The GPS receiver (Rcv.)?is not shown.

  The S1/2, F?=?1 to P1/2, F?=?1 optical electric dipole transition used for state preparation and readout is shown in purple (note that the source of this light is broad enough to not resolve Zeeman sublevels, so the line is meant to indicate any transition between the S1/2 F?=?1 and P1/2 F?=?1 manifolds that is consistent with selection rules). Also shown are the S1/2, F?=?0, mF?=?0 to S1/2, F?=?1, mF?=?0 magnetic-field-insensitive 40.5-GHz hyperfine clock transition (thick black arrow), and the ΔmF?=?±1 field-sensitive Zeeman lines at ±140?kHz (thin black arrows).

  Allan deviation without any corrections (red), with relativity corrections but no temperature corrections (green), and with both relativity and temperature corrections (black). Simulated expected clock performance with clock parameters during the run with environmental perturbations (solid blue) and without (dashed blue) is shown for comparison. All traces except the blue are overlapping Allan deviation. For reference, the orbital period of about T?=?6,000?s will result in expected peaks in the Allan deviation at 0.37T?≈?2,200?s (ref. 30).

  The orbital period is approximately 6,000?s at an altitude of 720?km.? The component of the fieldin the weakest shielding direction is plotted.? Shielding in the other two directions is over an order of magnitude higher so that the impact of variations on the clock is dominated by the component shown.

  The Allan deviation of the frequency shift associated with measured magnetic field variations on board the DSAC spacecraft is shown (red) assuming a worst-case sensitivity of 7?×?10?16?μT?1. Reference lines are also shown for expected multipole trap (dashed blue) and load trap (dashed black) operation noise floors (without LO noise aliasing effects for the multipole trap line). Error bars represent 68% confidence intervals.

  Signal size is the number of PMT counts measured at the line centre minus the counts at a detuning of one linewidth corresponding to the first minimum in a Rabi line trace. The slope gives an estimate of the number-dependent second-order Doppler shift while operating in the load trap. As a point of reference, the corresponding shift in the multipole trap would be 10–20 times smaller.

  Residuals are now plotted against temperature in the load trap. A linear fit gives a total temperature sensitivity of ?2.3(1.1)?×?10?15?°C?1.

  Temperature data shown for the 52-day dataset described in the main text. a, Long-term temperature variation in the load trap over 52?days correlated with changes in Sun beta angle. b, A 5-day subset showing 24-h temperature variations. c, A 1-day subset showing orbital temperature variation.

  Frequency data with the temperature effect removed (black dots) and fitted to a straight line (blue line), so as to place a limit of 4.6?×?10?16 per day on frequency shifts due to trace-gas evolution in the clock vacuum chamber.

  Total PMT counts in 8.1-s portions of each clock cycle as a function of time, showing excess counts due to passage through the SAA. Each passage is approximately 20?min, as shown for the expanded view (inset). The varying peak amplitude is due to spacecraft orbital precession, which varies the trajectory of the spacecraft in and out of the SAA on a daily timescale.