Measure of time (angle)
| Physical unit | |
|---|---|
| Unit name | Measure of time |
| Unit symbol | |
| Physical quantity (s) | Flat angle |
| dimension | |
| In SI units | |
| Derived from | Hour , minute , second |
| See also: angular dimensions | |
The measure of time , also called the hour , is an indication of the angle commonly used in astronomy in the units of measurement hours, minutes and seconds. The 360 ° angle is given as 24 hours. One hour therefore corresponds to an angle of 15 °. It establishes a connection between the change in the angle of a celestial body as the earth rotates and the time that has passed. For example, the growing hour angle of the sun in a solar hour to (on average) 15 ° or 1 (angular) hour. The right ascension angle 15 ° of a star corresponds to that sidereal hour that passes between the passage of the vernal equinox and that of the star through the celestial meridian .
Definition and notation
The following applies:
- Angle (in hours) = angle (in degrees ) / 15
Some values:
| time | angle | ||
|---|---|---|---|
| Hourly measure | Degree | Radians | |
| 1 day | 24 h | 360 ° | 2 π ≈ 6.283 |
| 1 hour | 1 h | 15 ° | π ⁄ 12 ≈ 0.262 |
| 4 m | 1 ° | π ⁄ 180 ≈ 0.0175 = 1.75 10 −2 | |
| 1 minute | 1 m | 15 '= 1 ⁄ 4 ° | π ⁄ 720 ≈ 0.00436 = 4.36 · 10 −3 |
| 4 s | 1 '= 1 ⁄ 60 ° ( arc minute ) | π ⁄ 10800 ≈ 0.000295 = 2.95 · 10 −4 | |
| 1 second | 1 s | 15 "= 1 ⁄ 240 ° | π ⁄ 43200 ≈ 0.0000727 = 7.27 · 10 −5 |
| 1 ⁄ 15 s = 0.0667 s | 1 "= 1 ⁄ 3600 ° ( arcsecond ) | π ⁄ 648000 ≈ 0.00000485 = 4.85 · 10 −6 | |
For example, 1 h 23 m 45 s (in hours) and 20 ° 56 '15 "(in degrees) mean the same thing. The abbreviations prime ′ and double prime ″ are not used for minutes and seconds of the hourly measure, in order to avoid confusion with the arc minutes and seconds of the degree measure. To distinguish it from the time units of the same name, the abbreviations h, m and s are superscripted for angle units.
The hour measure was formerly also called arc hour , in a misleading analogy to the arc minute and second of the angle, which are not associated with the "arc hour" but with the degree.
use
The specification of an angle in rotationally bound coordinate systems in time units in relation to the duration of the rotation enables an unconstrained access to the Earth Day for observation and phenomenology , and the associated conversions into the heliocentric coordinate system ( ecliptical coordinates ).
It is used in astrometry for the angles in the equatorial plane :
- the sidereal time , the angle between the celestial meridian of the observation location and the vernal equinox ;
- the right ascension , the length-related component of the equatorial coordinates, measured from the vernal equinox to the east;
- The common zero point of the scale (0 h ) of sidereal time and right ascension is the equinox (spring point), which is the ecliptically resting geocentric equatorial coordinate system
- the hour angle , the angle between a celestial body and the local meridian
- The zero point of the hour angle (0 h ) is the point of intersection between the local meridian and the equator in the rotating geocentric, but localized equatorial coordinate system
Both angles 'star time' and 'hour angle' are named because they depict the “star clock”, the starry sky rotating above the observer , or the earth rotating in relation to the star-fixed coordinate system, and have a specific temporal meaning.
Times and angles in terms of time can be formally added up without any problems. This is also helpful when converting mean local time into world time (mean local time at the prime meridian ): The geographical longitude of the location in the time measure corresponds exactly to the time difference in hours. Times and lengths in hours can then be added or subtracted immediately. The zero point of the scale is the geodetic prime meridian, see zone time for the formulas.
This measure is used in particular in the theory of sundials ( gnomonics ), which deals specifically with the mapping of astronomical spherical angles onto azimuthally projected time scales.
Due to modern, computer-aided astronomy, in which the permanent conversion of the astronomical space and time reference systems means hardly any more effort, the measure of time has lost its importance.
literature
- Hermann Mucke : Spherical coordinate systems . In: Modern Astronomical Phenomenology . 20th Sternfreunde Seminar, 1992/93, and 21st Seminar 1994. Planetarium of the City of Vienna and Austrian Astronomical Association , Vienna 1992, p. 27-32 .
- Hermann Mucke: Astronomical basics of the sundials . In: Sundials . 19th Sternfreunde Seminar, 1991. Planetarium of the City of Vienna and Austrian Astronomical Association, Vienna 1991, p. 29-48 .