1. 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
© C2PU, Observatoire de la Cote d’Azur,
Université de Nice Sophia-Antipolis

2. 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

3. 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

4. Earth’s motions and reference planes/directions

5. 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

6. 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

7. The motions of the Earth (I): orbital motion
NOT TO SCALE !
Orbit  ellipsis
Earth
a = km
e =
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 ( d)
sidereal year ( d)
tropical year ( d)
draconic year ( d) …
a.e
(e = eccentricity) a
(a = semi-major axis)
16/09/2018
C2PU-Team, Observatoire de Nice

8. The motions of the Earth (I): orbital motion
NOT TO SCALE !
Orbit  ellipsis
Earth
a = km
e =
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 ( d)
sidereal year ( d)
tropical year ( d)
draconic year ( d) …
a.e
(e = eccentricity) a
(a = semi-major axis)
16/09/2018
C2PU-Team, Observatoire de Nice

9. 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

10. 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

11. 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

12. 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

13. 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

14. 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

15. 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

16. 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

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

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

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

20. 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

21. 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

22. 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  years)
Nutation
(P  18.6 years)
Mean date
Ecliptic
pole
Mean 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

23. 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

24. About light...

25. 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

26. 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

27. 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

28. 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

29. 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

30. 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

31. 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

32. Space coordinates

33. 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

34. Angular units, angular formats
Degrees: 1 turn = 360°
Decimal format. example: ° (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: rad (French style: 1,612 rad)
Gradians: 1 turn = 400 gon(*) (only used in topography)
Decimal format. example: gon (French style: 53,256 gon)
Hours: 1 turn = 24 hrs (mostly used in astronomy)
Decimal format. example: 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

35. 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

36. 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

37. 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

38. 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

39. 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)

40. 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

41. 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

42. 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

43. 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/ :00 UTC
16/09/2018
C2PU-Team, Observatoire de Nice

44. 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

45. 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

46. 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

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

48. Time coordinates

49. 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

50. 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/ h 21m 12,2s (TL or UTC)
variants: :21:12,2 (TL or UTC)
:21:12,2 (TL or UTC)
14 janv :21:12,2 (TL or UTC)
British formats : example: 01/14/ h 21m 12,2s (LT or UTC)
variants: :21:12,2 (LT or UTC)
Jan. 14th, :21:12,2 (LT or UTC)
16/09/2018
C2PU-Team, Observatoire de Nice

51. 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, 12h00 UTC corresponds to JD = d
Example: August 2nd, 16h 41m 49.0s UTC corresponds to JD = d
Modified Julian Date (MJD):
Avoids too large numbers
By definition: MJD = JD – d
Example: August 2nd, 16h 41m 49.0s UTC corresponds to MJD = d
16/09/2018
C2PU-Team, Observatoire de Nice

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

53. Magnitudes

54. 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

55. 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

56. 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

57. C2PU-Team, Observatoire de Nice
For more informations
Lecture notes on general astronomy:
16/09/2018
C2PU-Team, Observatoire de Nice