Consider a planet orbiting the Sun, and let P1, P2, P3, and P4 be the planet’s position at...

Consider a planet orbiting the Sun, and let P1, P2, P3, and P4 be the planet’s position at four corresponding time instants t1, t2, t3, and t4 such that t2 − t1 = t4 − t3. Letting O denote the position of the Sun, determine the ratio between the areas of the orbital sectors P1 OP2 and P3 OP4. Hint: (1) The area of triangle OAB defined by the two planar vectors and as shown is given by Area ; (2) the solution of this problem is a demonstration of Kepler’s second law (see Section 1.1).

Figure P5.92