🚀 go-pugleaf

I have questions about the use of navigation state vectors by manned
spacecraft.  My understanding is that what is usually referred to as
the state vector is really two vectors, a position vector and a
velocity vector.  The vectors are in units of feet and feet/sec, and
are in a coordinate system with the z axis pointing at the mean
rotational axis of the earth, the x axis pointing at the mean vernal
equinox, and y axis perpendicular to both.

Are the spacecraft onboard computers continually updating the state
vector?  I could see where this might be a possibility for the shuttle
in earth orbit, but what about the Apollo missions?  I can't imagine
continually solving that kind of n-body problem with the limited
onboard computing resources available at that time.

For the Apollo missions there is also the question of the appropriate
coordinate system.  Did they use the geocentric-equatorial system
throughout, or did they do a coordinate transform when they got to the
moon?

In practice the state vector is often updated by the mission control
center.  This leads to the question of whether or not the spacecraft
can navigate if communications are lost.  It would seem that the ground
tracking network is in a better position to determine the position
vector, while the inertial measurement unit onboard the spacecraft is
the best source for establishing the velocity vector.  If the
spacecraft loses its state vector, can it reestablish one from scratch,
or must they get it from the ground?

Thanks in advance for any information anyone can provide about these
issues.

Paul Evans ple@erg.sri.com