Presentation on Equation of time

Presentation on Equation of Time

Presented By:Md. Nazmus Saqib Khan

ID 12075768Year: 4th

Session: 2011-12Department of MathematicsUniversity of Rajshahi-6205

IndexSome DefinitionsDefining Equation of TimeChief Causes of Equation of TimeGraphical RepresentationSome applicationsReferences

© Department of Mathematics, R.U.

Some DefinitionsApparent sun

Mean sunApparent solar

timeMean solar time

Transit

Hour Angle

Right Ascension


Some Definitions


Apparent sun: The sun we see in the sky is called apparent sun.

Mean sun: The mean sun is fictitious point which moves uniformly along the equator with the mean velocity of the sun along the ecliptic.

Some DefinitionsApparent Solar Time: Apparent solar time at any instant is the time that has elapsed since the preceding apparent midnight. Apparent midnight is the instant of the sun’s lower transit on the meridian.Apparent solar time is equal to the hour angle of the apparent sun.It is actually the time shown by a sundial. (Fig.1)

Fig.1: Roman Sundial© Department of Mathematics, R.U.

Some DefinitionsMean Solar Time: The mean solar time at any instant is the time that has elapsed since the lower transit of the mean sun. In other words, the time indicated by the mean sun is termed as mean solar time or simply mean time. Mean solar time is equal to the hour angle of the mean sun. It is actually our clock time. (Fig.2)

Fig.2: Mechanical Clock


Some DefinitionsTransit: The instant when any point on the celestial sphere is on the meridian of an observer is called the transit or culmination, of that point over that meridian. When it is on the half of the meridian containing the zenith is called upper transit; when it is on the other half it is called lower transit.(Fig.3)

Fig.3: Transit© Department of Mathematics, R.U.

Some DefinitionsHour Angle: It is the angle subtended at the pole between the observer’s meridian and the hour circle of the body. In the northern hemisphere, the hour angle is always measured from the south towards the west upto the hour circle of the heavenly body. (Fig.4)

Fig.4: Hour angle© Department of Mathematics, R.U.

Some DefinitionsRight ascension: It is the angular distance measured from the vernal equinox along the equator to the point of intersection of the equator with the hour circle through the body. It is measured from the vernal equinox eastwards from 0 to 360 degrees. (Fig.5) Fig.5: Right Ascension


Defining Equation of TimeSince observations made on the sun for the purpose of determining the time can give apparent time only, it is necessary to be able to find at any instant the exact relation between apparent and mean time. The difference between the two, which varies from -14m to +16m (nearly), is called the equation of time. This quantity may be found in the Nautical Almanac for each day of the year.© Department of Mathematics, R.U.

Defining Equation of TimeSo the equation of time at any instant at a given place is defined as the difference between the apparent solar time and mean solar time at that instant. Equation of time = Apparent solar time – Mean solar time

= H.A. of apparent sun – H.A. of mean sun

= R.A. of mean sun – R.A. of apparent sun Since, H.A. of a body = – R. A. of the body . [H.A. = Hour Angle R.A. = Right Ascension]© Department of Mathematics, R.U.

Chief Causes of Equation of TimeThe difference between the two kinds of time is due to several causes, the chief of which are:I. The inequality of the earth’s

angular motion in the orbit, andII. The fact that the apparent sun

is on the ecliptic while the mean sun is on the equator.


Graphical Representation

Table A. Equation of Time for 1910© Department of Mathematics, R.U.

Graphical Representation

Fig. 6: Graphical representation of Equation of Time© Department of Mathematics, R.U.

Some applications The equation of time is used to correct the sundial time. In

the late 17th and 18th centuries, equation clocks were made, which allowed the user to see or calculate apparent solar time, as would be shown by a sundial.

It is also used for many applications of solar energy. Machines such as solar trackers and heliostats have to move in ways that are influenced by the equation of time.

Civil time is the local mean time for a meridian that often passes near the center of the time zone, and may possibly be further altered by daylight saving time. When the apparent solar time that corresponds to a given civil time is to be found, the difference in longitude between the site of interest and the time zone meridian, daylight saving time, and the equation of time must all be considered.


Some applications

Fig.7: 8MW Horizontal Single Axis Tracker in Greece© Department of Mathematics, R.U.

Some applications

Fig. 8: Heliostat by the Viennese instrument maker Ekling (ca. 1850) © Department of Mathematics, R.U.

Some applications

Fig. 9: Standard Time Zone of the World© Department of Mathematics, R.U.

ReferencesSpherical Astronomy by W. M. Smart

Practical Astronomy by George L. Hosmer

Spherical Astronomy by SharmaAstronomy by K. K. DeThe Astronomical Almanac onlineWikipediaGoogle Images© Department of Mathematics, R.U.

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Thank You!© Department of Mathematics, R.U.

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Presentation on Equation of time