http://faculty.virginia.edu/skrutskie/ASTR3130
Astr 3130 Objectives
q
q
Understand sky motions.
Ø
Target accessibility vs. time of year.
Ø
Coordinate systems → Pointing a telescope/scheduling a program
Follow a photon from outside the atmosphere to a scientific paper.
Ø
Ø
Ø
Ø
Ø
Ø
Ø
Atmospheric transmission, turbulence, refraction
Image formation by a telescope.
Limitations to image quality – diffraction, seeing, aberration.
Detectors and capturing photons, conversion of photon signals to
numbers, image representation
Observing techniques
Image math and calibration
Photometric and astrometric extraction of point sources
•
Ø
q
Introduction to basic astronomy research tools
Quantitative analysis of results and associated statistics.
Write up lab results and develop professional skills
Ø
(paper and proposal writing)
Astr 3130 Grade Breakdown
Ø
Observing Notebook – 15%
Ø
Midterm – 15%
Ø
Lab Prep / Day Assignments – 20%
Ø
Labs – 40%
Ø
Final Assignment – 10%
The ASTR 3130 Iceberg
Astr 3130 Time Investments
q
Class – Tuesdays and Thursdays 11:00-12:15
q
Lab sections – Tuesday or Wednesday 9:00-11:00
Ø
q
Or as otherwise arranged (the standard!)
Alternative times driven by weather or extended field trips
Ø
e.g. Fan Mountain Observations
q
“Day” problems
q
Lab-prep quizzes
q
Observation, data reduction, and report writing
Astr 3130 Time Investments
q
Class – Tuesdays and Thursdays 11:00-12:15
q
Lab sections – Tuesday or Wednesday 9:00-11:00
Ø
q
Or as otherwise arranged (the standard!)
Alternative times driven by weather or extended field trips
Ø
e.g. Fan Mountain Observations
q
“Day” problems
q
Lab-prep quizzes
q
Observation, data reduction, and report writing
Teamwork vs. Individual Work
Astr3130 – o - Meter
Hardest course
you'll ever love
(Majewski odd years)
Why are they
doing this to
me????
(this semester?)
Astr 3130 Tools
q
Clear Sky Chart
q
SAOimage ds9
q
XEphem / Stellarium
q
Aperture Photometry Tool
q
IPython Notebook
Consider an experiment to measure π
•  Pi is an exact (irrational) number,
known to nature but not known to
the experiment you have devised.
Consider an experiment to measure π
•  Pi is an exact (irrational) number,
known to nature but not known to
the experiment you have devised.
•  You push a button and your
apparatus reads out 3.14276
•  Limited precision…
Consider an experiment to measure π
•  Pi is an exact (irrational) number,
known to nature but not known to
the experiment you have devised.
•  You push a button and your
apparatus reads out 3.14276
•  Limited precision…
•  Are you done?
•  Push the button again. If you
repeatedly get 3.14276 out of
the instrument you’re done.
Consider an experiment to measure π
•  Pi is an exact (irrational) number,
known to nature but not known to
the experiment you have devised.
•  You push a button and your
apparatus reads out 3.14276
•  Limited precision…
•  Are you done?
•  Push the button again. If you
repeatedly get 3.14276 out of
the instrument you’re done.
•  If you get other values out you
are characterizing the behavior
of your experimental aparatus.
Consider an experiment to measure π
•  Suppose you conduct 1000’s of
trials and make a histogram of the
number of times each measured
value occurred.
•  Your instrument gives you a
slightly different answer each
time (noise!).
3.1400
3.1410
3.1420
3.1430
Consider an experiment to measure π
•  Suppose you conduct 1000’s of
trials and make a histogram of the
number of times each measured
value occurred.
•  Your instrument gives you a
slightly different answer each
time (noise!).
•  Noise can be random/
Gaussian (as shown at right) or
can be pathologic (below). The
only way to tell the difference is
to conduct many trials.
3.1400
3.1410
3.1420
3.1430
Consider an experiment to measure π
•  Suppose you conduct 1000’s of
trials and make a histogram of the
number of times each measured
value occurred.
•  The nature of the uncertainty of
the individual experimental
measurements is now clear
and is characterized by the
standard deviation (σ) of the
set of experimental values (at
least for most well-behaved
experiments).
3.1400
3.1410
3.1420
3.1430
Consider an experiment to measure π
•  Suppose you conduct 1000’s of
trials and make a histogram of the
number of times each measured
value occurred.
•  The nature of the uncertainty of
the individual experimental
measurements is now clear
and is characterized by the
standard deviation (σ) of the
set of experimental values (at
least for most well-behaved
experiments).
•  68% of the samples will lie
within 1-sigma of the mean for
a Gaussian distribution.
3.1400
3.1410
3.1420
3.1430
Consider an experiment to measure π
•  Suppose you conduct 1000’s of
trials and make a histogram of the
number of times each measured
value occurred.
•  Note that about 1 in 100 times
a legitimate measurement lies
2.5 sigma from the mean.
•  32% of measurements are
more than 1 sigma away.
•  Outliers are a natural
consequence of measurement
•  Single measurements can be
dangerous.
3.1400
3.1410
3.1420
3.1430
Consider an experiment to measure π
•  Suppose you conduct 1000’s of
trials and make a histogram of the
number of times each measured
value occurred.
•  The uncertainty in the final
mean measured value –
estimated by the precision to
which you have determined the
peak of the distribution - is
quite small and much smaller
than the standard deviation by:
σ _ mean = σ _ distribution / Nsamples
•  Many imprecise measurements
can produce a precise result.
3.1400
3.1410
3.1420
3.1430
Calculate magnitude of planet IX
Northeast at night
Calculate magnitude of planet IX
Northeast at night
How bright is Planet 9?
•  A few timely words about magnitudes….
•  Recall the stellar magnitude system is a ranking system
•  1st, 2nd, 3rd...
•  1st through 6th magnitude were supposed to span the range of stars visible to
the eye.
•  6th magnitude is at the limit of human vision but the brightest star, Sirius, is
magnitude -1.6.
•  Quantitatively, 5 magnitudes difference corresponds to a factor of 100 in
brightness (flux). A 12th magnitude star is 100 times fainter than a 7th
magnitude star.
•  One magnitude difference corresponds to a factor of 2.512 in flux.
•  We worked out that Uranus would be around a million times (15 magnitudes) fainter
if moved from 18AU out to 700 AU. Since Uranus is about 6th magnitude. Planet
9 would be around 21st mag.
The Celestial Sphere
q
From our perspective on Earth the stars appear embedded on a
distant 2-dimensional surface – the Celestial Sphere.
The Celestial Sphere
q
q
Although we know better, it is helpful to use this construct to think
about how we see the night sky from Earth.
The Sphere turns, the Earth stays fixed. You stand on a particular
spot on the Earth…
Spheres
q
Some terminology
Ø
Great circle vs. small circle
§
Ø
For a rotating sphere there are two
well defined “pivots” - the poles and
a fundamental plane perpendicular to
the polar axis through the center of
the sphere.
§
Ø
Note that the circumference of a
small circle is cos(δ) smaller than the
great circle.
The fundamental plane defines a
great circle – the equator.
Meridians are great circles that
intersect the equator at 90 degrees
δ
Coordinates on Spheres
q
q
q
Two angles define a location on a spherical surface.
A prime meridian establishes the zeropoint of longitude
Longitudes increase positively in the direction opposite the planet's spin.
Local Perspective: Altitude, Azimuth, and Zenith
Altitude
0
270
180
90
Local (Altitude/Azimuth) coordinates
q
q
Azimuth measured positively toward the East from North
Altitude measured up from the Horizon plane
A Personal Perspective: Horizon and Zenith
A Personal Perspective: Horizon and Zenith
Summary
•  In the local system the horizon and meridian are great circles.
•  Lines of constant altitude are small circles.
•  The coordinates of stars change with time as they rise and set.
Reference Points on the Celestial Sphere
q
Extend the Earth's poles and equator onto the sky and you have
defined the celestial poles and celestial equator.
The Celestial Poles
q
The “North Celestial Pole” lies overhead for an observer at the
North Pole and on the horizon for an observer on the Equator
q
The altitude of the pole equals your latitude.
The Celestial Poles
q
The “North Celestial Pole” lies overhead for an observer at the
North Pole and on the horizon for an observer on the Equator
q
The altitude of the pole equals your latitude.
To Pole
The Celestial Poles
q
The “North Celestial Pole” lies overhead for an observer at the
North Pole and on the horizon for an observer on the Equator
Ø
The altitude of the pole equals your latitude.
Why is This Important?
§  As an observer you need to develop a comfortable “feel” for the accessible sky.
Ø  Where are your sources? Which are setting???
Ø  Which are too “low” for reasonable observation?
Ø  Will the Sun or Moon interfere?
•  For ground based observation the Earth is your spacecraft. It enforces hard limits on
your observations. The Earth hides ½ the sky from view.
•  In space (e.g. Hubble or Spitzer) there will be Sun and/or Earth avoidance
constraints.
For example…. “airmass”
•  The atmosphere attenuates
starlight and blurs images. A
shorter pathlength through the
atmosphere minimizes both
effects.
•  This equation applies to a plane parallel
atmosphere (not what is pictured at left,
nor is the “atmosphere” at left realistic)
•  The equation is a good approximation
for the modest zenith angles most
astronomers care about).
Angle c is the altitude
Angle b is the zenith angle, z
The Celestial Poles
q
The “North Celestial Pole” lies overhead for an observer at the
North Pole and on the horizon for an observer on the Equator.
Ø
The altitude of the pole equals your latitude.
The Celestial Poles
Ø
The rotating Earth makes it look like the Celestial Sphere
is spinning about the celestial poles.
http://www.atscope.com.au/BRO/warpedsky.html
The Celestial Poles
Ø
The rotating Earth makes it look like the Celestial Sphere
is spinning about the celestial poles.
http://www.atscope.com.au/BRO/warpedsky.html
Polaris, at the end of the handle of the Little
Dipper, conveniently (and temporarily) marks
the North Celestial Pole.
q
q
In the Southern Hemisphere
there is no good pole star (at
present).
Note that there are some
stars (near the pole) that
never set below the horizon “Circumpolar Stars”
Ø
Ø
q
For an observer at the North or
South pole every star is
circumpolar.
At the Equator there are no
circumpolar stars
Given the altitude of the pole,
circumpolar stars have
declinations between 90 and
90-latitude degrees in the
North, -90-latitude in the
South.
Polaris
The Celestial Equator in the Sky
q
The Celestial Equator is the locus of all points lying 90 degrees
from the celestial pole.
•
•
It is a great circle around the celestial sphere perpendicular to the
polar axis.
Since the celestial sphere “turns” around the poles. The celestial
equator is a fixed reference line in the sky (rotating over itself).
Ø
Ø
The celestial equator runs from the horizon due east, up in the sky (90lat) degrees and back down to the horizon due west.
Stars “above” the celestial equator have positive declination (at least as
seen from the North).
The Meridian
Ø
Every line of celestial longitude is a meridian of longitude, but we
recognize the line of longitude, or simply the great circle line,
running overhead as “THE” Meridian.
Locating Stars on the Celestial Sphere
q
Just like geographical coordinates on the
Earth each star has a celestial address.
§
This address is impermanent because
q
q
q
Stars move steadily as they randomly
drift in the Galaxy.
The coordinate system (tied to the Earth)
shifts as the Earth precesses like a top.
§  Precession is slow (26,000 years/
cycle) but even over a decade its
effects are significant.
Coordinates are the analog of latitude and longitude, called
Declination and Right Ascension respectively.
§
Declination is straightfoward and is simply the angular distance a star
lies above or below the celestial equator measured in degrees.
q
q
The north celestial pole is at a declination of +90 degrees
The declination of the bright star Vega is +38:47:01.9 (at least in the
year 2000 it was – more on that later), so +dd:mm:ss.s in general.
There is something wrong with the figure on this page. What is it?
Locating Stars on the Celestial Sphere
There is something wrong with the figure on this page. What is it?
Celestial Motion at Different Declination
Celestial equator
(circumpolar)
Stars trace out small circles on the celestial sphere at constant declination (a great
circle if the star lies on the equator) leading to behavior dependent on declination.
Right Ascension
q
Right Ascension (longitude) is trickier
§
If you point your finger at a particular Declination the declination value
remains unchanged, but Right Ascension ticks away as the sky
(actually the Earth) rotates.
§
Right Ascension is thus naturally measured in units of (sidereal) time –
hh:mm:ss.s
Ø
Ø
Ø
One hour of right ascension is 15 degrees of celestial longitude (not 15
angular degrees, except at the equator)
The sky rotates by at 15 arcseconds per second of time at the Equator
Since lines of RA converge toward the pole – a unit of RA spans a
different angle depending on Declination – a factor of cos(Dec) comes
into play.
Convergence of Longitude at the Pole
q
q
On Earth one degree of latitude (equivalent of declination) is
111.3 km at any latitude.
One degree of longitude is 111.3km * cos(latitude)
A minute of Right Ascension is 15 minutes of arc at the equator, but a smaller angle at
higher latitudes.
Right Ascension
q
In a sense, R.A. marks the passage of time on the sky.
q
As time passes different (increasing) R.A. coordinates are overhead.
q
If 8 hours R.A. is overhead right now, 9 hours R.A will be overhead in an hour.
q
q
Since stars rise in the east and set in the west, R.A. must increase toward the
east (left as you are facing south in the northern hemisphere) and decrease
toward the west.
Right Ascension/Longitude needs an arbitrary zeropoint (Greenwich
for Earth longitude, the “First Point of Aries” on the sky).
q
This celestial reference point is the intersection celestial equator and ecliptic
at of the location of the Sun at the Spring Equinox.
The Sun and the Celestial Sphere
q
As the Earth orbits the Sun we see the Sun in different locations
against the backdrop of stars.
The Earth reaches the same location in its orbit on the same
calendar date each year.
l
²  The Sun’s path amongst the stars (which is the Earth’s orbital path as seen from the
Sun) is called the Ecliptic.
²  The constellations through which the Ecliptic passes are the constellations of the
Zodiac. The Sun obscures your “birthsign” on your birthday.
•  The Sun’s apparent path around
the sky, inclined to the celestial
equator by the 23.5 degree tilt
of the Earth, crosses the
celestial equator at two points –
the Fall and Spring Equinox.
•  The Spring Equinox marks the
zeropoint of Right Ascension
Right Ascension and the Sun
q
The R.A. of the Sun is 0h 0m 0.00s at the moment of the Spring Equinox (12 h at
the Fall Equinox.)
q
q
At the Spring Equinox 12 hours R.A. is high in the midnight sky (opposite the
Sun). At the Fall Equinox 0 hours is overhead at midnight.
Each day the position of the Sun advances 3 m 56 s in R.A. (3m 56 seconds is
24 hours divided by 365.25 days in a year)
q
q
q
Consider the Sun on the first day of Spring at 0h 0m 0s R.A. and consider a
star at 2h 0m 0s R.A. at the same declination as the Sun
q
That star will set 2 hours after the Sun on the first day of Spring.
A day later that star will set 1 hour 56m 4s after the Sun (4 minutes earlier)
because the Sun’s R.A. is creeping up on the star’s. In a month the star will
be hidden behind the sun.
The stars rise and set approximately 4 minutes earlier each day, accumulating
to 2 hours earlier in the course of a month.
The Sidereal Difference
q
q
Daily activity on Earth is keyed to the mean solar day for obvious reasons.
Astronomers, however, care how the Earth is turned relative to the stars.
Solar vs. Sidereal Time
•  The Celestial Sphere turns completely once each 24 hour Sidereal Day
•  A 24 hour Sidereal Day plays out in 23 hours 56 minutes 4 seconds of
civil/solar time– the true rotation period of Earth
•  The Sun rises and sets on a slightly different schedule than the stars.
•  The difference arises from the changing perspective as the Earth
orbits the Sun.
•  While the Earth completes a rotation it moves 1/365th of the way
around its orbit.
•  It must turn for an extra 3 minutes and 56 seconds (24 hours /
365.25 days in a year) to get the Sun back to the “Noon” position.
•  The Solar Day, by definition, is the average time from Noon to Noon
and exactly 24.000 hours long.
•  The Sidereal Day – defining the rising and setting of the stars is 3m
56s shorter.
Solar vs. Sidereal Time
§  A Sidereal clock tracks star time – the clock keeps 24 hour time but completes a
24 hour cycle in 23h 56m 4s
§  A conventional clock can be made into a Sidereal clock by adjusting it to run
fast by about 4 minutes a day.
§  What’s the use of a Sidereal clock?
Ø  The time read by a Sidereal clock corresponds to the merdian of Right
Ascension that is overhead at that instant.
Ø  You can “set” a sidereal clock by observing a star of known R.A. crossing the
meridian
§  At Noon on the Spring Equinox a sidereal clock will read approximately 0 hours
(why approximately??)
§  Running fast, a Sideral clock accumulates a full hour in about two weeks (2
hours a month).
§  One month after the equinox a Sidereal clock will read 2 hours at Noon.
The Rising and Setting of the Stars
q
q
q
To reiterate… Our perspective on the Sun shifts as the Earth travels around in it’s
orbit.
The stars are so distant that the Earth orbital motion has very little effect.
Because of this shift in the perspective on the Sun, the same meridian of R.A. is
overhead 4 minutes earlier (really 3m 56s earlier) according to a solar clock each
day.
q
q
Said another way, a given star sets 3m 56s earlier each day.
The difference arises because we measure civil time relative to the passage of the
Sun in the sky.
q
q
The Earth travels 1/365th of its orbit around the Sun in a day. Our perspective
on the stars is 1/365th of 24 hours = 3 min 56 sec different.
The Suns position in R.A. increases this much each day.
q
The Sun moves steadily (almost) eastward to increasing R.A.
q
A given star sets 4 minutes earlier each day an hour earlier every 2
weeks.
The Sun and the Celestial Sphere
q
The Sun finds itself fixed at a different location on the celestial sphere each day
– as a result, on that day it behaves like any other given star, following a path
dictated by the rotation of the Earth.
•  On the Spring and Fall Equinox the Sun lies
on the celestial equator – declination = 0
•  At the Summer Solstice the declination of the
Sun is +23.5 degrees. At the Winter Solstice
the declination of the Sun is -23.5 degrees.
Back to Celestial Motion at Different Declination:
Solar Edition
Celestial equator
(circumpolar)
When the Sun lies on the celestial equator days are 12 hours long
The Sun can get as far as +/- 23.5 degrees from the celestial equator in declination.
Solar Apparent Motion at Different Declination
Short days
Low solar elevation
Long days
High solar elevation
A Review Perspective on Equatorial Coordinates
Precession of the Equinox
q
q
q
The location of the crossing
points of the ecliptic on the
celestial equator depend on the
direction of the Earth’s rotation
axis.
Due to Solar and Lunar tides the
Earth’s rotation axis precesses in
a circle of radius 23.5 degrees
with a period of 26,000 years.
The “pole star” changes
substantially over time as a
result.
Precession of the Equinox
q
q
q
The location of the crossing
points of the ecliptic on the
celestial equator depend on the
direction of the Earth’s rotation
axis.
Due to Solar and Lunar tides the
Earth’s rotation axis precesses in
a circle of radius 23.5 degrees
with a period of 26,000 years.
The “pole star” changes
substantially over time as a
result.
Precession of the Equinox
q
q
The location of the crossing
points of the ecliptic on the
celestial equator depend on the
direction of the Earth’s rotation
axis.
Since the intersection point at the
Spring Equinox defines 0h of
Right Ascension and since the
pole defines 90 degrees
declination a star’s coordinate
shifts over time due to
precession – substantially so
over decades or centuries
The Precession of the Equinox
Precession's Consequence
●
Stellar celestial coordinates must be constantly updated to account for
precession.
–
●
●
Telescope control systems automatically precess coordinates so that the
telescope correctly points to the “of date” position of the star given proper
input of current date, R.A., Dec, and epoch of the coordinates.
Star catalogs must be tied to a particular “epoch”. Typically the default epoch
changes every 50 years as even over this timescale the coordinate change can
become significant.
For the star Vega the coordinates are
–  18:36:56.3 +38:47:01.9
J2000.0 (J for Julian)
–  18:35:15.5 +38:44:24.7
B1950.0 (B for Besselian)
●
●
small differences, but large compared to many instrument fields-of-view.
Now in the computer age (and given the juicy J2000.0 round number epoch) it is
likely that catalog coordinates will stick to J2000.0 for centuries to come.
Other Consequences of Precession
Different Stars are circumpolar at different times.
•
3000 years ago the Big Dipper was circumpolar at our latitude.
Stars that currently never rise above our Southern horizon will be visible.
è  The Southern Cross will be visible from Charlottesville in 10,000 years.
è
Go home and prove it for yourself with Stellarium
Hour Angle
•  It is useful to have a measure of how far a star is from transiting
the meridian.
•  The Hour Angle denotes the -hh:mm:ss until transit or the
+hh:mm:ss since transit for a given star.
•  The Hour Angle is simply calculated as the difference between the
star’s R.A. and the current Sideral time.
•
H.A. = Sidereal Time - Right Ascension
•  A star whose Right Ascension matches the Sidereal Time is on
the meridan; H.A. = 0
•  A star’s airmass is a function of hour angle, reaching a minimum
when H.A. = 0
Transforming from R.A., Dec., and Hour Angle to
Altitude and Azimuth