1B11 Foundations of Astronomy Astronomical co-ordinates

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1B11 Foundations of AstronomyAstronomical
co-ordinates

• Liz Puchnarewicz
• emp_at_mssl.ucl.ac.uk
• www.ucl.ac.uk/webct
• www.mssl.ucl.ac.uk/

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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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1B11 Equatorial System
The Equatorial system is the one most generally
used. It is based on a projection of the Earths
equator and poles onto the celestial sphere. NCP
North Celestial Pole SCP South Celestial Pole
NCP d90O
d
a
Celestial horizon,d0O
-90O lt d lt 90O 0h lt a lt 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
Earths 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
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.
0h
1h
2h
RA
Dec
10O
1h 28m 40s 6O 50 10
0O
-10O
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1B11 Precession
The Earths 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
  2000.0 co-ordinates).

• Nutation is an additional wobble in the position
  of the Earths poles.
• It is mainly due to the precession of the Moons
  orbit, which has a period of 18.6 years.

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1B11 Some key points on the observers sky
observer
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1B11 Some key points on the observers sky
Stars rise in the East, transit the meridian and
set in the West
hour angle
star
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
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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
  observers 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 1130, stars with
RA11h30m are on the meridian
HA LST - RA
ie if a star is on the meridian, RA LST and HA
0. If LST is 1130, 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 Earths 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 1/365.2564 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.
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1B11 Universal Time
Universal Time (UT1) Greenwich Mean Time (GMT)
But UT1 uses the Earths 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 observers horizon.
A azimuth
h altitude
h
observer
A
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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
l ecliptic longitude measured in degrees,
0O-360O, eastwards from the First Point of Aries
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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.
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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 Earths
atmosphere due to the change in refractive index.
Zenith (no refraction)
real position
horizon
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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 lt 45O,
the correction to ZD, R, is given by where z
is the apparent zenith distance. At ZD gt 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.

1. Light has a finite velocity
2. The Earth moves relative to the star
3. 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 Earths
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 youre 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
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
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 p0.314 for 61 Cygni. In 1839,
  Henderson measured p0.74 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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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 Barnards Star, where
m 10.34 arcsec/year.
d
m
space velocity
vt
Vt tangential speed ddistance
(SI units m in radians/sec)
For vt in km/s, m in arcsec/year and d in parsecs.
Proper motion seen by Hipparcos