Time conversions

The following time conversions are accurate at the millisecond level. Some are exact while others have differences at the microsecond level.

System	Description	UT1	UTC	TT	TAI	GPS
UT1	Mean Solar Time	UT1	UTC = UT1 - DUT1	TT = UT1 + 32.184 s + LS - DUT1	TAI = UT1 - DUT1 + LS	GPS = UT1 - DUT1 + LS - 19 s
UTC	Civil Time	UT1 = UTC + DUT1	UTC	TT = UTC + 32.184 s + LS	TAI = UTC + LS	GPS = UTC + LS - 19 s
TT	Terrestrial (Ephemeris) Time	UT1 = TT - 32.184 s - LS + DUT1	UTC = TT - 32.184 s - LS	TT	TAI = TT - 32.184 s	GPS = TT - 51.184 s
TAI	Atomic Time	UT1 = TAI + DUT1 - LS	UTC = TAI - LS	TT = TAI + 32.184 s	TAI	GPS = TAI - 19 s
GPS	GPS Time	UT1 = GPS + DUT1 - LS + 19 s	UTC = GPS - LS + 19 s	TT = GPS + 51.184 s	TAI = GPS + 19 s	GPS

Definitions:

1. LS = TAI - UTC = Leap Seconds from http://maia.usno.navy.mil/ser7/tai-utc.dat
2. DUT1 = UT1 - UTC from http://maia.usno.navy.mil/ser7/ser7.dat or http://maia.usno.navy.mil/search/search.html

[edit] Sidereal time

Sidereal time is the measurement of time relative to a distant star (instead of solar time that is relative to the sun). It is used in astronomy to predict when a star will be overhead. Due to the orbit of the earth around the sun a sidereal day is 4 minutes (1/366th) less than a solar day.