BASICS FOR BASICS FOR
ASTRONOMICALASTRONOMICAL
OBSERVATIONSOBSERVATIONS
© C2PU, Observatoire de la Cote d’Azur,
Université de Nice Sophia-Antipolis
Jean-Pierre RivetCNRS, OCA,Dept. [email protected]
Where is my target ?
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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.
Where is my target ?
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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 directionof incoming light rays.
Atmospheric effects: Earth’s atmosphere perturbs the direction andintensity of light rays.
Earth’s motionsand reference
planes/directions
Coordinate systems
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Reference plane
Pol
ar a
xis
OriginZ
ero
dire
ctio
n
rPolar (spherical) coordinates:
(r, , )
PROBLEM:finding “good” referenceplane and zero direction.
The motions of the Earth (I):orbital motion
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Ecliptic plane
Earth orbit
Sun
Earth
NOT TO SCALE !
The motions of the Earth (I):orbital motion
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Orbit ellipsis
Sun = Focus
Earth
NOT TO SCALE !
a(a = semi-major axis)
a = 149.6 106 kme = 0.0167P = 1 “year”
a.e(e = eccentricity)
AphelionPerihelion … but what is a “year” ?depends the referencedirection chosen to start/stopthe chronometer !•anomalistic year (365.25964 d)•sidereal year (365.25637 d)•tropical year (365.24219 d)•draconic year (346.62008 d)•…
Center
The motions of the Earth (I):orbital motion
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Orbit ellipsis
Sun = Focus
Earth
NOT TO SCALE !
a(a = semi-major axis)
a = 149.6 106 kme = 0.0167P = 1 “year”
a.e(e = eccentricity)
AphelionPerihelion … but what is a “year” ?depends the referencedirection chosen to start/stopthe 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 …
The motions of the Earth (II):secular motions
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NOT TO SCALE !
AphelionPerihelion
Earth’s orbit now
The motions of the Earth (II):secular motions
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NOT TO SCALE !
Aphelion
Perihelion
Earth’s orbit in 3000 years
The motions of the Earth (II):secular motions
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NOT TO SCALE !
Aphelion
Perihelion
Earth’s orbit in 6000 years
The motions of the Earth (II):secular motions
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NOT TO SCALE !
Perihelion slowly shifts
Aphelion
Perihelion Parameters a and e slowly change
… because Earth and Sunare not alone in the Solar System !
Earth’s orbit in 9000 years
The motions of the Earth (III):proper motion
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Ecliptic plane
Equatorial plane
North equatorial pole
: Obliquity 23° 27’
P = 1 “day”
… but what is a “day” ?depends the referencedirection chosen to start/stopthe chronometer !•mean solar day (24 h)•sidereal day (23h 56m 04.09s)
North ecliptic pole
The motions of the Earth (III):proper motion
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Ecliptic plane
Earth orbit
Sun
NOT TO SCALE !
Equ
ator
ial p
lane
Equ
ator
ial p
lane
Wintersolstice
Summersolstice
Springequinox
vernal direction
Equ
ator
ial p
lane
vernal direction
vernal direction
Reference directions and planes
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Ecliptic plane
Equ
ator
ial p
lane
vernal direction
EclipticNorthpole
EarthNorthpole
Orbital and proper motionsof the Earth provide for2 reference planes and 2 polar directions
Reference directions and planes
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Ecliptic plane
Equ
ator
ial p
lane
vernal direction
EclipticNorthpole
EarthNorthpole
Orbital and proper motionsof the Earth provide for2 reference planes and 2 polar directions
… but in real life, things are a bit more complicated …
The motions of the Earth (IV):precession
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Ecliptic plane
Equ
ator
ial p
lane
Jan. 2000
EclipticNorthpole
EarthNorthpole
P 26 000 years
The motions of the Earth (IV):precession
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Ecliptic plane
Equ
ator
ial p
lane
Jan. 2010
EclipticNorthpole
EarthNorthpole
P 26 000 years
The motions of the Earth (IV):precession
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Ecliptic plane
Equ
ator
ial p
lane
Jan. 2020
EclipticNorthpole
EarthNorthpole
P 26 000 years
The motions of the Earth (IV):nutation
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Ecliptic plane
Equ
ator
ial p
lane
EclipticNorthpole
EarthNorthpole
P 18.6 years
The motions of the Earth (V):nutation
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Ecliptic plane
Equ
ator
ial p
lane
EclipticNorthpole
EarthNorthpole
P 18.6 years
The motions of the Earth (V):precession-nutation
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Eclipticpole Mean pole @ J2000
Mean pole @ date
True pole@ date Precession
(P 26 000 years) Nutation(P 18.6 years)
... becausethe Earth has no spherical symmetrythe Moon creates a torque onEarth’s equatorial bulge
Precession-nutation: slow motions of the rotation (polar) axis of the Earthw.r.t. an external (astronomical) reference frame (fixed stars of quasars)
Conclusion
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Earth’s motion is complex !!!
Must be taken into accountto define reliable reference systems andto find an astronomical object in the sky !
About light...
Light takes its time !
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NOT TO SCALE !
T = T0
Real position
at time T0
Moving object(asteroid, comet)
Earth
Photon sent
at time T0
Light takes its time !
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NOT TO SCALE !
T = T0 + distance / c0
Apparent position at
time T0 + distance / c0
Real position at
time T0 + distance / c0
Photon received at
time T0 + distance / c0
Earth’s velocity changes light’s direction
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Rain falls tilted on a running man... Photons falls tilted on a running planet...
Bradley effect
apparentposition
realposition
Light doesn’t go straight !
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Earth’s atmosphere
NOT TO SCALE !
Zeni
th
Star’sactual position
local horizon
Actual light path
Star’sapparent 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”.
Light doesn’t go straight !
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Earth’s atmosphere
NOT TO SCALE !
Zeni
th
Star’sactual position
local horizon
Actual light path
Star’sapparent position
Atmospheric refraction depends on:-star elevation-atmospheric pressure-temperature-relative humidity-air composition-wavelength
What is “airmass”
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e 0
10
km
Earth’s atmosphere
NOT TO SCALE !
e >> 10 km
Star at zenithAirmass = 1.0
Star closeto the horizonAirmass > 1.0
Airmass = e / e0 = function of elevation h(relative thickness of atmospheretrough which a star is seen)
local horizon
Rule of thumb:Avoid airmass > 2
Airmass turbulence and absorption
Conclusion
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Light propagation is complex !!!
Must be taken into accountto find an astronomical object in the sky !
Space coordinates
Coordinate systems
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Fundamental plane
Pol
ar a
xis
Origin
Zer
odi
rect
ion
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
Angular units, angular formats
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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
A fancy angular unit :the “hour”
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1 turn = 360o = 24 hours
¼ turn = 90o = 6 hours
½ turn = 180o = 12 hours
¾ turn = 270o = 18 hours
1 24 turn = 15o = 1 hour
Format for angles expressedin hours, minutes and seconds:5h 02m 01s
Format for angles expressedin 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
Ecliptic coordinates
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Ecliptic plane
Ecl
iptic
Nor
th
Sun
ve
rnal
dire
ctio
n
le
e
• Origin: Sun center (heliocentric) orSolar 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
several variants depending on whichdirection is chosen…J2000 coordinatesEOD coordinates
r
Equatorial coordinates
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Equatorial plane
Nor
th p
ole
Sun
ve
rnal
dire
ctio
n
• Origin: Earth center (geocentric) orobservatory 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 coordinatesEOD coordinates
r
Mount coordinates
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Equatorial plane
Nor
th p
ole
Sun
loca
l mer
idia
n
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 coordinatesfor a telescope equatorial mount,delivered by its angular encoders !!!
r
Beware !H angle defined from star meridian to local meridian !
Equatorial vs Mount coordinates
39
Local meridian direction
(rotates with the Earth)
Earth’s rotationTs : True Local Sidereal “Time” = the angle of rotation of the Earth : Right ascension of the starH : Hour angle of the star
H = Ts -
North pole
Obs.
ver
nal d
irecti
on
(fixed
, more
or le
ss)
Star
Star’s meridian direction (fixed, more or less)
Ts
H
Equatorialplane
Equatorial vs Mount coordinates
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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 starH : Hour angle of the star
H = Ts -
Star
Equatorial vs Mount coordinates
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Ts : True Local Sidereal “Time” = the angle of rotation of the EarthApproximately 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)
Horizontal coordinates
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Horizontal plane
Zen
ith
Sun
Hor
izon
tal N
orth
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
Sou
th
Convention:North: a = 0°East: a = 90°South: a = 180°West: a = 270°
Beware !a angle defined from star vertical plane to local North !
What is a “good” reference system ?
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• 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 catalogsand planets ephemeris computation softwares/servers.
What is a “handy” reference system ?
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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 arethose given by the telescope’s angular encoders
And the winner is :
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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 coordinatesand mount coordinates ....
Conversion flowchart
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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/C0”
Subtract delay
from observation
date
Correct for atmospheric refraction
Send to telescope
Do we need to care ?
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NO !
our software does it for you !
Time coordinates
What time is it ?
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• 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
What time is it ?
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• 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)
What time is it ?
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• 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
Do we need to care ?
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NO !
our software does it for you !
Magnitudes
Star brightness
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• Ancient Greek astronomers (Hipparchus, Ptolemy) used to divideall 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” twiceas 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 thebrightness of a reference star (Vega), considered as a 0 magnitude star.
• Magnitudes may be negative.
Color-dependence
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• 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 ofwavelength 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”.
Magnitudes of brightest stars
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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
For more informations
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https://www-n.oca.eu/rivet/00Francais/IntroAstro.html
Lecture notes on general astronomy: