If a planet has zero mass (m = 0), then Newton’s laws of motion reduce to r "(t) = 0 and the orbit is a straight line r(t) = r₀ + tv₀, where r₀ = r(0) and v₀ = r'(0) (Figure 1). Show that the area swept out by the radial vector at time t is A(t) = 1/2 ΙΙr₀ × v₀ΙΙt, and thus Kepler’s Second Law holds in this situation as well (because the rate of change of swept-out area is constant).

ro Sun Vo Planet r(t) =ro+tvo