Last revised 12 February 2009.

From time to time, Houston could update the onboard SV using tracking and other available date; but, generally, it was the AGC's job to update the SV at about two second intervals During coasting flight, with the engines off, the AGC used the Coasting Integration Routine (Section 5.2 in the GSOP) to update the SV. Although Earth was the dominant gravitational influence in earth orbit and, likewise the Moon in lunar orbit, the effects of both had to be included to update the SV with sufficient accuracy. The spacecraft orbit was similar to a Keplerian ellipse, but not quite identical. The Coasting Integration Routine made use of a venerable, 19th-century perturbation technique called Encke's Method.

During powered flight, the Average-G Routine was used in solving the equations of motion using (1)integrations of three-component dynamic acceleration provided by IMU Pulsed Integrating Pendulous Accelerometers (PIPAs) and (2) three-component values of gravitational acceleration.. A detailed description of the AGC can be found at Ron Burkey's comprehensive AGC site, especially the Guidance System Operations Plan (GSOP). A detailed discussion of the Average-G Routine used to update the SV during powered flight can be found in GSOP section 5.3.2.

Here is a brief description of the routine.

Let's imagine that State Vector was last updated to time,

Since the last update, a time interval Dt has passed and the PIPAs have accumulated a dynamic, vector velocity change,

The terms enclosed in square brackets can be thought of as the velocity updated halfway, to the time

So far, the routine has been using the gravitational acceleration it had a time,

Next, the velocity vector is updated

where
the gravity term uses the average of the values at the end of the
interval, **g(t+****Dt****), **and the value at
the beginning, **g(t****)** . Hence the
name of the routine.