1. BASICS FOR ASTRONOMICAL OBSERVATIONS © C2PU, Observatoire de la Cote d’Azur, Université de Nice Sophia-Antipolis Jean-Pierre Rivet CNRS, OCA, Dept. Lagrange jean-pierre.rivet@oca.eu

2. Where is my target ? 28/08/2015C2PU-Team, Observatoire de Nice2 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.

3. Where is my target ? 28/08/2015C2PU-Team, Observatoire de Nice3 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 ! 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.

4. Earth’s motions and reference planes/directions

5. Coordinate systems 28/08/2015C2PU-Team, Observatoire de Nice5 Reference plane Polar axis Origin Zero direction   r Polar (spherical) coordinates: (r, ,  ) PROBLEM: finding “good” reference plane and zero direction.

6. The motions of the Earth (I): orbital motion 28/08/2015C2PU-Team, Observatoire de Nice6 Ecliptic plane Earth orbit Sun Earth NOT TO SCALE !

7. The motions of the Earth (I): orbital motion 28/08/2015C2PU-Team, Observatoire de Nice7 Orbit  ellipsis Sun = Focus Earth NOT TO SCALE ! a (a = semi-major axis) a = 149.6 10 6 km e = 0.0167 P = 1 “year” a.e (e = eccentricity) Aphelion Perihelion … 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) … Center

8. The motions of the Earth (I): orbital motion 28/08/2015C2PU-Team, Observatoire de Nice8 Orbit  ellipsis Sun = Focus Earth NOT TO SCALE ! a (a = semi-major axis) a = 149.6 10 6 km e = 0.0167 P = 1 “year” a.e (e = eccentricity) Aphelion Perihelion … 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) … Center … but in real life, things are a bit more complicated …

9. The motions of the Earth (II): secular motions 28/08/2015C2PU-Team, Observatoire de Nice9 NOT TO SCALE ! Aphelion Perihelion Earth’s orbit now

10. The motions of the Earth (II): secular motions 28/08/2015C2PU-Team, Observatoire de Nice10 NOT TO SCALE ! Aphelion Perihelion Earth’s orbit in 3000 years

11. The motions of the Earth (II): secular motions 28/08/2015C2PU-Team, Observatoire de Nice11 NOT TO SCALE ! Aphelion Perihelion Earth’s orbit in 6000 years

12. The motions of the Earth (II): secular motions 28/08/2015C2PU-Team, Observatoire de Nice12 NOT TO SCALE ! Perihelion slowly shifts Aphelion Perihelion Parameters a and e slowly change … because Earth and Sun are not alone in the Solar System ! Earth’s orbit in 9000 years

13. The motions of the Earth (III): proper motion 28/08/2015C2PU-Team, Observatoire de Nice13 Ecliptic plane Equatorial plane North equatorial pole  : Obliquity  23° 27’ P = 1 “day” … 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) North ecliptic pole

14. The motions of the Earth (III): proper motion 28/08/2015C2PU-Team, Observatoire de Nice14 Ecliptic plane Earth orbit Sun NOT TO SCALE ! Equatorial plane Winter solstice Summer solstice Spring equinox  vernal direction Equatorial plane   vernal direction  vernal direction

15. Reference directions and planes 28/08/2015C2PU-Team, Observatoire de Nice 15 Ecliptic plane Equatorial plane  vernal direction  Ecliptic North pole Earth North pole Orbital and proper motions of the Earth provide for 2 reference planes and 2 polar directions

16. Reference directions and planes 28/08/2015C2PU-Team, Observatoire de Nice 16 Ecliptic plane Equatorial plane  vernal direction  Ecliptic North pole Earth North pole Orbital and proper motions of the Earth provide for 2 reference planes and 2 polar directions … but in real life, things are a bit more complicated …

17. The motions of the Earth (IV): precession 28/08/2015C2PU-Team, Observatoire de Nice 17 Ecliptic plane Equatorial plane  Jan. 2000  Ecliptic North pole Earth North pole P  26 000 years

18. The motions of the Earth (IV): precession 28/08/2015C2PU-Team, Observatoire de Nice 18 Ecliptic plane Equatorial plane  Jan. 2010 Ecliptic North pole Earth North pole P  26 000 years

19. The motions of the Earth (IV): precession 28/08/2015C2PU-Team, Observatoire de Nice 19 Ecliptic plane Equatorial plane  Jan. 2020 Ecliptic North pole Earth North pole P  26 000 years

20. The motions of the Earth (IV): nutation 28/08/2015C2PU-Team, Observatoire de Nice 20 Ecliptic plane Equatorial plane   Ecliptic North pole Earth North pole P  18.6 years

21. The motions of the Earth (V): nutation 28/08/2015C2PU-Team, Observatoire de Nice 21 Ecliptic plane Equatorial plane  Ecliptic North pole Earth North pole P  18.6 years

22. The motions of the Earth (V): precession-nutation 28/08/2015C2PU-Team, Observatoire de Nice 22 Ecliptic pole Mean pole @ J2000 Mean pole @ date True pole @ date Precession (P  26 000 years) Nutation (P  18.6 years)... because the Earth has no spherical symmetry the Moon creates a torque on Earth’s equatorial bulge Precession-nutation: slow motions of the rotation (polar) axis of the Earth w.r.t. an external (astronomical) reference frame (fixed stars of quasars)

23. Conclusion 28/08/2015C2PU-Team, Observatoire de Nice 23 Earth’s motion is complex !!! Must be taken into account to define reliable reference systems and to find an astronomical object in the sky !

24. About light...

25. Light takes its time ! 28/08/2015C2PU-Team, Observatoire de Nice25 NOT TO SCALE ! T = T 0 Real position at time T 0 Moving object (asteroid, comet) Earth Photon sent at time T 0

26. Light takes its time ! 28/08/2015C2PU-Team, Observatoire de Nice26 NOT TO SCALE ! T = T 0 + distance / c 0 Apparent position at time T 0 + distance / c 0 Real position at time T 0 + distance / c 0 Photon received at time T 0 + distance / c 0

27. Earth’s velocity changes light’s direction 28/08/2015C2PU-Team, Observatoire de Nice27 Rain falls tilted on a running man... Photons falls tilted on a running planet... Bradley effect apparent position real position

28. Light doesn’t go straight ! 28/08/2015C2PU-Team, Observatoire de Nice28 Earth’s atmosphere NOT TO SCALE ! Zenith Star’s actual position local horizon Actual light path Star’s apparent position Altitude-dependent atmospheric refraction index bends the light rays ! zero at zenith, max. near the horizon affects both H and  This is “atmospheric refraction”.

29. Light doesn’t go straight ! 28/08/2015C2PU-Team, Observatoire de Nice29 Earth’s atmosphere NOT TO SCALE ! Zenith Star’s actual position local horizon Actual light path Star’s apparent position Atmospheric refraction depends on: -star elevation -atmospheric pressure -temperature -relative humidity -air composition -wavelength

30. What is “airmass” 28/08/2015C2PU-Team, Observatoire de Nice30 e 0  10 km Earth’s atmosphere NOT TO SCALE ! e >> 10 km Star at zenith Airmass = 1.0 Star close to the horizon Airmass > 1.0 Airmass = e / e 0 = function of elevation h (relative thickness of atmosphere trough which a star is seen) local horizon Rule of thumb: Avoid airmass > 2 Airmass   turbulence and absorption 

31. Conclusion 28/08/2015C2PU-Team, Observatoire de Nice 31 Light propagation is complex !!! Must be taken into account to find an astronomical object in the sky !

32. Space coordinates

33. Coordinate systems 28/08/2015C2PU-Team, Observatoire de Nice33 Fundamental plane Polar axis Origin Zero direction   r Polar (spherical) coordinates: (r, ,  ) A reference system = -Origin point -Fundamental plane (or polar axis) -Zero direction A reference frame = -Reference system -Definition of time

34. Angular units, angular formats 28/08/2015C2PU-Team, Observatoire de Nice34 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: 5 h 02 m 01 s (Sumerian/Babylonian legacy) * from the Greek “  ”: angle

35. A fancy angular unit : the “hour” 28/08/2015C2PU-Team, Observatoire de Nice35 1 turn = 360 o = 24 hours ¼ turn = 90 o = 6 hours ½ turn = 180 o = 12 hours ¾ turn = 270 o = 18 hours 1 24 turn = 15 o = 1 hour Format for angles expressed in hours, minutes and seconds: 5 h 02 m 01 s Format for angles expressed 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 01 s or “two time-minutes” (deux minutes d’heure) for 02 m

36. Ecliptic coordinates 28/08/2015C2PU-Team, Observatoire de Nice36 Ecliptic plane Ecliptic North Sun  vernal direction lele e Origin: Sun center (heliocentric) or Solar System barycenter (barycentric) or other. Fundamental plane: Ecliptic plane Polar axis: Ecliptic North Zero direction:  vernal direction l e : ecliptic longitude (in degrees) e : ecliptic latitude (in degrees) r : heliocentric or barycentric distance several variants depending on which  direction is chosen… J2000 coordinates EOD coordinates r

37. Equatorial coordinates 28/08/2015C2PU-Team, Observatoire de Nice37 Equatorial plane North pole Sun  vernal direction   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 several variants depending on which  and polar directions are chosen… J2000 coordinates EOD coordinates r

38. Mount coordinates 28/08/2015C2PU-Team, Observatoire de Nice38 Equatorial plane North pole Sun local meridian H  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 These are the natural coordinates for a telescope equatorial mount, delivered by its angular encoders !!! r Beware ! H angle defined from star meridian to local meridian !

39. Equatorial vs Mount coordinates 39 Local meridian direction (rotates with the Earth) 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 H = Ts -  North pole Obs.  vernal direction (fixed, more or less) Star Star’s meridian direction (fixed, more or less)  Ts H Equatorial plane

40. Equatorial vs Mount coordinates 28/08/2015C2PU-Team, Observatoire de Nice40 North pole  vernal direction (fixed, more or less) Obs. Local meridian plane (rotates withe the Earth)  Ts H 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 H = Ts -  Star

41. Equatorial vs Mount coordinates 28/08/2015C2PU-Team, Observatoire de Nice41 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) H (t) = Ts (t) -  Time-dependent (rotation of the Earth) Constant (more or less) Thus, time-dependent (stars rise and set)

42. Horizontal coordinates 28/08/2015C2PU-Team, Observatoire de Nice42 Horizontal plane Zenith Sun Horizontal North a h 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 r East West South Convention: North: a = 0° East:a = 90° South:a = 180° West:a = 270° Beware ! a angle defined from star vertical plane to local North !

43. What is a “good” reference system ? 28/08/2015C2PU-Team, Observatoire de Nice43 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 (*) J2000 = 01/01/2000 12:00 UTC An improved version thereof (ICRS system) is used in astronomical catalogs and planets ephemeris computation softwares/servers.

44. What is a “handy” reference system ? 28/08/2015C2PU-Team, Observatoire de Nice44 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

45. And the winner is : 28/08/2015C2PU-Team, Observatoire de Nice45 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....

46. Conversion flowchart 28/08/2015C2PU-Team, Observatoire de Nice46 Get ICRS coordinates at reference date (J2000) Correct for target’s proper motion (compute ICRS coordinates at observation date) Change from ICRS to mount coordinates (correct for precession, nutation, parallax, Earth’s rotation) Correct for Bradley effect Compute target-telescope distance and the associated delay “distance/C 0 ” Subtract delay from observation date Correct for atmospheric refraction Send to telescope

47. Do we need to care ? 28/08/2015C2PU-Team, Observatoire de Nice47 NO ! our software does it for you !

48. Time coordinates

49. What time is it ? 28/08/2015C2PU-Team, Observatoire de Nice49 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

50. What time is it ? 28/08/2015C2PU-Team, Observatoire de Nice50 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 12 h 21 m 12,2 s (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 12 h 21 m 12,2 s (LT or UTC) variants: 2014-01-14 12:21:12,2 (LT or UTC) Jan. 14 th, 2014 12:21:12,2 (LT or UTC)

51. What time is it ? 28/08/2015C2PU-Team, Observatoire de Nice51 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 1 st, 4713 BC, 12h00” Example: January 1 st, 2000 @ 12h00 UTC corresponds to JD = 2451545.0000 d Example: August 2 nd, 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 2 nd, 2013 @ 16h 41m 49.0s UTC corresponds to MJD = 6506.69571 d

52. Do we need to care ? 28/08/2015C2PU-Team, Observatoire de Nice52 NO ! our software does it for you !

53. Magnitudes

54. Star brightness 28/08/2015C2PU-Team, Observatoire de Nice54 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 Log 10 ( I / I 0 ) where I is the brightness of the star under consideration, and I 0 is the brightness of a reference star (Vega), considered as a 0 magnitude star. Magnitudes may be negative.

55. Color-dependence 28/08/2015C2PU-Team, Observatoire de Nice55 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 “M V ”. The same holds for U, B, R, and I. If the whole spectrum is taken into account, the magnitude is said “bolometric”.

56. Magnitudes of brightest stars 28/08/2015C2PU-Team, Observatoire de Nice56 NameV 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 NameV 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

57. For more informations 28/08/2015C2PU-Team, Observatoire de Nice57 https://www-n.oca.eu/rivet/00Francais/IntroAstro.html Lecture notes on general astronomy: