Prof. John Hearnshaw ASTR211: COORDINATES AND TIME Coordinates and time Sections 9 – 17

Prof. John Hearnshaw ASTR211: COORDINATES AND TIME 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  ).

Prof. John Hearnshaw ASTR211: COORDINATES AND TIME  ⊙ +23  27 Mar 21 Jun 21 Sep 21 Dec 21 Mar 21  23  27 Declination of Sun is sin  ⊙ = sin  sin ⊙ ⊙  ecliptic longitude of Sun ~ days elapsed since March equinox

Prof. John Hearnshaw ASTR211: COORDINATES AND TIME

Prof. John Hearnshaw ASTR211: COORDINATES AND TIME 10. Altitude of Sun at culmination The Sun culminates at about noon (local time), at an altitude which depends on observer’s latitude and Sun’s declination. For N hemisphere observers a ⊙ = 90    +  ⊙ In S hemisphere a ⊙ = 90      ⊙ In either case  ⊙ may be >0  or <0 .

Prof. John Hearnshaw ASTR211: COORDINATES AND TIME Example: In Christchurch   43  32 S  Altitude of noon Sun on Dec 21 is: a ⊙ = 90   43  32  (  23  27)  69  55

Prof. John Hearnshaw ASTR211: COORDINATES AND TIME 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 23 h 56 m

Prof. John Hearnshaw ASTR211: COORDINATES AND TIME 2) The 1  /day increase in ecliptic longitude is not uniform (due to eccentricity of Earth’s orbit around Sun) 3) The rate of change of H for Sun depends on angle between ecliptic and parallels of declination.

Prof. John Hearnshaw ASTR211: COORDINATES AND TIME 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).

Prof. John Hearnshaw ASTR211: COORDINATES AND TIME 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 observer’s meridian at noon (12h) exactly.

Prof. John Hearnshaw ASTR211: COORDINATES AND TIME 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.

Prof. John Hearnshaw ASTR211: COORDINATES AND TIME

Prof. John Hearnshaw ASTR211: COORDINATES AND TIME

Prof. John Hearnshaw ASTR211: COORDINATES AND TIME 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.

Prof. John Hearnshaw ASTR211: COORDINATES AND TIME 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.

Prof. John Hearnshaw ASTR211: COORDINATES AND TIME Solar analemma

Prof. John Hearnshaw ASTR211: COORDINATES AND TIME Solar analemma and the equation of time

Prof. John Hearnshaw ASTR211: COORDINATES AND TIME 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 mean solar days. (Note: 1 year = lunar months.)

Prof. John Hearnshaw ASTR211: COORDINATES AND TIME 15. The Year Sun travels ~1  /day on ecliptic and so completes 360  in 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.

Prof. John Hearnshaw ASTR211: COORDINATES AND TIME Time for successive passages of Sun through the vernal equinox (  ) is the tropical year = 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.

Prof. John Hearnshaw ASTR211: COORDINATES AND TIME 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.

Prof. John Hearnshaw ASTR211: COORDINATES AND TIME 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.

Prof. John Hearnshaw ASTR211: COORDINATES AND TIME The origin of the seasons

Prof. John Hearnshaw ASTR211: COORDINATES AND TIME Diurnal paths of Sun at different seasons

Prof. John Hearnshaw ASTR211: COORDINATES AND TIME Origin of the seasons

Prof. John Hearnshaw ASTR211: COORDINATES AND TIME Solar illumination at different seasons

Prof. John Hearnshaw ASTR211: COORDINATES AND TIME 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).

Prof. John Hearnshaw ASTR211: COORDINATES AND TIME R.A. measured in h m s 360   24 h or15   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.)

Prof. John Hearnshaw ASTR211: COORDINATES AND TIME

Prof. John Hearnshaw ASTR211: COORDINATES AND TIME End of sections

Prof. John Hearnshaw ASTR211: COORDINATES AND TIME

Prof. John Hearnshaw ASTR211: COORDINATES AND TIME

Prof. John Hearnshaw ASTR211: COORDINATES AND TIME