Actually, if you want to see it simply, all the analysis and computation has to be
done with respect to the spacecraft. As long as the craft is expelling
mass at some speed, hence with some momentum, it gets equivalent
momentum in the opposite direction. That is how they can increase
their speed (or decrease it if they turn head to tail).
But your questionning is not fully unjustified, in the following
sense: this works because the mass expelled from the exhaust was
already going at the same speed as the spacecraft. It was carried
and accelerated by the spacecraft in the earlier parts of the flight.
This is actually a major problem. Much of the fuel carried by
spacecrafts when they leave earth is used only to lift and later accelerate the fuel that
will be needed later on, so that the useful payload is actually quite
small. The same problem will exist for most reaction crafts: the have first to carry and accelerate with themselves the mass they intend to exhaust later for propulsion.
But there are ways around it. Momentum can be increased either by increasing exhausted mass or by
increasing its speed. So the first improvement is to save on mass by increasing speed of exhaust. But
designing engines that exhaust matter at very high speed the
spacecraft can get momentum with very little mass exhausted.
This allows a larger payload as much less reactive mass needs to be
used for the same result.
This can be done, for example, with ionic
engines that exhaust ions accelerated at very high speed
The main drawback of these engines is that they have very low thrust,
so the craft gathers speed slowly. But that is often not a problem, except for
taking off from Earth or any planet with an atmosphere.
When there is no atmosphere, as is the case on the moon, spacecrafts
can accelerate to orbital speed almost horizontally (if supported while orbital speed is not attained and centrigugal force is still insufficient). Hence they can be
accelerated by ground devices and no longer need powerful engines for
takeoff. This however requires large installations that do not exist
Though they are more mass efficient, such spacecrafts still have to
carry the reactive mass they will exhaust. And they have to carry a
source of energy to accelerate that mass.
- science-fiction warning -
Solutions have been imagined to avoid these problems. One solution
would be to use electromagnetic fields to collect interstellar matter
that would then be accelerated as reactive mass for thrust. The
problem then is that this matter may not be moving at the same
velocity as the spacecraft and collecting it may induce a drag
on its velocity. But this is still workable if it is exhausted at a
speed that much exceed its speed relative to the craft when collected.
The drag induced by the collecting can be perceived as a head wind. It
can probably be reduced or eliminated altogether by simply channelling
this wind through the spacecraft exhaust acceleration system so that
it simply gets out faster than it came in, without ever moving in the
direction of the craft. That is typically the functionning mode of
ramjet engines used in some aircraft. The problem with ramjet is that
they only work when the craft is already moving at sufficient speed.
The next step is also to find in space the energy source that is use
to accelerate the reaction mass. The best know proposal is the Bussard
Strangely, one interesting source of ideas for powering motion might be with bacteria who extract, in many diverse way, the energy and the reactive mass they need from the surrounding medium. The problems are of course quite different technically, but still ... (just my own wild perception of it).