I think Newton would be very upset that you are all crediting Einstein for his "discovery."
And I think y'all are missing the point. Near the planet surface, the acceleration of gravity is nearly constant (9.8m/s^2) DOWN. If you are free falling (discounting the resistance of the atmosphere) you ARE NOT ACCELERATING. The accelerometer is correct. You would not experience acceleration and would be, essentially weightless. Some people make big bux selling plane rides that use just this phenomenon.
Orbiting spacecraft are counteracting the acceleration of gravity by spinning arount the planet core really fast. The centrifugal acceleration (v^2/r) is equivalent to the gravitational acceleration. Therefore, again, weightlessness.
The thing is, the acceleration due to gravity is pretty constant (actually it falls off as the square of the distance a(g)=G/(r^2) from the center of the source, but so long as you are confined to the atmosphere, it will be pretty constant.
Therefore if you are "still" you can expect to experience a constant acceleration (9.8m/s^2) down. All the time. This is easy to compensate for mathematically - just subtract it from the Z component of both accelerometers.
If you have two accelerometers connected together by a fixed distance, and one experiences less acceleration than the other, the assembly has begun rotating in the vertical plane. On the other hand, if one experiences more horizontal acceleration than the other, the assemply has begun rotating in that plane. If they are both experiencing the same acceleration they are RELATIVELY not moving. It is that relationship to one another that can be used to derive the attitude. Gravity cancels out. An attitude indicator will still read straight and level if the plane is falling, so long as it in falling level - as in under a parachute.
Really.
I don't mean to start up an argument and I respect the knowledge of the members here, but two accelerometers and a clock are all you need. Really.
Shawn Clark
[email protected]
http://en.wikipedia.org/wiki/Isaac_Newton
http://en.wikipedia.org/wiki/Gravity