# IERS Rapid Service / Prediction Center U.S. Naval Observatory

## Common Units and Conversions in Earth Orientation

### Units

• 1 mas = 1 milliarcsecond = 1 thousandth of a second of arc (for polar motion & nutation)
• 1 ms = 1 millisecond = 1 thousandth of a second of time (for UT1)
• 1 mas equals an equatorial shift at the Earth's surface of 3.1 cm
• 1 ms equals the time it takes for the Earth to spin 15 mas (46.5 cm at the equator)

### Conversions

• Modified Julian Date (MJD): MJD = Julian Date - 2,400,000.5 days
• UT2-UT1 = 0.022 sin(2*pi*T) - 0.012 cos(2*pi*T) - 0.006 sin(4*pi*T) + 0.007 cos(4*pi*T)
• T, the Besselian date, is given by T = 2000.000 + (MJD - 51544.03) / 365.2422
• TT = TAI + 32.184 seconds
• Since 00h 00m UTC 01 Jan 2017, the cumulative leap second count is: TAI-UTC = 37 seconds (exactly) and GPS Time-UTC = 18 seconds
• Users may compute Delta T using the relation Delta T = 32.184 s + (TAI - UTC) - (UT1 - UTC) where (TAI - UTC) is the cumulative number of leap seconds (UT1 - UTC) is a standard EOP product.