Discussion

Although we have a partial model for the dependence of the clock period on satellite temperature, there are still several difficulties in using this dependence to synthesize the clock phase solely from temperature data. The major difficulties include:
    (1) The period of the Ginga clock has a strange temperature dependence, with a sharp maximum near 18°C. This behavior complicates any attempt to correct the clock phase to millisecond accuracy. Unfortunately, this defect was not detected in the laboratory, and the relationship between clock period and satellite temperature must be established from operational data.
    (2) The temperature of the clock circuit cannot be determined directly, but must be estimated by a linear combination of the temperatures reported by nearby sensors. A minor problem is that the satellite temperatures are recorded with a precision of ~0.5°C, and the resulting uncertainty in the combination temperature propagates into the synthesized clock period. More importantly, our model of the clock temperature does not take into account any dependence on the satellite orientation. There are possibly large changes in the internal temperature stratification depending on which parts of the satellite are illuminated by the Sun.
    (3) Another difficulty is that the temperature-clock period relationship is based on temperatures and clock periods averaged over a satellite orbit. These averages therefore cover the ~1°C excursion in temperature and the ~5 µs excursion in clock period throughout the satellite day-night temperature cycle. Thus the relationship shown in Figure 5 is not representation of the true temperature-period relationship, but a smoothed version with the peak somewhat reduced. This is not a serious drawback if the relationship is used in the same manner it was constructed, with temperatures averaged over a satellite orbit, and then converted into the corresponding average clock periods.
    (4) There is a possible hysteresis in the clock circuit, with the clock rate depending not only on temperature but also on the rate of change of the temperature (Walls 1989).

To solve these problems would require extensive modelling of the clock rate as a function of many parameters. This would be a time-consuming and possibly hopeless endeavor. As an alternative, we suggest an ad hoc approach that minimizes most of the above problems. This procedure is intended for clock corrections across blocks of remote orbits; for contact orbits the error in time assignment is much less severe (see below). The synthesized clock phase tracks the true phase very well locally, on which long term drifts are superposed. The obvious explanation for these drifts is incomplete modeling of the clock temperature. We should be able to remove most of this drift by adding a slowly varying correction to the estimated clock temperature.

An approximation to this method which is easier to implement is an adjustment to the clock rate instead of the temperature. Whenever the relationship between temperature and clock period is nearly linear the two methods give almost identical results, but they will differ when the temperature is near the maximum in the temperature-clock period relationship. The result of applying this correction to the data in Figures 6a and 6b is shown in Figures 8a and 8b. In particular, Figure 8b shows the correction to the clock phase due to temperature variations between comparisons of the onboard clock with the KSC clock. As long as the satellite orientation remains fixed, and the temperature does not cross the maximum in the temperature-clock period relationship, this correction should be accurate to 2 or 3 ms.

For contact orbits, where clock comparisons are made on almost all passes over the ground station, the temperature drift in the clock phase is not a major problem. The error in time assignment is then dominated by variations in clock rate induced by the satellite day-night cycle. At the present time, we do not know whether the clock feels the full effect of the day-night temperature cycle, some 0.6°C in amplitude. As seen in Figure 7a, this cycle could induce a 0.5 ms term in the clock phase, and this would have an important bearing on the timing of millisecond pulsars. However, the only Ginga projects involving millisecond pulsars have been searches rather than long-term observations. The searches have been limited to 20 or 30 minute segments, over which the effect of the day-night cycle is relatively unimportant.