Overview

In many respects the navigation position fix obtained from celestial observations made aboard a spacecraft is similar to the problem encountered by the seagoing and airborne navigators. The fundamental differences are (1) the spacecraft problem is truly three dimensional and (2) the forces governing the motion of the spacecraft are far better known than the motions of the terrestrial seas and air masses. Therefore, although the first difference noted tends to complicate the problem, the second makes the task somewhat easier and the resulting computations and extrapolations capable of greater precision.

As the first step in the formulation of a navigation theory, we consider the processes involved in determining the position of a spacecraft by means of a celestial fix. For a completely onboard determination, the operation may comprise a sequence of any or all of the following types of measurements: (1) the angle between the lines of sight to selected pairs of celestial bodies, (2) the observation of star occupations. (3) the measurement of the apparent diameter of a planet, and (4) radar measurements. One further operation is implied in the fix, namely, the recording of time as indicated by the spacecraft clock. The intended result of these observations is the determination of the coordinates of spacecraft position together with, perhaps, a correction to the current clock reading. Here, we shall describe several possible forms of the required calculations and then relate the resultant errors in position and time estimates to the errors in the primary measurements.

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