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Equation of Time

From the Quicksilver Metaweb.

This is to explain what Isaac and Daniel were up to with the sundial - the equation of time

Stephensonia

Know your gnomon! Captain van Hoek or Dappa would have to sight real noon for navigation purposes daily.

Authored entries

Solar Time

edited from Wikipedia, the free encyclopedia.

Solar time is based on the idea that, when the sun reaches its highest point in the sky, it is noon. Apparent solar time is based on the apparent solar day, which is the interval between two successive returns of the sun to the local meridian[1]. Solar time can be measured by a sundial.

The length of a solar day varies throughout the year. This is because the Earth's orbit is an ellipse , and not a circle, and the Earth moves faster when it is nearest the Sun and slower when it is farthest from the sun (as it follows [http://en2.wikipedia.org/wiki/Kepler's_laws_of_planetary_motion Kepler's laws of planetary motion]). Because of this, apparent solar days are shorter in March and September than they are in June or December . (The amount of daylight also varies because of the 23.5º tilt of the Earth's axis . A tropical year is the length of time that the Sun , as viewed from the Earth , takes to return to the same position along the ecliptic (its path among the stars on the celestial sphere ). Position along the ecliptic is measured from the vernal equinox , one of the four cardinal points along the ecliptic.

Mean solar time is based on a fictional mean sun which travels at a constant rate throughout the year. The length of a mean solar day is a constant 24 hours throughout the year although, as noted above, the amount of daylight varies.

The difference between apparent solar time and mean solar time, which is sometimes as great as 15 minutes, is called the equation of time.

See also time, day, ecliptic, sundial, sidereal time

A pedantical note: The above is the standard explanation of apparent solar time and mean solar time found on most encyclopaedias, and it is "good enough" for most purposes; However, it contains a flaw. It is in the pass from apparent solar time is based on the apparent solar day, which is the interval between two successive returns of the sun to the local meridian . The length of a solar day varies throughout the year to Mean solar time is based on a fictional mean sun which travels at a constant rate throughout the year. The length of a solar day does not vary.

The last sentence makes as much sense as saying "mean time is based on a fictional mean ant which travels at a constant rate throughout the year around a fictional circle. Of course, if we had an actual ant which moved at a constant rate, we could check the length of the solar days against it, make observations of the sun, and say things like "from yesterdays' noon to today's noon 23 hours 59 minutes 15 seconds of constant-rate ant time have elapsed". But a fictional ant won't do the trick, because we can't measure its position in the fictional circle. So mean solar time is not based on it.

Time can only be measured by counting the repetitions of a phenomenon, be it natural like an astronomic observation or artifficial like the ticks of a clock. If we had a reliable enough clock, we could use it to count the number of clock-ticks from a noon to the next and say that the length of the solar days, according to the clock, varies throughout the year. Of course, if all of our clocks are made with 16 century technology so we can't rely on them, then we would be safer saying that, according to the Sun, clock rates vary throughout the year.

Up to the middle of the 20th century, mean time was based on observations of the Sun which were used to keep right the master clocks on which civil time was based.

In fact mean solar time was not based in the orbital motion of the sun around the Earth, on the apparent motion of stars around the Earth, on clocks, or on anything else. When it was used, mean solar time was based exclusively on observations of the apparent motion of the Sun around Earth. To "measure" mean solar time, first the apparent solar time (the position of the Sun) was observed, and then a mathematical correction was added to or substracted from it to get "mean" time. This correction was purely theoretical and based on theories of the motion of the Earth around the Sun, and the resulting "mean" time was found experimentally to agree with the best mechanical clocks up to the beginning of the 20th century.

Nowadays mean solar time is no longer used to keep clocks right, except in Saudi Arabia. Current atomic clocks are widely believed to be more reliable than the rotation of Earth, and the Universal Time scale (TU) our clocks are based on is based on them.

Universal time is never more than one second away from Greenwich's mean solar time. According to the atomic clocks, the rotation of the Earth gradually becomes slower, so leap seconds must be inserted occasionally in the TU scale to keep Greenwich mean noons near 12:00:00 TU.

The following table gives the equivalent in distance for five units of time. These units range from a day to a second:

  • 24 hours of time = 360° of longitude
  • 1 hour of time = 15° of longitude
  • 4 minutes of time = 1° of longitude
  • 1 minute of time = 15 minutes of longitude
  • 1 second of time = 15 seconds of longitude

Meridian

Meridian: In the Sky

In the sky, a meridian is an imaginary great circle on the celestial sphere that is perpendicular to the local horizon . It passes through the north point on the horizon, through the celestial pole , up to the zenith , and through the south point on the horizon.

Because it is fixed to the local horizon, stars will appear to drift past the local meridian as the earth spins. You can use an object's right ascension and the local sidereal time to determine when it will cross your local meridian, or culminate (see hour angle ).

The upper meridian is the half above the horizon, the lower meridian the half below it.

Meridian: On the Earth

On the earth, a meridian is a 'straight line' on the earth's surface between the North Pole and the South Pole (in fact, half of a great circle). Considering the meridian that passes through Greenwich, England, as establishing the meaning of zero degrees of longitude, or the prime meridian, any other meridian is identified by the angle, referenced to the center of the earth as vertex, between where it and the prime meridian cross the equator. As there are 360 degrees in a circle, the meridian on the opposite side of the earth from Greenwich (which forms the other half of a circle with the one through Greenwich) is 180° longitude, and the others lie between 0° and 180° of West longitude in the Western Hemisphere (west of Greenwich) and between 0° and 180° of East longitude in the Eastern Hemisphere (east of Greenwich). You can see the lines of longitude on most maps.

The term "meridian" comes from the Latin meridies , meaning "midday"; the sun crosses a given meridian midway between the times of sunrise and sunset on that meridian.

Analemma

The analemma is a figure-eight shaped plot of the position of the sun in the celestial sphere at noon of each day (at 24 hour intervals) of a calendar year. The vertical coordinate of a point corresponding to a date corresponds to the declination of the sun on that date, while the horizontal coordinate indicates whether the sun is "fast" or "slow" compared to mean time.

The deviation between solar time and mean time is due to the variation in the length of the synodic day, which is due to variation in the distance between the earth and the sun.

A discussion of the derivation of this curve can be found at the following address: discussion of the analemma

TBA