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Euler’s and Barker’s equations: A geometric derivation of the time of flight along parabolic trajectories

Published online by Cambridge University Press:  01 August 2016

Alex Pathan
Alex Pathan*
Affiliation:
45 Hutcliffe Wood Road, Sheffield S8 0EY, e-mail: [email protected]
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Extract

The parabolic orbit is rarely found in nature although the orbits of some comets have been observed to be very close to parabolic. The parabola is of interest mathematically because it represents the boundary between the open and closed orbit forms. An object moving along a parabolic path is on a oneway trip to infinity never being able to retrace the same orbit again. The velocity of such an object is the escape velocity and its total energy is zero.

Type
Articles
Information
The Mathematical Gazette , Volume 92 , Issue 523 , March 2008 , pp. 39 - 49
Copyright
Copyright © The Mathematical Association 2008

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References

1. Pathan, A., A geometric derivation and a solution of Barker’s equation for the time of flight along parabolic trajectories, Journal of the British Interplanetary Society, 58 (March/April 2005) pp. 82–89.Google Scholar
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