$${M_e = \int_0^{2\pi} \frac{J_e d\Omega}{d\Sigma} = \int_0^{2 \pi} L_e \cos \theta d \Omega = \int_0^{2\pi} d \varphi \int _0^{\pi/2} L_0 \cos \theta \sin \theta d\theta}$$