BASICS FOR ASTRONOMICAL OBSERVATIONS Version 02, 14/04/2015 BASICS FOR ASTRONOMICAL OBSERVATIONS Conférence présentée à PARSEC, le 1er octobre 2005. Jean-Pierre Rivet CNRS, OCA, Dept. Lagrange jean-pierre.rivet@oca.eu © C2PU, Observatoire de la Cote d’Azur, Université de Nice Sophia-Antipolis

C2PU-Team, Observatoire de Nice Where is my target ? Stars, asteroids, planets, etc. are never where the catalogs pretend. Several reasons for that: Kinematic effects: Celestial objects are moving (proper motion). Fastest to slowest: artificial satellites, Moon, planets/asteroids, stars, extragalactic objects. Geometric effects: Earth’s motions are complex. So, Earth-based telescopes and reference catalogs use different frameworks (different origin points, and different axes), and they are moving one w.r.t each other. 16/09/2018 C2PU-Team, Observatoire de Nice

Where is my target ? So, lots of computations are needed Physical effects: 1) light takes some time to travel, so, moving objects are no longer where they appear to be. 2) Earth’s velocity modifies the apparent direction of incoming light rays. Atmospheric effects: Earth’s atmosphere perturbs the direction and intensity of light rays. So, lots of computations are needed to take into account all these effects, and to be able to drive your telescope to the right direction ! 16/09/2018 C2PU-Team, Observatoire de Nice

Earth’s motions and reference planes/directions

C2PU-Team, Observatoire de Nice Coordinate systems Polar (spherical) coordinates: (r, , ) Polar axis r  Origin  PROBLEM: finding “good” reference plane and zero direction. Reference plane direction Zero 16/09/2018 C2PU-Team, Observatoire de Nice

The motions of the Earth (I): orbital motion NOT TO SCALE ! Ecliptic plane Earth orbit Earth Sun 16/09/2018 C2PU-Team, Observatoire de Nice

The motions of the Earth (I): orbital motion NOT TO SCALE ! Orbit  ellipsis Earth a = 149.6 106 km e = 0.0167 P = 1 “year” Sun = Focus Perihelion Center Aphelion … but what is a “year” ? depends the reference direction chosen to start/stop the chronometer ! anomalistic year (365.25964 d) sidereal year (365.25637 d) tropical year (365.24219 d) draconic year (346.62008 d) … a.e (e = eccentricity) a (a = semi-major axis) 16/09/2018 C2PU-Team, Observatoire de Nice

The motions of the Earth (I): orbital motion NOT TO SCALE ! Orbit  ellipsis Earth a = 149.6 106 km e = 0.0167 P = 1 “year” … but in real life, things are a bit more complicated … Sun = Focus Perihelion Center Aphelion … but what is a “year” ? depends the reference direction chosen to start/stop the chronometer ! anomalistic year (365.25964 d) sidereal year (365.25637 d) tropical year (365.24219 d) draconic year (346.62008 d) … a.e (e = eccentricity) a (a = semi-major axis) 16/09/2018 C2PU-Team, Observatoire de Nice

The motions of the Earth (II): secular motions NOT TO SCALE ! Aphelion Perihelion Earth’s orbit now 16/09/2018 C2PU-Team, Observatoire de Nice

The motions of the Earth (II): secular motions NOT TO SCALE ! Aphelion Perihelion Earth’s orbit in 3000 years 16/09/2018 C2PU-Team, Observatoire de Nice

The motions of the Earth (II): secular motions NOT TO SCALE ! Aphelion Perihelion Earth’s orbit in 6000 years 16/09/2018 C2PU-Team, Observatoire de Nice

The motions of the Earth (II): secular motions Aphelion Perihelion NOT TO SCALE ! Earth’s orbit in 9000 years Perihelion slowly shifts Parameters a and e slowly change … because Earth and Sun are not alone in the Solar System ! 16/09/2018 C2PU-Team, Observatoire de Nice

The motions of the Earth (III): proper motion North ecliptic pole North equatorial pole  : Obliquity  23° 27’ Equatorial plane Ecliptic plane … but what is a “day” ? depends the reference direction chosen to start/stop the chronometer ! mean solar day (24 h) sidereal day (23h 56m 04.09s) P = 1 “day” 16/09/2018 C2PU-Team, Observatoire de Nice

The motions of the Earth (III): proper motion NOT TO SCALE ! Spring equinox Ecliptic plane Summer solstice Equatorial plane  Equatorial plane Sun Equatorial plane  vernal direction Winter solstice Earth orbit  vernal direction  vernal direction 16/09/2018 C2PU-Team, Observatoire de Nice

Reference directions and planes Ecliptic North pole Earth North pole Orbital and proper motions of the Earth provide for 2 reference planes and 2 polar directions Ecliptic plane  Equatorial plane  vernal direction 16/09/2018 C2PU-Team, Observatoire de Nice

Reference directions and planes Ecliptic North pole Earth North pole Orbital and proper motions of the Earth provide for 2 reference planes and 2 polar directions Ecliptic plane  … but in real life, things are a bit more complicated … Equatorial plane  vernal direction 16/09/2018 C2PU-Team, Observatoire de Nice

The motions of the Earth (IV): precession Ecliptic North pole P  26 000 years Earth North pole Ecliptic plane  Equatorial plane  Jan. 2000 16/09/2018 C2PU-Team, Observatoire de Nice

The motions of the Earth (IV): precession Ecliptic North pole P  26 000 years Earth North pole Ecliptic plane Equatorial plane  Jan. 2010 16/09/2018 C2PU-Team, Observatoire de Nice

The motions of the Earth (IV): precession Ecliptic North pole P  26 000 years Earth North pole Ecliptic plane Equatorial plane  Jan. 2020 16/09/2018 C2PU-Team, Observatoire de Nice

The motions of the Earth (IV): nutation Ecliptic North pole Earth North pole P  18.6 years Ecliptic plane  Equatorial plane  16/09/2018 C2PU-Team, Observatoire de Nice

The motions of the Earth (V): nutation Ecliptic North pole Earth North pole P  18.6 years Ecliptic plane Equatorial plane  16/09/2018 C2PU-Team, Observatoire de Nice

The motions of the Earth (V): precession-nutation Precession-nutation: slow motions of the rotation (polar) axis of the Earth w.r.t. an external (astronomical) reference frame (fixed stars of quasars) True pole @ date Precession (P  26 000 years) Nutation (P  18.6 years) Mean pole @ date Ecliptic pole Mean pole @ J2000 ... because the Earth has no spherical symmetry the Moon creates a torque on Earth’s equatorial bulge 16/09/2018 C2PU-Team, Observatoire de Nice

Conclusion Earth’s motion is complex !!! Must be taken into account to define reliable reference systems and to find an astronomical object in the sky ! 16/09/2018 C2PU-Team, Observatoire de Nice

About light...

C2PU-Team, Observatoire de Nice Light takes its time ! NOT TO SCALE ! Moving object (asteroid, comet) Real position at time T0 Photon sent at time T0 T = T0 Earth 16/09/2018 C2PU-Team, Observatoire de Nice

C2PU-Team, Observatoire de Nice Light takes its time ! NOT TO SCALE ! Apparent position at time T0 + distance / c0 Real position at time T0 + distance / c0 Photon received at time T0 + distance / c0 T = T0 + distance / c0 16/09/2018 C2PU-Team, Observatoire de Nice

Earth’s velocity changes light’s direction Rain falls tilted on a running man... Photons falls tilted on a running planet... apparent position real position Bradley effect 16/09/2018 C2PU-Team, Observatoire de Nice

Light doesn’t go straight ! NOT TO SCALE ! Altitude-dependent atmospheric refraction index bends the light rays ! zero at zenith, max. near the horizon affects both H and  Zenith local horizon Earth’s atmosphere This is “atmospheric refraction”.  Star’s apparent position Actual light path Star’s actual position 16/09/2018 C2PU-Team, Observatoire de Nice

Light doesn’t go straight ! NOT TO SCALE ! Atmospheric refraction depends on: star elevation atmospheric pressure temperature relative humidity air composition wavelength  Zenith local horizon Earth’s atmosphere Star’s apparent position Actual light path Star’s actual position 16/09/2018 C2PU-Team, Observatoire de Nice

C2PU-Team, Observatoire de Nice What is “airmass” NOT TO SCALE ! Star at zenith Airmass = 1.0 Airmass = e / e0 = function of elevation h (relative thickness of atmosphere trough which a star is seen) local horizon e0  10 km Earth’s atmosphere Airmass   turbulence and absorption  e >> 10 km Rule of thumb: Avoid airmass > 2 Star close to the horizon Airmass > 1.0 16/09/2018 C2PU-Team, Observatoire de Nice

Conclusion Light propagation is complex !!! Must be taken into account to find an astronomical object in the sky ! 16/09/2018 C2PU-Team, Observatoire de Nice

Space coordinates

C2PU-Team, Observatoire de Nice Coordinate systems Polar (spherical) coordinates: (r, , ) Polar axis r  Origin A reference system = Origin point Fundamental plane (or polar axis) Zero direction  Fundamental plane A reference frame = Reference system Definition of time direction Zero 16/09/2018 C2PU-Team, Observatoire de Nice

Angular units, angular formats Degrees: 1 turn = 360° Decimal format. example: 41.234° (French style: 41,234°) Sexagesimal format. example: 41° 14’ 02.4’’ (Sumerian/Babylonian legacy) Radians: 1 turn = 2 rad (mostly used in mathematics and computation) Decimal format. example: 1.612 rad (French style: 1,612 rad) Gradians: 1 turn = 400 gon(*) (only used in topography) Decimal format. example: 53.256 gon (French style: 53,256 gon) Hours: 1 turn = 24 hrs (mostly used in astronomy) Decimal format. example: 5.0336 h (French style: 5,0336 h) Sexagesimal format. example: 5h 02m 01s (Sumerian/Babylonian legacy) * from the Greek “”: angle 16/09/2018 C2PU-Team, Observatoire de Nice

A fancy angular unit : the “hour” Format for angles expressed in hours, minutes and seconds: 5h 02m 01s in degrees, minutes and seconds: 75° 30’ 15’’ Phonetic disambiguation: Say “fifteen arc-seconds” (quinze seconds d’arc) for 15’’ or “thirty arc-minutes” (trente minutes d’arc) for 30’ Say “one time-second” (une seconde d’heure) for 01s or “two time-minutes” (deux minutes d’heure) for 02m 1 turn = 360o = 24 hours 1 24 turn = 15o = 1 hour ¼ turn = 90o = 6 hours ½ turn = 180o = 12 hours ¾ turn = 270o = 18 hours 16/09/2018 C2PU-Team, Observatoire de Nice

C2PU-Team, Observatoire de Nice Ecliptic coordinates Origin: Sun center (heliocentric) or Solar System barycenter (barycentric) or other . Fundamental plane: Ecliptic plane Polar axis: Ecliptic North Zero direction:  vernal direction le : ecliptic longitude (in degrees) e: ecliptic latitude (in degrees) r : heliocentric or barycentric distance Ecliptic North r e Sun le several variants depending on which direction is chosen… J2000 coordinates EOD coordinates Ecliptic plane vernal direction  16/09/2018 C2PU-Team, Observatoire de Nice

Equatorial coordinates Origin: Earth center (geocentric) or observatory position (topocentric) or other . Fundamental plane: Equatorial plane Polar axis: Geographic North pole Zero direction:  vernal direction  : right ascension (in hours !)  : declination (in degrees) r : geocentric or topocentric distance North pole r  Sun  several variants depending on which  and polar directions are chosen… J2000 coordinates EOD coordinates Equatorial plane vernal direction  16/09/2018 C2PU-Team, Observatoire de Nice

C2PU-Team, Observatoire de Nice Mount coordinates Origin: observatory position (topocentric). Fundamental plane: Equatorial plane Polar axis: Geographic North pole Zero direction: Local meridian H : hour angle (in hours !)  : declination (in degrees) r : topocentric distance North pole r  Sun H These are the natural coordinates for a telescope equatorial mount, delivered by its angular encoders !!! Equatorial plane local meridian Beware ! H angle defined from star meridian to local meridian ! 16/09/2018 C2PU-Team, Observatoire de Nice

Equatorial vs Mount coordinates North pole Star Earth’s rotation Ts : True Local Sidereal “Time” = the angle of rotation of the Earth  : Right ascension of the star H : Hour angle of the star Obs. H = Ts -  Equatorial plane  H Star’s meridian direction (fixed, more or less) Ts  vernal direction (fixed, more or less) Local meridian direction (rotates with the Earth)

Equatorial vs Mount coordinates Star Earth’s rotation Local meridian plane (rotates withe the Earth) H H = Ts -   Ts Obs. North pole  vernal direction (fixed, more or less) Ts : True Local Sidereal “Time” = the angle of rotation of the Earth  : Right ascension of the star H : Hour angle of the star 16/09/2018 C2PU-Team, Observatoire de Nice

Equatorial vs Mount coordinates H(t) = Ts(t) -  Constant (more or less) Thus, time-dependent (stars rise and set) Time-dependent (rotation of the Earth) Ts : True Local Sidereal “Time” = the angle of rotation of the Earth Approximately linear with time: 1 turn in 23h 56m 04.09s (sidereal day) 16/09/2018 C2PU-Team, Observatoire de Nice

Horizontal coordinates Origin: observatory (topocentric). Fundamental plane: Equatorial plane Polar axis: Geographic North pole Zero direction: Local meridian a : azimuth (in degrees) h : elevation (in degrees) r : topocentric distance Zenith r South h Sun East West Convention: North: a = 0° East: a = 90° South: a = 180° West: a = 270° a Horizontal plane Horizontal North Beware ! a angle defined from star vertical plane to local North ! 16/09/2018 C2PU-Team, Observatoire de Nice

What is a “good” reference system ? Fundamental plane must be steady w.r.t. distant celestial objects (quasars) Zero direction must be steady w.r.t. distant celestial objects (quasars) Origin must have constant velocity w.r.t. distant celestial objects (quasars) EXAMPLE: the “J2000” coordinates Fundamental plane: mean (nutation corrected) equator at J2000* Zero direction: mean (nutation corrected) vernal direction at J2000* Origin: barycenter of Solar System An improved version thereof (ICRS system) is used in astronomical catalogs and planets ephemeris computation softwares/servers. (*) J2000 = 01/01/2000 12:00 UTC 16/09/2018 C2PU-Team, Observatoire de Nice

What is a “handy” reference system ? Must be directly connected to your telescope EXAMPLE: The topocentric mount coordinates Fundamental plane: true Earth’s equator Zero direction: meridian (south) direction Origin: your observatory The two angles in this reference system are those given by the telescope’s angular encoders 16/09/2018 C2PU-Team, Observatoire de Nice

And the winner is : BOTH ! Catalogs or ephemeris servers give target’s J2000 coordinates (actually, ICRS coordinates) at a reference date Your telescope needs mount coordinates conversions are needed between ICRS coordinates and mount coordinates .... 16/09/2018 C2PU-Team, Observatoire de Nice

Conversion flowchart Get ICRS coordinates at reference date (J2000) Correct for target’s proper motion (compute ICRS coordinates at observation date) Subtract delay from observation date Change from ICRS to mount coordinates (correct for precession, nutation, parallax, Earth’s rotation) Compute target-telescope distance and the associated delay “distance/C0” Correct for Bradley effect Correct for atmospheric refraction Send to telescope 16/09/2018 C2PU-Team, Observatoire de Nice

Do we need to care ? NO ! our software does it for you ! 16/09/2018 C2PU-Team, Observatoire de Nice

Time coordinates

C2PU-Team, Observatoire de Nice What time is it ? Several ways to DEFINE the current date/time (time scales) True local solar time Mean local solar time Greenwich Mean (solar) Time (GMT  UT0, UT1) Legal Time (LT) Atomic International Time (AIT) Universal Time Coordinate (UTC) Ephemeris Time (ET) Terrestrial Time (TT) Terrestrial Dynamic Time (TDT) Barycentric Dynamic Time (BDT) GPS time LORAN time … LT = UTC + 1 hour ( + 1 hour) Time zone DST summer time 16/09/2018 C2PU-Team, Observatoire de Nice

C2PU-Team, Observatoire de Nice What time is it ? Several ways to WRITE the current date/time (time formats) Common date-time formats Julian date (JD) Modified Julian Date (MJD) … Common date-time formats: French formats : example: 14/01/2014 12h 21m 12,2s (TL or UTC) variants: 14-01-2014 12:21:12,2 (TL or UTC) 2014-01-14 12:21:12,2 (TL or UTC) 14 janv. 2014 12:21:12,2 (TL or UTC) British formats : example: 01/14/2014 12h 21m 12,2s (LT or UTC) variants: 2014-01-14 12:21:12,2 (LT or UTC) Jan. 14th, 2014 12:21:12,2 (LT or UTC) 16/09/2018 C2PU-Team, Observatoire de Nice

C2PU-Team, Observatoire de Nice What time is it ? Julian date (JD): Avoid ambiguities in date formats (DD/MM/AAAA vs MM/DD/AAAA) Ease calculations of time intervals Bypass the “October 1582” problem (Julian vs Gregorian calendars). Uses a single positive number to state both date and time with arbitrary accuracy Julian date = “number of days elapsed since January 1st, 4713 BC, 12h00” Example: January 1st, 2000 @ 12h00 UTC corresponds to JD = 2451545.0000 d Example: August 2nd, 2013 @ 16h 41m 49.0s UTC corresponds to JD = 2456507.19571 d Modified Julian Date (MJD): Avoids too large numbers By definition: MJD = JD – 2450000.5 d Example: August 2nd, 2013 @ 16h 41m 49.0s UTC corresponds to MJD = 6506.69571 d 16/09/2018 C2PU-Team, Observatoire de Nice

Do we need to care ? NO ! our software does it for you ! 16/09/2018 C2PU-Team, Observatoire de Nice

Magnitudes

C2PU-Team, Observatoire de Nice Star brightness Ancient Greek astronomers (Hipparchus, Ptolemy) used to divide all naked-eyes visible stars in 6 brightness categories called “Magnitudes”. This scale was reversed: Magnitude 1 corresponded to the brightest stars; Magnitude 6 corresponded to the faintest stars visible with naked eyes. This scale was logarithmic: stars of magnitude “n” were “seen” twice as bright as stars of magnitude “n+1”. In 1856, Norman Robert Pogson proposed a quantitative relationship: M = -2.5 Log10( I / I0 ) where I is the brightness of the star under consideration, and I0 is the brightness of a reference star (Vega), considered as a 0 magnitude star. Magnitudes may be negative. 16/09/2018 C2PU-Team, Observatoire de Nice

C2PU-Team, Observatoire de Nice Color-dependence Stars have different surface temperatures, thus different “colors”. Hence, the brightness of a star depends on the observation wavelength Several “Photometric systems” exist, each one defining a set of wavelength bands (filters) through which observations are done. Some standard bands: U, B, V, R, I (Ultraviolet, Blue, Visible, Red, Infrared). Magnitude measured through V band filter is called “V magnitude” and denoted “MV”. The same holds for U, B, R, and I. If the whole spectrum is taken into account, the magnitude is said “bolometric”. 16/09/2018 C2PU-Team, Observatoire de Nice

Magnitudes of brightest stars Name V Magnitude Sirius -1.46 Canopus -0.72 Rigil Kentaurus -0.27 Arcturus -0.04 Vega 0.00 Capella 0.08 Rigel 0.12 Procyon 0.34 Betelgeuse 0.42 Name V Magnitude Achernar 0.50 Adar 0.60 Altair 0.77 Aldebaran 0.85 Spica 1.04 Antares 1.09 Pollux 1.15 Fomalhaut 1.16 Deneb 1.25 16/09/2018 C2PU-Team, Observatoire de Nice

C2PU-Team, Observatoire de Nice For more informations Lecture notes on general astronomy: https://www-n.oca.eu/rivet/00Francais/IntroAstro.html 16/09/2018 C2PU-Team, Observatoire de Nice