Equatorial Telescope Mounting

Star Catalogs simbad IRSA

The Meridian 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 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 Earth) rotates Right Ascension is thus naturally measured in units of time hh:mm:ss.s One hour of right ascension is 15 degrees The sky rotates by at 15 arcseconds per second at the Equator 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.

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. 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 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.

Transit Telescopes

Variation in Earth Rotation The rotation rate of the Earth changes due to tides, internal motions, and shifting of water and ice on the surface. The second itself is precisely fixed thus UT1 drifts relative to TAI. These effects integrate to full seconds over 1-2 years.

Leap Seconds

Solar vs. Sidereal Time 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. The Solar Day, by definition, is exactly 24.0000 hours long. 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 The time on a Sidereal clock equals the meridian of Right Ascension that is overhead at the moment. At Noon on the Spring Equinox R.A.=00:00:00.0 is overhead by definition.

The Sidereal Difference 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 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 ( negative HA means prior to transit). A star is at its highest altitude (and lowest airmass) when HA=0

Zenith Angle and Airmass The complement of the altitude angle, the zenith angle, measures the angular separation of a star from the point overhead. A star that is just rising or setting has a zenith angle of z=90. 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 or... plane parallel is good enough

Airmass Curves

Alt/Az Equatorial Conversion 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 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 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. Modified Julian Date is JD 2400000.5 The time above is MJD 56678.667 The 0.5 shifts the start of an MJD to midnight rather than noon

Sunrise Sunset Factors influencing sunrise/sunset time you tell me... or... what time does the Sun set on the Spring Equinox? it's not 6:00 p.m...

Twilight (s) Twilight is the effect of the Sun shining on the atmosphere while the disk of the Sun is below the horizon.

Twilight (s) Note that the sky is blue due to Rayleigh scattering (a 1 / λ4 effect). Night happens earlier in the infrared. 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? In order of increasing brightness integrated starlight (unavoidable) zodiacal light (brighter in the ecliptic, unavoidable) airglow (variable and terrestrial) light pollution (geographic) 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 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. 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. Extragalactic work occurs in dark time faint fuzzies 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: Earth rotates counterclockwise looking down on the North Pole Moon revolves counterclockwise. First quarter Moon is ahead of the Sun along the Ecliptic. 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 Because the Earth is a spinning top, the direction of its pole in the sky is fixed (at least over short timescales). Of course, this consistency of tilt is related to the cause of the seasons.

Precession 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 It takes 26,000 years for the Earths pole to trace out a full circle on the sky. That circle is 47 degrees in diameter (2 x 23 ½)

The Effects of Precession on Astronomers It takes 26,000 years for the Earths pole to trace out a full circle on the sky. That circle is 47 degrees in diameter (2 x 23 ½) That moving target is the pole of the equatorial coordinate system.

Precession's Consequence Different Stars are circumpolar at different times. 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. The Southern Cross will be visible from Charlottesville in 10,000 years.

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.

Calculating Precession 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 We've seen one significant example of a spherical coordinate transformation Equatorial (plus H.A.) to Altitude-Azimuth Precession represents another similar (but usually more subtle transformation). Similar equations apply. You are transforming from one equator to another. 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 The Ecliptic Ecliptic Coordinates The Galactic Plane Galactic Coordinates

Galactic Coordinates