Coordinates on EarthCoordinates on Earth

LatitudeLatitude and and longitudelongitude coordinate system: coordinate system:

Lafayette::

Lat. = 40°.5 NLong. = 87° W

Greenwich, UK:

Lat. = 51.5° NLong. = 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 The circle through youryour South, Zenith, North South, Zenith, North points is your points is your celestial meridian celestial meridian (am/pm)(am/pm)

• Stars are ‘stuck’ on the celestial sphere

• Solar system bodies move around on it

Motion of the Celestial SphereMotion of the Celestial Sphere

stars appear to move stars appear to move counterclockwise counterclockwise around the around the north north celestial polecelestial pole

make one full rotation make one full rotation each each siderealsidereal day day

same star will cross same star will cross observer’s meridian observer’s meridian 23h56m later23h56m later

Time lapse photo, facing north.

Sidereal vs. Solar DaySidereal vs. Solar Day

ConsequencesConsequences

A particular star rises 4 min earlier each A particular star rises 4 min earlier each night, according to your watchnight, according to your watch

Any star takes 23h56m to arrive back at Any star takes 23h56m to arrive back at your southern meridian (upper transit)your southern meridian (upper transit)

Motion of night sky

The Ecliptic PlaneThe Ecliptic Plane

In the course of one day:In the course of one day:– the Sun moves very slightly the Sun moves very slightly

on the celestial sphereon the celestial sphere

– the whole celestial sphere the whole celestial sphere rotates once around the rotates once around the EarthEarth

Plot the position of the Sun Plot the position of the Sun each day on the celestial each day on the celestial sphere sphere the eclipticthe ecliptic

Ecliptic is Inclined 23.5 Ecliptic is Inclined 23.5 degrees to celestial degrees to celestial equatorequator

E W

S

N

June

March & Sept

December

Changes of seasonsChanges of seasons

1st day of Summer and Winter = solstices.1st day of Summer and Winter = solstices.

In the northern hemisphere:In the northern hemisphere:– longest (June 22) and shortest (Dec 22) days longest (June 22) and shortest (Dec 22) days

of the yearof the year– at local noon on June 22, Sun is as high in at local noon on June 22, Sun is as high in

the sky as it ever gets.the sky as it ever gets.

Seasons are reversed for the southern Seasons are reversed for the southern hemisphere.hemisphere.

EquinoxesEquinoxes1st day of Spring and Fall = equinoxes:1st day of Spring and Fall = equinoxes:– Sun is on the celestial equatorSun is on the celestial equator– the only days on which the Sun rises exactly due the only days on which the Sun rises exactly due

east and sets exactly due westeast and sets exactly due west– exactly 12 hours of daylight (everywhere)exactly 12 hours of daylight (everywhere)

March equinox ~ Mar. 21March equinox ~ Mar. 21

September equinox ~ Sept. 23September equinox ~ Sept. 23

Due to northern/southern hemisphere season Due to northern/southern hemisphere season confusion, ‘vernal equinox’ is being phased outconfusion, ‘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 timee.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 ≠ (-3 + 10/60 + 20/3600) degrees e.g. -0d11m25s ≠ sign(0)*(0 + 11/60 + 25/3600) degrees!

http://www.vlba.nrao.edu/astro/messages/dec-0/dec-0

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 LatitudesThe Sky at Different LatitudesAltitude of celestial pole above horizon Altitude of celestial pole above horizon equals your latitude equals your latitude (animation)(animation)

Stars A and B will rise in the east, reach transit at the observer’s meridian, and Stars A and B will rise in the east, reach transit at the observer’s meridian, and set in the westset in the west

Star C never rises/sets, but goes through upper and lower transit on observer’s Star C never rises/sets, but goes through upper and lower transit on observer’s meridian – it is meridian – it is circumpolarcircumpolar

AB

C

Hour AngleHour Angle

How far away a How far away a star is from upper star is from upper transittransit

Positive if star has Positive if star has already reached already reached upper transit, upper transit, negative otherwisenegative otherwise

Measured in h:m:sMeasured in h:m:s

HA of star = RA on southern meridian – RA of star

Sidereal TimeSidereal Time

Time system based on motion of the Time system based on motion of the celestial sphere.celestial sphere.

Exactly 24 sidereal hours pass between Exactly 24 sidereal hours pass between successive upper transits of a star.successive upper transits of a star.

Local sidereal time = RA of any star that is Local sidereal time = RA of any star that is currently at upper transit.currently at upper transit.

HA of star = LST – RA of the starHA of star = LST – RA of the star

ComplicationsComplications

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

Earth’s rotation creates two high tides and Earth’s rotation creates two high tides and two low tides per day in most places.two low tides per day in most places.– High tide times vary regionallyHigh tide times vary regionally

Moon also raises smaller body tides on the Earth’s surface

Tides are all aboutTides are all about differential differential forcesforces

- these vary as 1/distance- these vary as 1/distance33

Earth’s rotation carries the bulge ahead of Moon-Earth line

- friction of water with sea floor slows down Earth’s rotation

Consequences of TidesConsequences of Tides

Changes Earth’s rotation:Changes Earth’s rotation:– tidal braking: days are getting longer by millisecond/centurytidal braking: days are getting longer by millisecond/century– axis precession: Vega will be the new pole star in 14,000 A.D.axis precession: Vega will be the new pole star in 14,000 A.D.

Synchronization of Moon’s rotation & revolutionSynchronization of Moon’s rotation & revolution– same side now always faces the Earthsame side now always faces the Earth– eventually Earth’s rotation will synchronize with the Moon’s, eventually Earth’s rotation will synchronize with the Moon’s,

and sidereal day = sidereal month = 47 (current) daysand sidereal day = sidereal month = 47 (current) days

Increase in Moon’s orbitIncrease in Moon’s orbit– receding a few cm/year (Earth’s bulge pulls Moon forward in its receding a few cm/year (Earth’s bulge pulls Moon forward in its

orbit)orbit)

Axial PrecessionAxial Precession

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

Precession of EquinoxesPrecession of EquinoxesEarth’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 EquinoxesPrecession of EquinoxesMovement 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 CoordinatesBarycentric CoordinatesThe 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 1829-10, with a 0.500 year period.– subsequently retracted since Earth’s elliptical orbit was incorrectly

subtracted when they converted their data to barycentric coordinates.

Aberration of StarlightAberration of Starlight

International Celestial Reference SystemInternational Celestial Reference System(ICRS)(ICRS)

Centered on solar system barycenter (inside the Sun)Centered on solar system barycenter (inside the Sun)– doesn’t change over time (except due to measurement refinements)doesn’t change over time (except due to measurement refinements)

Based on the apparent positions of distant quasars (so far away Based on the apparent positions of distant quasars (so far away they have zero parallax)they have zero parallax)– originally measured in optical (hard to do!)originally measured in optical (hard to do!)– now measured via radio interferometry to microarcsecond precisionnow measured via radio interferometry to microarcsecond precision

Very close to J2000 equatorial system (78 milliarcsec difference in Very close to J2000 equatorial system (78 milliarcsec difference in north pole position)north pole position)

ICRS is the fundamental reference for GPS:ICRS is the fundamental reference for GPS:– find Earth’s orientation w.r.t. ICRSfind Earth’s orientation w.r.t. ICRS– find location of GPS satellites w.r.t. Earthfind location of GPS satellites w.r.t. Earth– find your location on Earth w.r.t. GPS satellitesfind your location on Earth w.r.t. GPS satellites

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