Three-body problem - A test of escape valid even for very small mutual distances

Details Three-body problem - A test of escape valid even for very small mutual distances Three-body problem - A test of escape valid even for very small mutual distances

Oct 1983

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983buda.iafcr....m&link_type=abstract

International Astronautical Federation, International Astronautical Congress, 34th, Budapest, Hungary, Oct. 10-15, 1983. 9 p.

Astronomy and Astrophysics

Astronomy

Angular Momentum, Escape Velocity, Solar Orbits, Three Body Problem, Euler Equations Of Motion, Hyperbolic Trajectories, Moments Of Inertia, Orbit Calculation

Scientific paper

An analytical investigation of escape from a three-body system is presented, using the Jacobi decomposition of three-body motion. The third body is defined as isolated whenever the Sundman function exceeds the critical values associated with the three collinearly central families of Euler motions, and it is shown that an isolated third body escapes when it has hyperbolic velocity. This escape test can also be used to calculate the lower bound on triple close approaches and to define the phase-space region in which bounded motions occur. Sample calculations for realistic systems show that this region is smaller than generally expected. The method is also applied to the sun-Jupiter-Saturn system: Jupiter can never escape from this system, and Saturn can approach neither the sun nor Jupiter. The orbit of Saturn will remain larger than 9.41 AU and have an inclination less than 42 deg, but the escape of Saturn is not precluded. An analytical investigation of escape from a three-body system is presented, using the Jacobi decomposition of the three-body motion. Isolation of the third body is determined to occur when the Sundman function becomes larger than the three critical values associated with the collinearly central Euler-motion families, and escape takes place whenever an isolated third body has a hyperbolic velocity.

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