Let ϕ ϕ be the initial fuel mass fraction on board and m 0 the initial fueled-up mass of the rocket. Divide the total mass of fuel ϕ ϕ m 0 into N discrete pellets each of mass m p = ϕ ϕ m 0 / N . The remaining mass of the rocket after ejecting j pellets is then m = m 0 ( 1 − − j ϕ ϕ / N ) . The overall speed change after ejecting j pellets is the sum Δ Δ v = v eff ∑ ∑ j = 1 j = N ϕ ϕ / N ( 1 − − j ϕ ϕ / N ) ( 1 − − j ϕ ϕ / N + ϕ ϕ / N )