<P> Earth's rate of rotation must be integrated to obtain time, which is Earth's angular position (specifically, the orientation of the meridian of Greenwich relative to the fictitious mean sun). Integrating + 1.7 ms / d / cy and centring the resulting parabola on the year 1820 yields (to a first approximation) 31 × (year − 1820 / 100) 2 seconds for ΔT . Smoothed historical measurements of ΔT using total solar eclipses are about + 17190 s in the year − 500 (501 BC), + 10580 s in 0 (1 BC), + 5710 s in 500, + 1570 s in 1000, and + 200 s in 1500 . After the invention of the telescope, measurements were made by observing occultations of stars by the Moon, which allowed the derivation of more closely spaced and more accurate values for ΔT . ΔT continued to decrease until it reached a plateau of + 11 ± 6 s between 1680 and 1866 . For about three decades immediately before 1902 it was negative, reaching − 6.64 s . Then it increased to + 63.83 s at 2000 and + 70.25 s at mid 2017 . It will continue to increase at an ever - faster (quadratic) rate in the future . This will require the addition of an ever - greater number of leap seconds to UTC as long as UTC tracks UT1 with one - second adjustments . (The SI second as now used for UTC, when adopted, was already a little shorter than the current value of the second of mean solar time .) Physically, the meridian of Greenwich in Universal Time is almost always to the east of the meridian in Terrestrial Time, both in the past and in the future . + 17190 s or about 4 ⁄ h corresponds to 71.625 ° E . This means that in the year − 500 (501 BC), Earth's faster rotation would cause a total solar eclipse to occur 71.625 ° to the east of the location calculated using the uniform TT . </P> <P> All values of ΔT before 1955 depend on observations of the Moon, either via eclipses or occultations . The angular momentum lost by the Earth due to friction induced by the Moon's tidal effect is transferred to the Moon, increasing its angular momentum, which means that its moment arm (its distance from the Earth) is increased (for the time being about + 3.8 cm / year), which via Kepler's laws of planetary motion causes the Moon to revolve around the Earth at a slower rate . The cited values of ΔT assume that the lunar acceleration (actually a deceleration, that is a negative acceleration) due to this effect is dn / dt = − 26" / cy, where n is the mean sidereal angular motion of the Moon . This is close to the best estimate for dn / dt as of 2002 of − 25.858 ± 0.003" / cy so ΔT need not be recalculated given the uncertainties and smoothing applied to its current values . Nowadays, UT is the observed orientation of the Earth relative to an inertial reference frame formed by extra-galactic radio sources, modified by an adopted ratio between sidereal time and solar time . Its measurement by several observatories is coordinated by the International Earth Rotation and Reference Systems Service (IERS). </P>

What is the relationship between delta x and delta t in a quadratic relationship