Laplace limit
In mathematics, the Laplace limit is the maximum value of the eccentricity for which the series solution to Kepler's equation converges. It is approximately
- 0.66274 34193 49181 58097 47420 97109 25290.
Kepler's equation M = E − ε sin E relates the mean anomaly M with the eccentric anomaly E for a body moving in an ellipse with eccentricity ε. This equation cannot be solved for E in terms of elementary functions, but the Lagrange reversion theorem yields the solution as a power series in ε:
Laplace realized that this series converges for small values of the eccentricity, but diverges when the eccentricity exceeds a certain value. The Laplace limit is this value. It is the radius of convergence of the power series.
See also
References
- Finch, Steven R. (2003), "Laplace limit constant", Mathematical constants, Cambridge University Press, ISBN 978-0-521-81805-6.
External links
- Weisstein, Eric W., "Laplace Limit", MathWorld.
- "Sloane's A033259 ", The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
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