If a planet has zero mass (m = 0), then Newtons laws of motion reduce to r (t) = 0 and

Chapter 13, Problem 40

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If a planet has zero mass (m = 0), then Newtons 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 r0 v0 t, and thus Keplers Second Law continues to hold (the rate is constant). Sun Planet r0 v0 r(t) = r0 + tv0