On a
prograde planet like the
Earth, the
sidereal day is shorter than the
solar day. At time 1, the
Sun and a certain distant
star are both overhead. At time 2, the planet has rotated 360° and the distant star is overhead again (1→2 = one sidereal day). But it is not until a little later, at time 3, that the Sun is overhead again (1→3 = one solar day). Or more simply, 1-2 is a complete
rotation of the Earth, but because the revolution around the Sun affects the
angle the sun hits a position on the Earth, 1-3 is how long it takes
noon to return
Solar times are measures of the apparent position of the Sun on the celestial sphere. They are not actually the physical time, but rather hour angles, that is, angles expressed in time units. They are also local times in the sense that they depend on the longitude of the observer.
Apparent solar time
Apparent solar time or true solar time is the hour angle of the Sun. It is based on the apparent solar day, which is the interval between two successive returns of the Sun to the local meridian. Note that the solar day starts at noon, so apparent solar time 00:00 means noon and 12:00 means midnight. Solar time can be measured by a sundial.
The length of a solar day varies throughout the year for two reasons. First, Earth's orbit is an ellipse, not a circle, so the Earth moves faster when it is nearest the Sun (perihelion) and slower when it is farthest from the Sun (aphelion) (see Kepler's laws of planetary motion). Second, due to Earth's axial tilt, the Sun moves along a great circle (the ecliptic) that is tilted to Earth's celestial equator. When the Sun crosses the equator at both equinoxes, the Sun is moving at an angle to the equator, so the projection of this tilted motion onto the equator is slower than its mean motion; when the Sun is farthest from the equator at both solstices, the Sun moves parallel to the equator, so the projection of this parallel motion onto the equator is faster than its mean motion (see tropical year). Consequently, apparent solar days are shorter in March (26–27) and September (12–13) than they are in June (18–19) or December (20–21). These dates are shifted from those of the equinoxes and solstices by the fast/slow Sun at Earth's perihelion/aphelion.
Mean solar time
Mean solar time conceptually is the hour angle of the fictitious mean Sun, assuming the Earth rotates at a constant rate. Currently (2009) this is realized with the UT1 time scale, which is constructed mathematically from very long baseline interferometry observations of the diurnal motions of radio sources located in other galaxies, and other observations.[1] Though the amount of daylight varies significantly, the length of a mean solar day does not change on a seasonal basis. However, the length of a mean solar day increases at a rate of approximately 1.4 milliseconds each century. It was exactly 86,400 (i.e. 24 hours × 60 minutes/hour × 60 seconds/minute) SI seconds in approximately 1820. Currently, the length of a mean solar day is approximately 86400.002 SI seconds.[2] An apparent solar day may differ from a mean solar day by as much as nearly 22 seconds shorter to nearly 29 seconds longer.[citation needed] Because many of these long or short days occur in succession, the difference builds up so that mean time is greater than apparent time by about 14 minutes near February 6 and mean time is less than apparent time by about 16 minutes near November 3. An analemma is a graph of this relationship.[3] Since these periods are cyclical, they do not accumulate from year to year. The difference between apparent solar time and mean solar time is called the equation of time.
The length of the mean solar day is increasing due to the tidal acceleration of the Moon by the Earth, and the corresponding deceleration of the Earth by the Moon.
History
Many methods have been used to simulate mean solar time throughout history. The earliest were clepsydras or water clocks, used for almost four millennia from as early as the middle of the second millennium BC until the early second millennium. Before the middle of the first millennium BC, the water clocks were only adjusted to agree with the apparent solar day, thus were no better than the shadow cast by a gnomon (a vertical pole), except that they could be used at night.
Nevertheless, it has long been known that the sun moves eastward relative to the fixed stars along the ecliptic. Thus since the middle of the first millennium BC, the diurnal rotation of the fixed stars has been used to determine mean solar time, against which clocks were compared to determine their error rate. Babylonian astronomers knew of the equation of time and were correcting for it as well as the different rotation rate of stars, sidereal time, to obtain a mean solar time much more accurate than their water clocks. This ideal mean solar time has been used ever since then to describe the motions of the planets, Moon, and Sun.
Mechanical clocks did not achieve the accuracy of Earth's "star clock" until the beginning of the 20th century. Even though today's atomic clocks have a much more constant rate than the Earth, its star clock is still used to determine mean solar time. Since sometime in the late 20th century, Earth's rotation has been defined relative to an ensemble of extra-galactic radio sources and then converted to mean solar time by an adopted ratio. The difference between this calculated mean solar time and Coordinated Universal Time (UTC) is used to determine whether a leap second is needed. (The UTC time scale now runs on SI seconds, and the SI second, when adopted, was already a little shorter than the current value of the second of mean solar time.[4])
See also
References
- ^ McCarthy, D. D. & Seidelmann, P. K. (2009). TIME From Earth Rotation to Atomic Physics. Weinheim: Wiley-VCH Verlag GmbH & Co. KGaA. ISBN 978-3-527-40780-4. pp. 68, 326.
- ^ "Leap Seconds". Time Service Department, United States Naval Observatory. 1999. http://tycho.usno.navy.mil/leapsec.html. Retrieved November 13, 2007.
- ^ McCarthy, D. D. & Seidelmann, P. K. (2009). TIME From Earth Rotation to Atomic Physics. Weinheim: Wiley-VCH Verlag GmbH & Co. KGaA. ISBN 978-3-527-40780-4. p. 11.
- ^ :(1) In "The Physical Basis of the Leap Second", by D D McCarthy, C Hackman and R A Nelson, in Astronomical Journal, vol.136 (2008), pages 1906-1908, it is stated (page 1908), that "the SI second is equivalent to an older measure of the second of UT1, which was too small to start with and further, as the duration of the UT1 second increases, the discrepancy widens." :(2) In the late 1950s, the cesium standard was used to measure both the current mean length of the second of mean solar time (UT2) (result: 9192631830 cycles) and also the second of ephemeris time (ET) (result:9192631770 +/-20 cycles), see "Time Scales", by L. Essen, in Metrologia, vol.4 (1968), pp.161-165, on p.162. As is well known, the 9192631770 figure was chosen for the SI second. L Essen in the same 1968 article (p.162) stated that this "seemed reasonable in view of the variations in UT2".
External links