375(6): Definition of alpha and epsilon of the Ellipse

If X and Y are found from the integration of Eqs. (9) and (10), they should obey Eq. (8) in the non relativistic limit, using astronomical data for alpha and epsilon from tables. If the relativistic equation ((11) is solved numerically then Eq. (8) will no longer be obeyed. This is one way of relating alpha and epsilon to X and Y. As shown in Note 375(2), Eq. (1) for the offset Cartesian ellipse is equivalent to r = alpha / (1 + epsilon cos phi)), the polar equation of the ellipse. The ellipse is offset because m orbits M and M is at one focus of the ellipse, not at its centre. There are many ways of developing these equations. Horst’s discovery of Eq. (11) by computer algebra is very interesting and it can be applied to the Hulse Taylor binary pulsar.


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