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) r 0 tv 0 , where r 0 r(0) and v 0 r '(0) (Figure 1) Show that the area swept out by the radial vector at time t is A(t) 1 2 r 0 v 0 t, and thus Keplers Second Law holds in this situa...

Integrating rt 0 gives The constant c is r0 v0 That ...

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

Question:

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