Download Lecture 10

Astronomical coordinate systems
ASTR320
Monday October 3, 2016
The Earth rotates about its axis
• Rotates west to
east
• The sun rises
and sets...
The Earth rotates about its axis
The Earth rotates about its axis
Where was this
picture taken?
Definitions
Astrometry
• Measure the
position of stars on
the celestial
sphere
Angular measures
• 360 degrees in a circle
• 60 arcminutes in a degree
• 60 arcseconds in an arcminute
• ½ degree = angular size of Sun & Moon
All astronomers know that there are
206265 arcseconds in 1 radian
The celestial sphere
Constellations
• The International Astronomical Union (IAU) divides the
sky into 88 regions that it officially recognizes as
constellations
Equirectangular plot of declination vs. right ascension of modern constellations.
From wikipedia.org.
Coordinate systems
• In astronomy we deal with spherical coordinate systems
• A spherical coordinate system is defined by two great
circles, one goes through the poles of the other
Coordinate systems
• Any two great circles can define coordinate system, but
only a few make sense:
“Prime meridian”
Coordinate
system
Principal great
circle
Coordinates
Observer’s or
Horizon
Observer’s horizon North-south
meridian
Altitude, azimuth
Equatorial/
celestial
Projection of
Earth’s equator
Head of Aries—
vernal equinox
Right ascension, α,
declination δ
Ecliptic
Plane of Earth’s
revolution
Head of Aries—
vernal equinox
Right ascension, α,
declination δ
Galactic
Plane of Milky
Way
Galactic center
Galactic longitude,
l, Galactic latitude,
b
Observer’s coordinate system
• Altitude, h, from the horizon
along the vertical circle (the
great circle including the
zenith and the object)
• Zenith distance, z = 90o - h
• Azimuth, A, measured from
the North Point (intersection
of the meridian with the true
horizon in the north)
becoming positive toward
East
• The meridian is the vertical
circle including the zenith
and celestial poles
From Kaler, The Ever-Changing Sky.
Observer’s coordinate system
―Astronomical triangle‖:
• Hour angle, t (an
important angle for
observers)
• Zenith angle, Z
• Parallactic
angle, P (important, e.g.,
in spectroscopy and other
applications where one
needs to understand the
effects of atmospheric
refraction, which are
always along the vertical
circle)
From Kaler, The Ever-Changing Sky.
Equatorial coordinate system
• Right ascension, α,
measured from
the vernal equinox.
– Traditionally measured
in hours, minutes of
time, seconds of time,
but trend now towards
use of degrees
• Declination , δ,
measured from
the celestial equator to
the celestial poles.
From Mihalas & Binney, Galactic Astronomy
Ecliptic coordinate system
•
•
•
•
•
•
•
The ecliptic is the path of the Sun
in the sky (Earth’s orbital plane).
The obliquity of the ecliptic is
23o 27'.
The moon orbits within 5o of the
ecliptic.
Planets orbit within 7o 0' of the
ecliptic (except Pluto 17o 09').
Zodiacal light, zodiacal dust, lie
along this plane
Intersection of the ecliptic and
celestial equator define the vernal
equinox (location of the Sun on
March 21) and autumnal
equinox (location of the Sun on
Sep. 22).
The Vernal equinox defines the
zero-point of the right ascension
coordinates.
From Mihalas & Binney, Galactic Astronomy
Galactic coordinate system
• The Galactic equator is
chosen to be that great
circle on the sky
approximately aligned with
the Milky Way mid-plane.
• This plane is inclined by
62o 36' to the celestial
equator.
• The North Galactic Pole is
at α = 12h 49m, δ = +27° 24'
in 1950 equinox, and best
observed at night in the
Northern Hemisphere
spring
From Mihalas & Binney, Galactic Astronomy
Galactic coordinate system
• Galactic latitude, b, is
measured from the
Galactic equator to the
Galactic poles.
• Galactic longitude, l, is
measured eastward
around the equator in
degrees.
• The definition of l =
0o is given by the
location of the Galactic
Center.
From http://www.astr.ua.edu/ay102/Lab9/Lab_9_Coord.html.
Galactic coordinate system
• Use an Eulerian transformation to convert equatorial to
Galactic coordinates:
sinb = sinδ sinδNGP - cosδ cosδNGP sin(α - α0)
cos(l - l0) cosb = cos(α - α0) cosδ
sin(l - l0) cosb = sinδ cosδNGP + cosδ sinδNGP sin(α - α0)
• With the definition of the North Galactic Pole:
equinox
αNGP
δNGP
α0
l0
1950
12:49.0 =
192.25o
27:24
18:49.0 =
282.25o
33.00o
2000
12:51.4 =
192.85o
27:08
18:51.4 =
282.85o
32.93o
Precession of the equinoxes
• The precession of the
Earth is a 25,800 year
periodic wobble of the
direction of the Earth's
axis of rotation.
• This is a major effect
that can be detected
nightly, and which has
a large effect on
coordinates over the
period of years.
Precession of the equinoxes
• Because the Earth spins, it
is in fact a little fatter around
the equator by one part in
298.
• The Earth is 43 km larger in
diameter across the equator
than from pole to pole (a
radius of 6378 km toward
the equator compared to
6357 km toward the poles).
• Being 0.33% closer to the
Earth's center at the pole,
translates to 0.67% greater
weights measured on the
surface of the Earth at the
poles than at the equator.
Precession of the equinoxes
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•
Because the Moon orbits the
Earth in a plane that is within 5
degrees of the ecliptic, typically
the Moon is not aligned with the
Earth's equatorial bulge (unless
the Moon is on the Celestial
Equator).
Thus the Moon generally is at an
angle to the equatorial bulge, and
tugs on the Earth's bulge.
There are also smaller
contributions from the Sun and
planets attempting gravitationally
to do the same thing (the Sun is
only on the celestial equator twice
a year and at all other times of the
year it is pulling the Earth's bulge
toward the ecliptic plane).
These external forces on the
spinning Earth creates the
precessional "wobble" in the
Earth's motion.
From Abell's Exploration of the Universe, Ed. 3.
Precession of the equinoxes
• For the Earth, the
precession acts to slowly
change the direction that
the Earth's rotational pole
points.
• The direction of the Earth's
North and South Celestial
Poles rotate to different
points on the Celestial
Sphere with a 25,800 year
cycle.
• The orbital axis of the Earth
stays fixed in space but
the rotational
axis constantly changes
direction.
From Kaler, The Ever-Changing Sky.
Precession of the equinoxes
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•
•
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Presently the Earth's North Pole
points to Polaris, but 14,000 years
ago it pointed towards Vega.
The star gamma Cephei is the
next northern pole star (it will be 3
degrees from the NCP in 2200
years).
Note that it is not the location of
the rotational pole on the
Earth that is changing, but where
that pole points on the Celestial
Sphere
Note also that if the direction of
the poles is changing, so too is the
direction of the equator of the
Earth as projected on the sky.
Precession of the equinoxes
• If the position of the celestial poles and equators are changing on
the celestial sphere, this means that the celestial coordinates of
objects, which are defined by reference to the celestial equator and
celestial poles, must also be constantly changing.
• Because of this change in the direction of the Earth's pole with time,
the coordinate systems of RA and DEC that we adopt for one epoch
are actually different for other epochs.
• The effects are quite noticeable, almost an arcminute a year along
the ecliptic.
• When you give the coordinates of an object you also must specify
the year that corresponds to those coordinates (because they will be
significantly different in future years).
• This specified year for the coordinates is called the EQUINOX of the
coordinates.
– NOTE: A common mistake made by even senior astronomers is to call the
year of the coordinates the "epoch" of the coordinates. This is wrong.
Precession of the equinoxes
• Astronomers tend to use "standard" years, like 1950,
2000, 2050 when they cite the Equinox of the
coordinates.
• Presently we see most people using "J2000.0"
coordinates.
• Coming to a telescope with coordinates precessed to the
wrong year is one of the most common mistakes by
observers.
• A mistake of 50 years in the coordinate system (most
typical) will general move your object of interest off a
typical CCD field of view.
Precession of the equinoxes
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Because the plane of the Earth's orbit
is fixed, the position of the ecliptic is
fixed.
But since the position of the Celestial
Equator is changing, the position of
the Vernal and Autumnal Equinoxes
(where the Celestial Equator and the
ecliptic cross) slowly shifts with time.
In this figure, if the NCP is coming at
you, the front side of the Celestial
Equator is going down and the back
side of the Celestial Equator is going
up.
This means that the position of the
Vernal Equinox is sliding to the left (or,
to the right from the Earth's point of
view).
The motion of the equinoxes
is westward along the ecliptic because
of the motion of the equator.
From Kaler, The Ever-Changing Sky.
Precession of the equinoxes
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•
•
Since in a 25,800 year period the
Vernal Equinox will slide 360 degrees,
we have that the annual motion of the
Vernal Equinox (and Autumnal
Equinox) is 360o/(25800 yrs) =
50.3"/yr.
Since the Vernal Equinox is slipping,
the dates when the Sun is in a given
constellation slowly changes.
This is why the months associated with
certain "signs of the zodiac" do not
match with the Sun's true position with
respect to them, which is how the
dates of the "houses" were originally
defined.
From Kaler, The Ever-Changing Sky.
Precession of the equinoxes
• Another effect of precession is to complicate the definition of
a year.
• A sidereal year is the time between the Sun appearing across
a given star = 365.2564 days.
• A Solar (or tropical) year is the time between successive
Vernal Equinoxes = 365.2422 days.
• The difference is because the Sun is every day
moving eastward along the ecliptic while the Vernal Equinox
is slipping westward.
– Thus, the Sun has less than 360 degrees to move to go from one
Vernal Equinox to the next, because the Vernal Equinox is moving
towards the Sun.
– The Solar year is 20 minutes shorter than a sidereal year because it
takes 20 minutes for the Sun to move 50.3 arcsecs.