(2)
Hence equal areas are swept over by the radius vector in equal times.
If P be the acceleration towards O, we have
| v | dv | = −P | dr | |
| ds | ds |
(3)
since dr/ds is the cosine of the angle between the directions of r and δs. We will suppose that P is a function of r only; then integrating (3) we find
1⁄2v2 = − ∫ P dr + const.,
(4)
which is recognized as the equation of energy. Combining this with (1) we have
| h2 | = C − 2 ∫ P dr, |
| p2 |