Coordinates and time

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Coordinates and time Sections 9 17
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• 9. Declination of Sun
• ?? changes throughout the year between the limits
  
• ? 23?27? at the June solstice,
• to ? ?? ? 23?27? at the December solstice
• (respectively Jun 21, Dec 21)
• 0? at the equinoxes
• (Mar 21 ? is at ? Sept 21 ? is at ?).

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?? 23?27?
?23?27?
Mar 21 Jun 21 Sep 21 Dec 21 Mar 21
Declination of Sun is sin ?? sin ? sin ?? ?? ?
ecliptic longitude of Sun days elapsed
since March equinox
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10. Altitude of Sun at culmination The Sun
culminates at about noon (local time), at an
altitude which depends on observers latitude
and Suns declination.
For N hemisphere observers a? 90? ? ?
?? In S hemisphere a?
90? ? ? ? ?? In either case ?? may be gt0? or lt0?.
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Example In Christchurch ? ? 43? 32? S ?
Altitude of noon Sun on Dec 21 is
a? 90? ? 43? 32? ? (? 23? 27?)
? 69? 55?
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11. Simple concepts of time-keeping The day
This is approximately the time interval between
two successive meridian passages of the Sun at a
given location. Note that 1) Sun is itself
moving along ecliptic at 1?/day, so Earth must
turn about 361? in 24 hours, or 360? in 23h 56m
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• The 1?/day increase in ecliptic longitude is not
  uniform (due to eccentricity of Earths orbit
  around Sun)
• 3) The rate of change of H for Sun depends on
  angle between ecliptic and parallels of
  declination.

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12. The equation of time The mean Sun is a
fictitious point on the equator that transits
the meridian at equal time intervals that is,
its hour angle changes at a uniform rate. The
apparent Sun this is the actual or true
position of the Sun. It is on the ecliptic. The
mean and apparent Suns can differ in H by up to
16m 20s (on Nov 4) or 4? in angular separation
(in the right ascension coordinate).
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The equation of time E is defined by
E H (apparent ?) H (mean ?) The mean Sun is
used to define mean solar time. In mean solar
time the mean Sun transits across the observers
meridian at noon (12h) exactly.
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The equation of time is a correction to apparent
solar time (sundial time) to reduce it to mean
solar time (in which all days have same
length). App. solar time mean solar
time E. If E is ve, true Sun crosses meridian
before mean Sun (ie. before noon). Sundial time
is then ahead of mean solar time.
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13. The solar analemma Suppose the position of
the Sun is recorded daily in equatorial
coordinates (H, ?), at the same mean solar time
each day. At each date H? will vary according
to the equation of time H? (apparent) H? (mean)
E (t) While ?? will be given by its annual
variation sin ?? sin ? sin ??(t) Hence at any
time of year t the solar coordinates describe a
locus in sky (H, ?) known as the solar analemma.
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The solar analemma Suppose a fixed
camera photographs the sky at noon every day of
the year so that all the images are superimposed
on the same film. The different positions of the
Sun throughout the year will describe a
figure- of-eight known as the solar analemma.
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Solar analemma
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Solar analemma and the equation of time
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14. The month Based on cycle of lunar
phases New moon ? First quarter ? (no part of
disk illuminated) Full moon ? Last quarter ? New
moon (full disk illuminated) One such cycle is
a lunation or lunar month, equal to 29.53 mean
solar days. (Note 1 year 12.37 lunar months.)
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15. The Year Sun travels 1?/day on ecliptic and
so completes 360? in 365.256 mean solar
days. This interval is called the sidereal year
as Sun is in same position relative to
background stars after elapse of 1 sidereal year.
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Time for successive passages of Sun through the
vernal equinox (?) is the tropical year
365.242 mean solar days. The
difference between sidereal and tropical years
amounts to 20m 24s. The cause is the slow
retrograde (westwards) motion of the First Point
of Aries (?) by 50.2 arc s annually. This
phenomenon is termed precession of the
equinoxes. Precessional period 25,800 years.
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The sidereal year is the true orbital period of
Earth. The tropical year is the length of one
cycle of seasonal changes, and is in practice
the year on which the civil calendar is based.
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16. The seasons (spring, summer, autumn,
winter) These are determined by the right
ascension and declination of the Sun, which
depend on time of year as a result of obliquity
of ecliptic (23? 27?). Warmer climate in summer
because (i) longer hours of daylight (see
section 23d) (ii) higher altitude of Sun in sky
means rays reach surface less obliquely ?
greater insolation. (iii) Higher altitude of Sun
in sky leads to less absorption in terrestrial
atmosphere.
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The origin of the seasons
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Diurnal paths of Sun at different seasons
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Origin of the seasons
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Solar illumination at different seasons
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17. Equatorial coordinate system (Part 2) The
system (hour angle, declination), or (H, ?), has
property that H for a given star depends on time
of observation and on longitude of observer. The
coordinates (right ascension, declination)
(written R.A., dec or ?, ?) provide an
equatorial system in which ? is fixed for each
object (independent of time of observation,
longitude).
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R.A. measured in h m s 360? ? 24 h or 15? ?
1 h or 1? ? 4 m R.A. increases eastwards
around equator (note H increases
westwards). R.A. 0 h on meridian through the
First Point of Aries, ?. Because ? is (very
nearly!) a fixed direction with respect to the
stars, it follows that the coordinates (?, ?)
specify fixed directions in space relative to the
stars. (This statement is approximate because of
precession and because the stars are also in
motion.)
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End of sections 9 - 17
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