spherical positioning

[KenWittlief]

I think we are getting lost in the terminology here.

Gyros: originally referred to mechanical devices that spin like a top, with very low friction bearings (gimbles). The gyros would be spun up with with the system on the ground, in a known orientation, and that was your reference point for the duration of the flight. From the angles on each gimble (or bearing axis) you could tell which way your vehicle was pointing, and by the change of those reading you could calculate rotational velocity and acceleration

For several years FIRST included yaw rate sensors in the kit of parts - referred to as 'solid state gyros'. This gets confusing because the yaw rate sensors measured the RATE at which you were turning on one given axis. To get the angle you have to integrate the reading over time, and to get the acceleration you had to measure the derivative (rate of change) of the sensor output.

Still with me?

There are also linear accelerometers available. These measure your acceleration in a linear direction. (thats why they are called accelerometers, they measure acceleration). To get velocity you have it integrate the reading over time, and to get position you have to integrate the velocity over time.

So an accelerometer will indicate gravity. But heres the problem with the original question. To find which way is up you must assume no other force is acting on the vehicle - no one is pushing you, there is no wind, and also, your vehicle is not spinning and causeing a centrifical force (that would feel like acceleration or artifical gravity).

Under a very limited set of conditions you could use a 'downward' pointing accelerometer to determine which way is up: very limited. If you are freefalling, or in orbit, or being moved by an outside force, or spinning, then you need much more information to know which way is up.

the amount of time it takes for your 'gimbal readings' to drift off was the measure of the quality of your navigation system. The error rate was measured in degrees per hour (drift). The better the system, the lower the drift rate.

For the Apollo missions the astronauts took periodic readings of stars, to measure the drift rates and zero out the accumulated error (drift).