Page "Schwarzschild geodesics" Paragraph 36

To recover the Newtonian solution for the planetary orbits, one takes the limit as the Schwarzschild radius r < sub > s </ sub > goes to zero.

In this case, the third root u < sub > 3 </ sub > becomes roughly 1 / r < sub > s </ sub >, and much larger than u < sub > 1 </ sub > or u < sub > 2 </ sub >.

Therefore, the modulus k tends to zero ; in that limit, sn becomes the trigonometric sine function