There are at least 3 accelerations in DGIV

1. ACC displayed on Surface MFD. It shows the rate of change of ship's velocity. This would have been closest to the

definition of acceleration, except that Surface MFD considers only the length (modulus) of the velocity vector. In

physics, though, change of the speed direction without change of its amount is still acceleration.

2. Acceleration on the D3 display. It shows the acceleration experienced by the crew. This is the acceleration of the

ship due to all forces, except gravity. Unless I am missing something, in Orbiter this leaves us with engine thrust and

aerodynamic forces (lift + drag).

3. ACC (bottom line) on Engine Display. This is the acceleration of the ship due to engine thrust not considering any

other forces

ACC [ m/s^2 ] = Thrust [ N ] / Ship mass [ kg ]

In case of a circular orbit and pro- or retro-burn this happens to be the actual acceleration of the ship.

So if you want to calculate at what distance from a Moon base to start braking, the initial approximation could be

(typical numbers for DGIV in "Moon" configuration, launch from KSC):

ACC = 260 kN (= 260,000 N) / 16500 kg = 15.76 m/s^2

If the orbital velocity is V = 1640 m/s, the "stopping distance" of DGIV will be

V^2 / (2 * ACC) = 85.3 km

But as I said this is just the initial approximation. What we are ignoring is:

A. As the orbital velocity decreases, part of the thrust should be directed "up" to prevent the ship from impacting the

surface short of the target.

B. As the ship burns fuel, its mass decreases, and, given constant thrust, its acceleration increases.

Both affect the stopping distance in opposite ways: A increases it and B decreases it.

Unfortunately, it is not possible to derive a simple formula for the stopping distance that takes A and B into account.

However, as a worst case estimate, you can consider that a portion of the engine acceleration counters the gravity

during the entire braking. Then the "useful" (for reducing the horizontal velocity) acceleration would be

Sqrt( ACC^2 - g^2)

where g is the acceleration at the surface. 9.81 m/s^2 for the Earth, 1.62 m/s^2 for the Moon.

V^2 / (2 * Sqrt( ACC^2 - g^2)) = 85.8 km

Luckily, due to the high thrust / mass ratio of DGIV and low Moon gravity, the optimistic and pessimistic estimates are

very close.