Time lrg

Grunt Productions 2007

TimeTime

A brief by Lance GrindleyA brief by Lance Grindley


Origins of TimeOrigins of Time

• Apparent motion of the Sun around the Apparent motion of the Sun around the Ecliptic takes one year.Ecliptic takes one year.

• One rotation of the Earth on its axis One rotation of the Earth on its axis (measured relative to the Sun) takes one (measured relative to the Sun) takes one solar day.solar day.

• Period of the Moon’s revolution round the Period of the Moon’s revolution round the earth was one month (now arbitrary period).earth was one month (now arbitrary period).

• A week is the length of time for the Moon to A week is the length of time for the Moon to progress from one phase to the next.progress from one phase to the next.


Solar DaySolar Day

• Interval elapsed between two Interval elapsed between two successive transits of the Sun across successive transits of the Sun across the same meridianthe same meridian

• Apparent solar day is not a fixed length:Apparent solar day is not a fixed length:– orbits of planets are ellipsesorbits of planets are ellipses– the radius vector sweeps out equal areas the radius vector sweeps out equal areas

in equal periods of timein equal periods of time– time is measured around the plane of the time is measured around the plane of the

equator (inclined at 23equator (inclined at 2311//22oo to ecliptic) to ecliptic)


Orbiting BodyOrbiting Body

Body moves faster along orbit

Equal areas swept by radius vector


Local Mean TimeLocal Mean Time

• System based solely on longitude.System based solely on longitude.

• Based on earth’s rotation of 15Based on earth’s rotation of 15oo per hour. per hour.

• Four minute time difference for every Four minute time difference for every degree in longitude.degree in longitude.

• Impractical for normal time keeping but Impractical for normal time keeping but used in astronomics to measure positions used in astronomics to measure positions relative to the Observer’s Meridian.relative to the Observer’s Meridian.


Action of SundialAction of SundialGreenwichObserver’s

Longitude

Sun Dial

Sun

Ante meridian

Sun’s Apparent Movement


Use of Time in AstroUse of Time in Astro

• NA lists the position of all heavenly bodies NA lists the position of all heavenly bodies in terms of hour angle and declination.in terms of hour angle and declination.

• Greenwich Hour Angle (GHA) is increasing Greenwich Hour Angle (GHA) is increasing at a rate of 0.25 min of arc per second.at a rate of 0.25 min of arc per second.

• Hour angle relative to our position is Hour angle relative to our position is referred to as the Local Hour Angle (LHA).referred to as the Local Hour Angle (LHA).

• LHA is found from GHA plus longitude LHA is found from GHA plus longitude East or minus longitude West.East or minus longitude West.


The Local Hour AngleThe Local Hour Angle

Local Hour Angle

Pole

Meridian of Star

Equator

Observer’s Meridian


Hour AnglesHour Angles

Earth Rotation Greenwich

Meridian

Apparent Rotation Westward

Greenwich Hour Angle (GHA)


Longitude West

Local Hour Angle (LHA)


Longitude EastLongitude East

Greenwich Meridian

Greenwich Hour Angle (GHA)


Longitude East

Local Hour Angle (LHA)


Calculating LHACalculating LHA

• Universal Time (GMT) must be used.Universal Time (GMT) must be used.

• Obtain hourly prediction of GHA from the Nautical Obtain hourly prediction of GHA from the Nautical Almanac.Almanac.

• Obtain increment in hour angle based on minutes Obtain increment in hour angle based on minutes past the hour (buff pages of NA).past the hour (buff pages of NA).

• Apply correction for DR longitude subtracting for Apply correction for DR longitude subtracting for W and adding for E.W and adding for E.

• N.B. 360N.B. 360oo can be added or subtracted at any time. can be added or subtracted at any time.


Questions???Questions???

Time lrg

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