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**1B11 Foundations of Astronomy Astronomical co-ordinates**

Liz Puchnarewicz

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**1B11 Positions of astronomical sources**

The most important parameter you can know about any astronomical source is its position on the sky. Why? Isolate, identify and re-visit the source Check for transient sources, supernovae etc. Associate sources at different wavelengths By grouping stars into constellations, our ancestors developed the first system for unambiguously identifying celestial sources. Now, we use co-ordinate systems based on angular distance scales. Constellations and star names

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**More co-ordinate systems**

1B11 Equatorial System The Equatorial system is the one most generally used. It is based on a projection of the Earth’s equator and poles onto the celestial sphere. NCP = North Celestial Pole SCP = South Celestial Pole NCP d=90O d a Celestial horizon,d=0O -90O < d < 90O 0h < a < 24h SCP d=-90O More co-ordinate systems

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1B11 RA and Dec Right Ascension, RA or a, is measured in hours and a full circle (360O) = 24 hours. There are 60 minutes of time in one hour, and 60 seconds of time in one minute (h,m,s). Declination, Dec or d, is measured in degrees from –90O at the SCP to +90O at the NCP. There are 60 arcminutes in one degree and 60 arcseconds in one arcminute (O,’,’’). The zero-point for Dec is on the celestial horizon which is a projection of the Earth’s equator on the sky. The zero point for RA is defined as the position of the Sun in the sky at the Vernal Equinox (~21 March), the point at which the Sun crosses the equator from South to North. It is also known as the “First Point of Aries” (although it is now in Pisces) and it is measured eastwards.

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**1B11 Astronomical co-ordinates**

Celestial equator SCP NCP Celestial sphere d Earth star a Vernal equinox East 1” is the angular diameter of 1p at 4km!

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**1B11 Star maps and catalogues**

The positions (RA, Dec) of stars can now be mapped and catalogued. 2h 1h 0h RA Dec +10O 1h 28m 40s +6O 50’ 10” 0O -10O

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**Orbital plane (ecliptic)**

1B11 Precession The Earth’s rotation axis precesses in space due to the gravitational pull of the Sun and the Moon. Precession (once every 26,000 years). 1.4O westwards per century. 23.5O Moon Earth Orbital plane (ecliptic) Sun equatorial bulge rotation axis

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**1B11 Precession and Nutation**

Precession occurs due to the gravitational pull of the Sun and the Moon (mostly the Moon). Over 26,000 years, the positions of the celestial poles and the equinoxes change with respect to the stars. Thus it is always necessary to specify a date for equatorial co-ordinates (currently using co-ordinates). Nutation is an additional wobble in the position of the Earth’s poles. It is mainly due to the precession of the Moon’s orbit, which has a period of 18.6 years.

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**1B11 Some key points on the observer’s sky**

90-f f = latitude Earth rotates Zenith stars star meridian NCP SCP N S W E horizon observer

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**1B11 Some key points on the observer’s sky**

Stars rise in the East, transit the meridian and set in the West hour angle Zenith NCP SCP star meridian N S W E horizon celestial equator

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1B11 Time systems Solar day = time between successive transits of the Sun = 24 hours Sidereal day = time between successive transits of the Vernal Equinox = 23 hours 56min 04sec 1 sidereal day 4min extra rotation

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1B11 Solar vs sidereal Sidereal day is about 4mins shorter than the solar day. Relative to the (mean) solar time, the stars rise 4mins earlier each night (about 2 hours each month). We define 0h Local Sidereal Time (LST) as the time when the Vernal Equinox lies on the observer’s meridian. LST = Hour angle of the Vernal Equinox For the Greenwich Meridian: GST = H. A. of the Vernal Equinox at Greenwich LST = GST + longitude east of Greenwich

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**1B11 Key relations – LST, RA and HA**

Local Sidereal Time = Right Ascension on the meridian So, for example, if LST = 11:30, stars with RA=11h30m are on the meridian HA = LST - RA ie if a star is on the meridian, RA = LST and HA = 0. If LST is 11:30, a star with RA = 10h30m has HA = 1h; ie it is one hour past the meridian. key points on the sky

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1B11 Solar time Apparent solar time is the time with respect to the Sun in the sky (ie the time told by a sundial). The apparent solar day is not constant over the year due to: Eccentricity of the Earth’s orbit Inclination of the ecliptic to the equator Mean solar time: define a point on the Equator (the “mean sun”) which moves eastwards at the average rate of the real Sun, such that the mean solar day is 1/ of a sidereal year. (local) mean solar time = HA of mean sun + 12 hours GMT = HA mean sun at Greenwich + 12 hours

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1B11 Equation of time The difference between apparent solar time and mean solar time is called the equation of time and ranges from between –14m15s to +16m15s. May21 Jan21 Nov21 Sep21 Jul21 Mar21 +15m +10m +5m 0m -5m -10m -15m

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**Universal Time (UT1) = Greenwich Mean Time (GMT)**

1B11 Universal Time Universal Time (UT1) = Greenwich Mean Time (GMT) But UT1 uses the Earth’s rotation as its “clock” so has some irregularities including general slowing of rotation. International Atomic Time (TAI) uses atomic clocks which are more accurate so a modified version of UT is used, Co-ordinated Universal Time (UTC) Zero point for TAI was defined as UT1 on 1958 January 1. UTC = TAI + an integral number of seconds and is maintained to be within 0.9s of UT1 using leap seconds.

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**1B11 Topocentric (horizon) co-ordinates**

Co-ordinates relative to an observer’s horizon. A = azimuth Zenith h = altitude meridian h N S W E horizon A observer

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**1B11 Topocentric co-ordinates (cont.)**

Altitude = h = angular distance above the horizon. Zenith distance = ZD = 90 - h Azimuth = A = angular bearing of an object from the north, measured eastwards. eg. 0O = due north and 90O = due east

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**1B11 Ecliptic co-ordinates**

Useful when studying the movements of the planets and when describing the Solar System. b = ecliptic latitude measured in degrees, 0O-90O, north or south K (= ecliptic north pole) ecliptic l = ecliptic longitude measured in degrees, 0O-360O, eastwards from the First Point of Aries NCP equator

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**1B11 Galactic co-ordinates**

Useful when considering the positions and motions of bodies relative to our stellar system and our position in the Galaxy. NGP; b=90O SGP Galactic equator GC b l l = 0O l = 90O l = 180O l = 270O

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**1B11 Galactic co-ordinates (cont.)**

l = Galactic longitude Measured with respect to the direction to the Galactic Centre (GC). The Galaxy is rotating towards l = 90O. b = Galactic latitude The North Galactic Pole (NGP) lies in the northern hemisphere. The subscripts I and II are used to differentiate between the older Ohlsson system and the new IAU system of Galactic co-ordinates, ie lII, bII are IAU co-ordinates.

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**1B11 Celestial position corrections**

The position for any celestial object is not necessarily its true position – a number of factors must be taken into account: Atmospheric refraction Aberration of starlight Parallax Proper motion

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**1B11 Atmospheric refraction**

Starlight is refracted on entering the Earth’s atmosphere due to the change in refractive index. Zenith (no refraction) apparent position real position horizon Sun at sunset 35’

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**1B11 Atmospheric refraction (cont.)**

Atmospheric refraction always increases the altitude of an object (ie it always reduces the zenith distance). The constant of refraction can be measured by using the transits of a circumpolar star. Refraction depends on the wavelength of the light observed. For ZD < 45O, the correction to ZD, R, is given by: where z is the apparent zenith distance. At ZD > 45O, the curvature of the Earth must be taken into account. Near ZD = 90O, special empirical tables are used.

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**1B11 Aberration of starlight**

James Bradley was trying to measure stellar parallax, when he discovered the effects of stellar aberration. Light has a finite velocity The Earth moves relative to the star The combination of velocities “moves” the star position by up to 20”.49. q v = c = 3x105 km/s q v = 29.8 km/s

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**1B11 Aberration of starlight (cont.)**

This was a very important discovery. It was the first experimental confirmation of the Earth’s motion about the Sun. It confirmed the speed of light, first estimated only 50 years before. It showed that sources trace an ellipse around the sky in the course of a year with a semi-major axis of 20”.49 and semi-minor axis of 20”.49sinb (where b is the ecliptic latitude). The effect is the same one that makes raindrops appear to be coming towards you when you’re driving through the rain. Ecliptic co-ordinates

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1B11 Parallax When things close to you move faster than those further away.

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**1B11 Calculating parallax**

Note that the parallactic angles L T M qM qT qL In one year, the Earth moves around an ellipse with semi-major axis of 149,600,000 km. 1 Astronomical Unit (AU) = 149,600,000 km Use this to measure the distances to nearby stars.

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**1B11 Parallax in Astronomy**

distant stars p is the parallax angle p nearby star D 1AU

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1B11 Parallax (cont.) In one year, a nearby star will trace out an ellipse on the sky due to parallax. Semi-major axis = p Semi-minor axis = p sin b (b = ecliptic latitude) Note the similarity with aberration – however the magnitude of aberration is constant for every object in the sky. Parallax depends on the distance to the object. Also, parallax is on a much smaller scale than aberration. Stellar aberration

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1B11 Stellar distance Measuring p provides the only direct way of calculating stellar distances. An object with p = 1 arcsec would lie 1 parsec away D (parsecs) = 1/p 1 parsec = 3.086x1016m = 206,265 AU = 3.26 light years Parallax was first measured by Bessel in 1838 who measured p=0”.314 for 61 Cygni. In 1839, Henderson measured p=0”.74 for a Centauri. Our closest star is Proxima Centauri: p = 0”.764, D = 1.31pc

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1B11 Proper motion Each star, including our Sun, has its own intrinsic space motion. The component of this motion, combined with that of the Sun, projected on the sky, is known as Proper Motion, m.

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**Proper motion seen by Hipparcos**

1B11 Proper motion (cont.) m is measured in arcseconds per year. It has components in RA and Dec: ma, md. Largest proper motion known is for Barnard’s Star, where m = arcsec/year. d m vt space velocity Vt = tangential speed d=distance (SI units; m in radians/sec) For vt in km/s, m in arcsec/year and d in parsecs. Proper motion seen by Hipparcos

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