A space probe of mass M is moving with uniform velocity v far from earth and from other massive bodies,and it is planned to deflect from its trajectory through an angle theta by firing from it a suitable mass at velocity v.Derive an expression for the suitable mass m

Answer 1

Space probe momentum change
= (M-m)v sin theta
= ejected mass momentum = m v

m/(M-m) = sin theta

M/m -1 = csc theta

m/M = 1/[1 + csc theta]