both cases.
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