# Re: starship-design: Deceleration scheme

```Timothy van der Linden writes:
> I'm not sure what you mean with "things" but it simply is not true that
> higher exhaust velocities are best.

This is really very simple.

v = p / E (p = momentum, E = total energy)

m^2 = E^2 - p^2 (m = mass)

If you start with with a quantity m of fuel at rest, it also has a total
energy E.  If you then react the fuel, you will have a smaller quantity
of mass m1 of moving particles, but the same total energy E in the
reaction products (simply, conservation of energy), and a consequent
nonzero p.  You will get the most zing for your starship if you maximize
p -- the higher p is, the higher the resultant velocity of the starship
when you burn a certain amount of fuel.  For a given E, what's the
highest p you can get?  Simply enough, if you convert all the fuel
into photons, then m = 0 and p = E.  In any other case p < E and your
ship is going slower given the same amount of fuel.

Now, this isn't the same as Ken's analysis of slowing a ship down using
beamed power going in the same direction as the ship and reaction mass.
In order for the ship to slow down it has to eject reaction mass; if it
doesn't lose mass it can't slow down, and the best it can do is stay at
a constant speed by completely ignoring the beam.  My analysis applies
to self-fueled ships only, because the "box" in which the energy and
momentum conservation apply contains only the ship and its fuel.  The
"box" for Ken's situation contains both a quantity of photons moving in
the same direction as the ship, the ship itself, and the reaction mass
it carries; the ship slows down by throwing reaction mass ahead of
itself.  Similarly, the Forward retrosail (using a reflecting sail sent
out ahead of the ship to reflect beamed power back to the ship to slow
it down) slows down the ship at the cost of accelerating the sail, and
with rather painful ineffiency since the back-reflected photons get
seriously redshifted as the forward reflector accelerates.

```