Transcript 1B11 Foundations of Astronomy Star names and magnitudes

1B11
Foundations of Astronomy
Astronomical co-ordinates
Liz Puchnarewicz
[email protected]
www.ucl.ac.uk/webct
www.mssl.ucl.ac.uk/
1B11 Positions of astronomical sources
The most important parameter you can know about any
astronomical source is its position on the sky.
Why?
1. Isolate, identify and re-visit the source
2. Check for transient sources, supernovae etc.
3. 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
1B11 Equatorial System
NCP
d=90O
d
a
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
SCP
d=-90O
Celestial
horizon,d=0O
-90O < d < 90O
0h < a < 24h
More co-ordinate systems
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.
1B11 Astronomical co-ordinates
NCP
Celestial
sphere
Earth
star
a
Celestial
equator
Vernal
equinox
SCP
d
East
1” is the
angular
diameter of 1p
at 4km!
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
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
Earth
equatorial
bulge
Moon
Orbital plane
(ecliptic)
rotation
axis
Sun
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
Earth’s poles.
• It is mainly due to the precession of the Moon’s orbit, which
has a period of 18.6 years.
1B11 Some key points on the observer’s sky
Earth
rotates stars
f = latitude
Zenith
star
NCP
meridian
90-f
E
observer
N
horizon
S
W
SCP
1B11 Some key points on the observer’s sky
hour
angle
NCP
Zenith
Stars rise in the East,
transit the meridian and
set in the West
star
meridian
E
N
horizon
S
celestial
equator
W
SCP
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
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
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
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:
1. Eccentricity of the Earth’s orbit
2. 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
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.
+15m
+10m
+5m
0m
-5m
-10m
-15m
May21
Jul21
Sep21
Nov21
Jan21
Mar21
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.
1B11 Topocentric (horizon) co-ordinates
Co-ordinates relative to an observer’s horizon.
A = azimuth
h = altitude
Zenith
meridian
h
N
horizon
E
A
observer
W
S
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
1B11 Ecliptic co-ordinates
Useful when studying the movements of the planets and
when describing the Solar System.
b = ecliptic latitude
measured in degrees,
K (= ecliptic north pole) 0O-90O, north or south
l = ecliptic longitude
measured in degrees,
0O-360O, eastwards
from the First Point of
Aries
NCP
equator
ecliptic
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
Galactic
equator
GC
b
SGP
l = 90O
l = 180O
l
l = 270O
l = 0O
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.
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:
1. Atmospheric refraction
2. Aberration of starlight
3. Parallax
4. Proper motion
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
35’
Sun at
sunset
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:
R  k tanz
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.
1B11 Aberration of starlight
James Bradley was trying to measure stellar parallax, when
he discovered the effects of stellar aberration.
2. The Earth moves relative to the
star
q
3. The combination of velocities
“moves” the star position by up to
20”.49.
29 .8
tan q 
3  10 5
 q  20".49
q
v = c = 3x105 km/s
1. Light has a finite velocity
v = 29.8 km/s
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 semiminor 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
1B11 Parallax
When things close to you move faster than those further
away.
1B11 Calculating parallax
Note that the parallactic angles
M
qM  q T  qL
qM
T
qT
In one year, the Earth moves
around an ellipse with semimajor axis of 149,600,000 km.
L
1 Astronomical Unit (AU)
= 149,600,000 km
qL
A
B
Use this to measure the
distances to nearby stars.
1B11 Parallax in Astronomy
distant stars
p is the
parallax angle
1AU
p  tan p 
D
nearby star
p
D
1AU
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
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
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.
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 = 10.34 arcsec/year.
d
m
vt
Vt = tangential speed
d=distance
v t  md
(SI units; m in
radians/sec)
v t  4.74md
space
velocity
For vt in km/s, m in
arcsec/year and d in parsecs.
Proper motion seen by Hipparcos