Consider a planet in an elliptical orbit around the sun moving from A to A1 having an angular displacement of dθ in time dt. Then, the sector area dA covered in time dt would be half of the product of the planet's radial distance and the arc rdθ. The sector velocity dA/dt would then be equal to half of r2dθ/dt. Here, dθ/dt is the planet's angular velocity. Thus, multiplying the equation by the planet's mass gives the sector velocity in terms of the planet's angular velocity. However, mr2ω is the planet's angular momentum. Therefore, the sector velocity equals the ratio of the planet's angular momentum to two times its mass. Kepler's second law states that if a planet takes the same time dt to move from B to B1, then the sector area under the arc BB1 would be equal to the area under the arc AA1. Therefore, the sector velocity is constant, implying that the angular momentum remains conserved.