Conversions
Visual Representation
General Conversions
System |
Description |
UT1 |
UTC |
TT |
TAI |
GPS |
UT1 |
Mean Solar Time |
UT1 |
= UT1 – DUT1 |
= UT1 + 32.184 s + LS -
DUT1 |
= UT1 - DUT1 + LS |
= UT1 - DUT1 + LS - 19 s |
UTC |
Civil Time |
= UTC +DUT1 |
UTC |
= UTC + 32.184 s + LS |
= UTC + LS |
= UTC + LS - 19 s |
TT |
Terrestrial (Ephemeris)
Time |
= TT – 32.184 s – LS +DUT1 |
= TT – 32.184 s – LS |
TT |
= TT - 32.184 s |
= TT - 51.184 s |
TAI |
Atomic Time |
= TAI + DUT1 – LS |
= TAI – LS |
= TAI + 32.184 s |
TAI |
=
TAI - 19 s |
GPS |
GPS Time |
= GPS + DUT1 - LS + 19 s |
= GPS – LS + 19 s |
= GPS + 51.184 s |
= GPS + 19 s |
GPS |
|
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UT0 |
UT1 with polar motion |
UT0 = UT1 + tan(lat) (x sin(long) + y cos(long)) x and y are pole offsets
published in IERS Bulletin A |
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UT2 |
UT1 corrected for seasonal variations
in Earth’s rotational speed |
UT2 = UT1 + 0.022sin(2πt) -
0.017cos(2πt) - 0.007sin(4πt) + 0.006cos(4πt) t = 2000.0 + (MJD –
51544.03) / 365.2422 |
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|
Besselian day fraction |
t as calculated above |
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TDT |
Terrestrial Dynamical Time |
TDT = TAI + 32.184 s |
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TDB |
Barycentric Dynamic Time |
TDB = TT + 0.001658 sin(g)
+ 0.000014 sin(2g) seconds g = 357.53 + 0.9856003 (JD
– 2451545.0) |
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TCG |
Geocentric Coordinate Time |
TCG – TT = 6.969290134*10-10(MJD
– 43144.0)86400s |
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GMST |
Greenwich Mean Sidereal
Time (equation links GMST directly to UT1) |
GMST (in seconds at
UT1 = 0) = 24110.5841 + 8640184.812866*T + 0.093104*T2 –
0.0000062*T3 T = d / 56525 d = JD – 2451545.0 |
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GAST |
Greenwich Apparent Sidereal
Time |
GAST = GMST + (equation of the equinoxes) |
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LMST |
Local Mean Sidereal Time |
LMST = GMST + (observer’s east longitude) |
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“LAST” |
“Local Apparent Sidereal
Time” |
= GAST + (observer’s east longitude) |
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LST |
Local Mean Sidereal Time |
Hour Angle = LST – Right ascension |
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TCB |
Barycentric Coordinate Time |
TCB = TDB + LB(JDTCB – T0)
86400 +TDB0 LB = 1.550519768×10−8 TDB0 = −6.55×10−5 s T0 = 2443144.5003725 JDTCB = TCB Julian date (quantity = T0 1977
January 1 00:00:00 TAI) |
Important Time Differences
LS |
Leap Seconds (on reference
sheet) |
LS = TAI - UTC |
ΔT |
Time Difference |
ΔT = TT – UT |
DUT1 |
|
DUT1 = UT1 - UTC |
Julian Dates
|
Epoch |
Calculation |
Julian Date |
12h Jan 1, 4713 BC |
|
Reduced JD |
12h Nov 16, 1858 |
JD − 2400000 |
Modified JD |
0h Nov 17, 1858 |
JD − 2400000.5 |
Truncated JD |
0h May 24, 1968 |
floor (JD − 2440000.5) |
Dublin JD |
12h Dec 31, 1899 |
JD − 2415020 |
Lilian date |
Oct 15, 1582[9] |
floor (JD − 2299159.5) |
Rata Die |
Jan
1, 1 proleptic Gregorian calendar |
floor (JD − 1721424.5) |
Unix Time |
0h Jan 1, 1970 |
(JD − 2440587.5) × 86400 |
Mars Sol Date |
12h Dec 29, 1873 |
(JD − 2405522)/1.02749 |