It is difficult to gauge by eye
the sublight acceleration available to SW vessels seen in ANH. The
countdown of the Death Star's approach to Yavin IV gives us very firm
capabilities for both the battle station and the starfighters scrambled
to intercept it.

The battle station has ~6

g
of sustained acceleration based on careful analysis of this countdown.

It is
clearly not designed for tactical maneuvering.

Fighters, on the other hand, have an acceleration around 85-200

g.

This is
further clarified by the travel of the Millenium Falcon from
Tatooine, which indicates sublight acceleration of around 80

g.

This
suggests the lower end of estimates of fighter acceleration to be
correct, as the Falcon also engages in the battle of Yavin.

We know that the mechanism driving TIE fighters are ion engines. From
the VFX used for all ships, it would appear that all ships use ion
engines for high-thrust applications. From the novelization, it is
clear that repulsorlifts are sufficient to get into orbit, however.

Over the
comm system of the Death Star, a voice announces that the Death Star is

"Orbiting planet at maximum
velocity. The moon with the Rebel base will be in range in thirty
minutes." The assorted diagrams of the Death Star's approach to
Yavin IV show that

"in
range" refers to having line-of-sight to the moon, as in
the image below:

Averaging the Death Star and the moon's positions relative to Yavin, we
find that the Death Star averages 1.5 radii from the center of Yavin
(red and violet circle),
while the moon averages 2 radii from the center (green circle). We may
assume Yavin has a radius of 50,000±25,000 km.

A little quick trigonometry demonstrates that the gas giant
protects the moon
for only 136 degrees of arc (yellow), making the absolute maximum
distance
traveled by
the Death Star (violet arc) outside of the 3.56 times the radius of
Yavin. If the Death Star began traveling directly towards Yavin, this
distance is at most half this.

Given a time of 30 minutes, this gives us a maximum average speed of
49±25 km/s. For a straight-line
path, this would requires 55±27m/s

^{2} of acceleration,
or

~6

g.

Another way to model this is to assume the Death Star to be
traveling in a circle at uniform speed, based on the

"maximum velocity"
comment. For uniform circular motion, acceleration is v

^{2}/r,
or up to ~28 m/s

^{2}. Yavin can be assumed to provide most of
this acceleration.

X and Y
Wing fighters were launched when the Death Star was between 20 and 15
minutes from attacking the Rebel base, beginning their attack run
before the 7 minute mark. We may safely assume they operated at maximum
sustained acceleration in approaching the Death Star, and spent
10±3 minutes approaching it.

This is a far simpler problem. The trigonometry mentioned in the above
section (see diagram for summary; actual trigonometry left as an
exercise for the reader) gives
us the precise position from which the Death Star may fire. The
distance is three times the radius of Yavin from the moon, or
150,000±75,000 km.

First, the X and Y Wings accelerate towards the Death Star until halted
by impact with its magnetic field. This is a least-time intercept, and
gives
us 830±650 m/s

^{2} - 85±66

g.

Second, the X and Y Wings brake on their own, matching the Death Star's
incoming velocity of around 99 kps. This gives us 2000±1600 m/s

^{2},
or 200±160

g^{}.

During the
novelization's detailed description of the heros' escape from Tatooine,
we hear of the

"baleful
lemon eye of Tatooine shrinking rapidly." This implies
that the Falcon is several planetary diameters out already. A page or
so later, the Falcon is still

"a
few minutes yet" from a safe hyper limit, which could be as
much as 6 planetary diameters from the surface.

We may therefore reasonably guess the Falcon to have traveled the last
half of the trip in three to five minutes - the most likely
interpretation of

"a few"
- and therefore traveled ~75,000 km in 5-10 minutes at maximum
acceleration from zero. This means a net average forward
acceleration of 740±250 m/s

^{2},
or 76±25

g.