wrote:

Homework problem:

Given:

A. A light sail.

B. A light sail that is also a "solar cell" and uses the electricity to
power an ion rocket.

Assume equal mass for A and B (at the start), that everything is 100%
efficient and your speed is nowhere near relativistic.

At the start, do you get more "go" from B or are they the same? Why?


The answer is clearly "B", right up until you run out of propellant.
Then it's "A", because you don't have to carry any propellant.

Choosing an exhaust velocity (which implies a subset of possible engine
designs) is fundamentally a trade off between the costs of launching (1)
propellant mass and (2) an energy source. For chemical rockets, the
mass/energy ratio and hence the ideal exhaust velocity is implied by the
propellant you choose because it is also the energy source.

But if you've got a lot of energy available, as from a nuclear reactor
or big solar array, then your propellant doesn't have to be its own
energy source. By using the reactor or solar array as the energy source,
you can eject your propellant at much higher velocities with something
like an ion engine and get that much more impulse from each unit of
propellant mass.

But if you're trying to save energy, then you want a *low* exhaust
velocity. The ultimate example of this is a car, which uses the entire
earth as its reaction mass. That's why few cars are rocket powered;
aside from the noise and lack of safety, they just aren't very
fuel-efficient. Unfortunately, spacecraft can't carry the earth with
them to push on once they're in space. A space elevator would come
close, though.

Phil