Coordinates on Earth Latitude and longitude coordinate system: Lafayette :: Lat. = 40°.5 N Long. = 87° W Greenwich, UK : Lat. = 51.5 ° N Long. = 0° W Longitudes are either E or W of Greenwich (no +/-)

The official prime meridian (WGS84) is no longer fixed on the ground Airy’s is 100m to the east Bradley’s Flamsteed House

Earth’s surface in GPS system is represented by a reference ellipsoid Geodetic latitude (GPS)

The Celestial Sphere The circle through your South, Zenith, North points is your celestial meridian (am/pm)

Stars are ‘stuck’ on the celestial sphere Solar system bodies move around on it

Motion of the Celestial Sphere stars appear to move counterclockwise around the north celestial pole make one full rotation each sidereal day same star will cross observer’s meridian 23h56m later Time lapse photo, facing north.

Sidereal vs. Solar Day

Consequences A particular star rises 4 min earlier each night, according to your watch Any star takes 23h56m to arrive back at your southern meridian (upper transit)

Motion of night sky

The Ecliptic Plane In the course of one day: –the Sun moves very slightly on the celestial sphere –the whole celestial sphere rotates once around the Earth Plot the position of the Sun each day on the celestial sphere  the ecliptic Ecliptic is Inclined 23.5 degrees to celestial equator

E W S N June March & Sept December

Changes of seasons 1st day of Summer and Winter = solstices. In the northern hemisphere: –longest (June 22) and shortest (Dec 22) days of the year – at local noon on June 22, Sun is as high in the sky as it ever gets. Seasons are reversed for the southern hemisphere.

Equinoxes 1st day of Spring and Fall = equinoxes: – Sun is on the celestial equator – the only days on which the Sun rises exactly due east and sets exactly due west – exactly 12 hours of daylight (everywhere) March equinox ~ Mar. 21 March equinox ~ Mar. 21 September equinox ~ Sept. 23 September equinox ~ Sept. 23 Due to northern/southern hemisphere season confusion, ‘vernal equinox’ is being phased out

March equinox September equinox

Equatorial Coordinate System RA (α) = Right ascension, measured in h:m:s eastward of the March equinox (1h = 15 degrees) Dec (δ) = Declination, measured in degrees north (+) or south (-) of the celestial equator March

Caveats 1.Be careful not to confuse minutes of arc with minutes of time e.g.: 23h12m32s = 15*(23+12/60+32/3600) degrees, but 23d12’32” = 23+12/60+32/3600 degrees 2. Watch out for negative declinations near zero: e.g.: -3d10m20s ≠ ( / /3600) degrees e.g. -0d11m25s ≠ sign(0)*(0 + 11/ /3600) degrees!

What is the approximate sky area of this image in square arcminutes? Why does the RA scale increase from right to left?

The Sky at Different Latitudes Altitude of celestial pole above horizon equals your latitude (animation)

Stars A and B will rise in the east, reach transit at the observer’s meridian, and set in the west Star C never rises/sets, but goes through upper and lower transit on observer’s meridian – it is circumpolar A B C

Hour Angle How far away a star is from upper transit Positive if star has already reached upper transit, negative otherwise Measured in h:m:s HA of star = RA on southern meridian – RA of star

Sidereal Time Time system based on motion of the celestial sphere. Exactly 24 sidereal hours pass between successive upper transits of a star. Local sidereal time = RA of any star that is currently at upper transit. HA of star = LST – RA of the star HA of star = LST – RA of the star

Complications (or why the word ‘astrometry’ is usually prefaced by ‘painstaking’)

Earth’s rotation creates two high tides and two low tides per day in most places. – High tide times vary regionally Moon also raises smaller body tides on the Earth’s surface

Tides are all about differential forces - these vary as 1/distance 3

Earth’s rotation carries the bulge ahead of Moon-Earth line - friction of water with sea floor slows down Earth’s rotation

Consequences of Tides Changes Earth’s rotation: –tidal braking: days are getting longer by millisecond/century –axis precession: Vega will be the new pole star in 14,000 A.D. Synchronization of Moon’s rotation & revolution Synchronization of Moon’s rotation & revolution –same side now always faces the Earth –eventually Earth’s rotation will synchronize with the Moon’s, and sidereal day = sidereal month = 47 (current) days Increase in Moon’s orbit Increase in Moon’s orbit –receding a few cm/year (Earth’s bulge pulls Moon forward in its orbit)

Axial Precession

North Celestial Pole moves around ecliptic pole: –one cycle takes about 25,800 years

Precession of Equinoxes Earth’s north- south axis shows a long term precession, and also short-term, small amplitude oscillations (nutation) Intersection point of celestial equator and ecliptic (March equinox) moves over time

Precession of Equinoxes Movement of equinoxes means the RA and dec coordinates of a star change with time. (Same for any Earth-based sky coordinate system). Every coordinate must therefore always include a reference date – –the word ‘equinox’ is used to describe the coordinate system’s reference point on that date – –the word ‘epoch’ is used to describe the star’s position on that date (since stars can have small proper motions on the celestial sphere) equinox J2000: coordinates as they were on Jan 1, 2000 equinox B1950: coordinates on Jan 1, 1950 ‘B’ and ‘J’ refer to different calendar year systems (!)

Barycentric Coordinates The motion of a telescope on the surface of the Earth can affect the apparent coordinates of a star. – –timing measurement of events also affected, e.g. eclipses Useful to introduce coordinates on a celestial sphere centered on the barycenter of the solar system (inertial frame) – –must remove Earth’s axial precession and nutation – –also remove Earth’s orbital motion around the Sun 1991: British astronomers announced discovery of the 1st exoplanet. Located around the pulsar PSR , with a year period. – –subsequently retracted since Earth’s elliptical orbit was incorrectly subtracted when they converted their data to barycentric coordinates.

Aberration of Starlight

International Celestial Reference System (ICRS) Centered on solar system barycenter (inside the Sun) –doesn’t change over time (except due to measurement refinements) Based on the apparent positions of distant quasars (so far away they have zero parallax) –originally measured in optical (hard to do!) –now measured via radio interferometry to microarcsecond precision Very close to J2000 equatorial system (78 milliarcsec difference in north pole position) ICRS is the fundamental reference for GPS: –find Earth’s orientation w.r.t. ICRS –find location of GPS satellites w.r.t. Earth –find your location on Earth w.r.t. GPS satellites

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