prof. john hearnshaw astr211: coordinates and time coordinates and time sections 9 – 17

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ASTR211: COORDINATES AND TIME

Coordinates and time

Sections 9 – 17

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9. Declination of Sun

⊙ changes throughout the year between the limits = + = +2327 at the June solstice, to = = 2327 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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⊙ +2327

Mar 21 Jun 21 Sep 21 Dec 21 Mar 21

2327

Declination of Sun issin ⊙ = 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 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.

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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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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.

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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 observer’s 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 timeH⊙ (apparent) = H⊙ (mean) + E (t)

While ⊙ will be given by its annual variationsin ⊙ = 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 cameraphotographs the sky at noonevery day of the year sothat all the images are superimposed on the samefilm. The different positionsof the Sun throughout theyear will describe a figure-of-eight known as the solaranalemma.

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Solar analemma

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Solar analemmaand the equationof 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 s360 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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prof. john hearnshaw astr211: coordinates and time coordinates and time sections 9 – 17

Documents

time coordinates

time slide

john hearnshaw astr211

time sections

noon local time

equinox slide

sin sin ecliptic longitude

suns declination