[zgvtcmhj] Radian of a solar day

2pi radianofasolarday = 1 solar day = 24 hour

1 radianofasolarday = 3 hour 49 minute 11 second

1 milliradianofasolarday = 13.75 second

1 hour = 261.8 milliradianofasolarday
1 minute = 4.3 milliradianofasolarday
1 second = 73 microradianofasolarday

We specify solar day assuming angle calculations relative to the sun are the most likely to be useful.  radianofasiderealrotationperiod also might be useful.  Not sure where radianofasiderealday might be useful.

Note well that the sun's motion around the sky is not quite circular, see analemma.

Similarly:

2pi radianofatropicalyear = 1 tropical year = 365.2421897 day = 31556925.19 second

1 radianofatropicalyear = 58 day

1 second = 31.69 nanoradianofatropicalyear

Note well that Earth's orbital speed around the sun is not constant because Earth's orbit is an ellipse, so the mapping between time and the position in the seasonal cycle is complicated.

For astronomers:

2pi radianofasideralyear = 365.256363004 day = 31558149.7635 second

Note well that Earth's orbital speed around the sun is not constant because Earth's orbit is an ellipse, so the mapping between time and Earth's location in space is complicated.