Equatorial Telescope Mounting
Star Catalogs
simbad
IRSA
The Meridian
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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.
Right Ascension
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Right Ascension (longitude) is trickier
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If you point your finger at a particular Declination the declination value
remains unchanged, but Right Ascension ticks away as the sky
(actually Earth) rotates
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Right Ascension is thus naturally measured in units of time –
hh:mm:ss.s
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One hour of right ascension is 15 degrees
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The sky rotates by at 15 arcseconds per second at the Equator
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Since lines of RA converge toward the pole – 1 minute of RA spans a
different angle depending on Declination – a factor of cos(Dec) comes
into play.
Right Ascension/Longitude needs an arbitrary zeropoint
(Greenwich on Earth, the “First Point of Aries” on the sky).
This reference point is the intersection celestial equator and
ecliptic at of the location of the Sun at the Spring Equinox.
Hour Angle
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The Hour Angle of a star is the time until (East) or since (West) it
crosses or has crossed the meridian.
The Hour Angle is simply the Right Ascension of the star minus
the current sidereal time.
Which Way is the Earth Turned:
Apparent Solar Time
The direction in which the Earth is turned at your location has
everything to do with what is up in the sky.
Apparent Solar Time is literally that.
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Measure the position of the Sun in the sky to determine Earth's rotation angle relative
to the Sun.
The Earth's elliptical orbit (Kepler's second law in particular) imposes a drift in
apparent solar time relative to mean solar time.
Average out these variations – establish a Mean Solar Day
Modern Time Keeping
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Define a second: 9,192,631,770 cycles of the hyperfine cesium-133
transition.
Beat that second without fail and without regard for which way the Earth
is turned – International Atomic Time (TAI)
Track the variations in Earth rotation – particularly the tidal slowing due to
the Moon's torque on the Earth – Keep a time that tracks Earth rotation
(UT1).
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Either requires a variable second or a precision TAI-UT1 offset.
Beat time at a steady rate but put in a step correction when needed to
approximate UT1 to within a second - Coordinated Universal Time (UTC)
All of these measures determine how the Earth is turned relative to the
Sun. As astronomers we care about how the Earth is turned relative to
the stars.
Transit Telescopes
Variation in Earth Rotation
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The rotation rate of the Earth changes due to tides, internal
motions, and shifting of water and ice on the surface.
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The second itself is precisely fixed thus UT1 drifts relative to TAI.
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These effects integrate to full seconds over 1-2 years.
Leap Seconds
Modern Time Keeping
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Define a second: 9,192,631,770 cycles of the hyperfine cesium-133
transition.
Beat that second without fail and without regard for which way the Earth
is turned – International Atomic Time (TAI)
Track the variations in Earth rotation – particularly the tidal slowing due to
the Moon's torque on the Earth – Keep a time that tracks Earth rotation
(UT1).
–
●
●
Either requires a variable second or a precision TAI-UT1 offset.
Beat time at a steady rate but put in a step correction when needed to
approximate UT1 to within a second - Coordinated Universal Time (UTC)
All of these measures determine how the Earth is turned relative to the
Sun. As astronomers we care about how the Earth is turned relative to
the stars.
Solar vs. Sidereal Time
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The Sun rises and sets on a slightly different schedule than the stars.
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The difference arises from the changing perspective as the Earth orbits
the Sun.
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While the Earth completes a rotation it moves 1/365th of the way around
its orbit.
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The Solar Day, by definition, is exactly 24.0000 hours long.
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It must turn for an extra 24 hours/365.25 (= about 4 minutes) to get the
Sun back to “Noon”
The Sidereal Day – defining the rising and setting of the stars - is 3m
56s shorter and represents the true rotation period of the Earth.
A Sidereal clock keeps star time – it keeps 24 hour time, but
completes a cycle in 23h 56m 4s of Solar time
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The time on a Sidereal clock equals the meridian of Right Ascension that
is overhead at the moment.
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At Noon on the Spring Equinox R.A.=00:00:00.0 is overhead by
definition.
The Sidereal Difference
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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.
Hour Angle
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The Hour Angle of a star is the time until (East) or since (West) it
crosses or has crossed the meridian.
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The Hour Angle is simply the Right Ascension of the star minus the
current sidereal time ( negative HA means prior to transit).
A star is at its highest altitude (and lowest airmass) when HA=0
Zenith Angle and Airmass
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The complement of the altitude angle, the “zenith angle”,
measures the angular separation of a star from the point
overhead.
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A star that is just rising or setting has a zenith angle of z=90.
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A star overhead has a zenith angle of zero.
The “airmass” of a star measures the number of atmospheric
thicknesses a star's light is passing through on its way to the
observer and equals the secant of the zenith angle.
–
Since the atmosphere attenuates starlight, knowing the airmass is
critical to precision stellar photometry.
*
z
horizon
altitude
one
atmosphere
Angle c is the altitude
Angle b is the zenith angle, z
1
Airmass =
= sec( z )
cos( z )
For a plane parallel atmosphere
(not what is pictured at left, but a
good approximation for the small
zenith angles most astronomers
care about).
airmass = sec ( z ) =
−1
((sin (lat )∗sin (dec)) + cos(lat )∗cos (dec)∗cos( H.A))
Extreme Airmass
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or... plane parallel is good enough
Airmass Curves
Alt/Az Equatorial Conversion
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The airmass equation derives directly from the conversion of
Equatorial coordinates (including hour angle) to altitude and
azimuth.
sin (alt ) = ((sin (lat )∗sin (dec)) + cos (lat )∗cos(dec)∗cos( H.A))
sin (az ) =
−sin ( HA)∗cos(dec)
cos(alt )
Alt/Az Equatorial Conversion
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The airmass equation derives directly from the conversion of
Equatorial coordinates (including hour angle) to altitude and
azimuth.
H is hour angle
a is altitude
A is Azimuth
P is the equatorial pole
Z is the zenith
φ is the latitude
One more time topic - Julian Date
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Astronomers need to time tag observations in a convenient
way since Month/Day/Year is cumbersome
Julian Date is the number of days (and decimal fraction
thereof) since noon Jan 1, 4713 B.C.
The Julian date for 2014 January 21 11:00:00.0 EST is
JD 2456679.167
This number is a bit cumbersome and early (Sputnik era)
computations did not want to waste storage on the
unnecessary leading digits.
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Modified Julian Date is JD – 2400000.5
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The time above is MJD 56678.667
The 0.5 shifts the start of an MJD to midnight rather than noon
Sunrise Sunset
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Factors influencing sunrise/sunset time
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you tell me.... or... what time does the Sun set on the Spring
Equinox? it's not 6:00 p.m....
Twilight (s)
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Twilight is the effect of the Sun shining on the atmosphere
while the disk of the Sun is below the horizon.
Twilight (s)
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Note that the sky is “blue” due to Rayleigh scattering
(a 1 / λ4 effect).
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“Night” happens earlier in the infrared.
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Typically it is dark enough to observe at the end of civil twilight.
Twilight Effects
The Belt of Venus
Twilight Effects
Crepuscular Rays
The Belt of Venus
Twilight Effects
Noctilucent clouds
How Dark Is the Night Sky?
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In order of increasing brightness
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integrated starlight (unavoidable)
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zodiacal light (brighter in the ecliptic, unavoidable)
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airglow (variable and terrestrial)
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light pollution (geographic)
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moonlight (schedule around)
A high-quality mountain top site (limited by the first three) will
have a sky brightness of V~22 mag/arcsec2
Light pollution quickly degrades this value (see maps via the
Clear Sky Chart)
Moonlight is a form of light pollution. The full moon degrades
V-band sky brightness by 4 magnitudes (only 2 magnitudes in
the red)
Airglow
Moon Brightness vs. Phase
The Color of Moonlight
The Moon is grey so moonlight is similar in color to sunlight, just several hundred
thousand times fainter.
That Pesky Moon
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The apparent magnitude of the Sun is -26.4. The Moon is
-12.7. Note quite a million times fainter.
One cycle of phases every 29.5 days.
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Full Moon occurs roughly the same time every month.
The Full Moon is several times brighter than 2 “half” moons
due to particle phase effects – backscattering.
Telescope time is assigned according to “dark”, “bright”, and
sometimes “grey” conditions.
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Extragalactic work occurs in “dark” time – faint fuzzies
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Infrared work, bright targets, and spectroscopy happen in
“bright” time
SDSS Observing Report
---- Observing Summary ---During first 4.5 hours, it was clear with poor seeing. 2.0-2.7".
Then it was high clouds, partly cloudy with better seeing. 1.3-1.7".
We closed for last two hours due to nearby radar and thick clouds.
We observed
cart 10, pl
cart 15, pl
cart 11, pl
3 BOSS plates,
7332. 4 exposures.
7330, 3 exposures.
7260. 7 exposures. DONE
5 APOGEE plates
cart 5, pl 7204.
cart 4, pl 7213.
cart 7, pl 7215.
cart 1, pl 5618.
2XABBA,
2XABBA.
2XABBA.
2XABBA.
Dark
missing 93, 96, faint 128, 131.
faint, 182, 284.
No missing or faint fibers.
Faint: 227, 270.
Bright
Lunar Phase vs. Rising and Setting
Lunar Phases
Keep in mind:
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Earth rotates “counterclockwise”
looking down on the North Pole
Moon revolves counterclockwise.
First quarter Moon is “ahead” of the
Sun along the Ecliptic.
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At the Spring Equinox the first
quarter Moon will be at the
Summer Solstice location (high
positive declination) “3-months”
ahead of the Sun.
Last quarter Moon lags 3-months
“behind” (or is 9 months ahead...)
Precession
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Because the Earth is a spinning top, the direction of its pole in the
sky is fixed (at least over short timescales).
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Of course, this consistency of tilt is related to the cause of the seasons.
Precession
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Like any top under torque, however, the spin axis precesses
slowly over time.
Because the celestial poles and equator define the RA/Dec
“equatorial” coordinate system the “of-date” coordinates of a star
change slightly from day to day and significantly over decades.
26000
years
Precession's Consequence
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It takes 26,000 years for the Earths pole to trace out a full circle
on the sky.
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That circle is 47 degrees in diameter (2 x 23 ½)
The Effects of Precession on Astronomers
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It takes 26,000 years for the Earths pole to trace out a full circle
on the sky.
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That circle is 47 degrees in diameter (2 x 23 ½)
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That moving target is the pole of the equatorial coordinate system.
Precession's Consequence
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Different Stars are circumpolar at different times.
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3000 years ago the Big Dipper was circumpolar at our latitude. It's not
anymore.
Stars that currently never rise above our Southern horizon will be
visible.
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The Southern Cross will be visible from Charlottesville in 10,000 years.
Precession's Consequence
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Stellar celestial coordinates must be constantly updated to account
for precession.
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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
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18:36:56.3 +38:47:01.9
J2000.0 (J for Julian)
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18:35:15.5 +38:44:24.7
B1950.0 (B for Besselian)
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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.
Calculating Precession
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Like the transformation between equatorial and alt-az
coordinates illustrated below. Correcting for precession is a
coordinate transformation (pole and equinox shift) that can be
calculated with spherical trigonometry.
H is hour angle
a is altitude
A is Azimuth
P is the equatorial pole
Z is the zenith
φ is the latitude
Various Spherical Coordinate Systems
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We've seen one significant example of a spherical coordinate
transformation – Equatorial (plus H.A.) to Altitude-Azimuth
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Precession represents another similar (but usually more subtle
transformation). Similar equations apply. You are
transforming from one “equator” to another.
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Basically one is shifting the pole to define a new fundamental
plane (celestial equator → horizon in this case)
Computers now do this so you don't have to....
Other fundamental planes are defined by
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The Ecliptic → Ecliptic Coordinates
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The Galactic Plane → Galactic Coordinates
Galactic Coordinates
Galactic Coordinates