(5)
which completely determines the path except as to its orientation with respect to O.
If the law of attraction be that of the inverse square of the distance, we have P = μ/r2, and
| h2 | = C + | 2μ | . |
| p2 | τ |
(6)
Now in a conic whose focus is at O we have
| l | = | 2 | ± | 1 | , |
| p2 | r | a |
(7)
where l is half the latus-rectum, a is half the major axis, and the upper or lower sign is to be taken according as the conic is an ellipse or hyperbola. In the intermediate case of the parabola we have a = ∞ and the last term disappears. The equations (6) and (7) are identified by putting
l = h2/μ, a = ± μ/C.