BASICS FOR ASTRONOMICAL OBSERVATIONS © C2PU, Observatoire de la Cote d’Azur, Université de Nice...

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 ?

21/04/23 C2PU-Team, Observatoire de Nice 2

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 ?


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


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


Ecliptic plane

Earth orbit

Sun

Earth

NOT TO SCALE !



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



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


NOT TO SCALE !

AphelionPerihelion

Earth’s orbit now



NOT TO SCALE !

Aphelion

Perihelion

Earth’s orbit in 3000 years



NOT TO SCALE !

Aphelion

Perihelion




NOT TO SCALE !

Perihelion slowly shifts

Aphelion

Perihelion Parameters a and e slowly change

… because Earth and Sunare not alone in the Solar System !


The motions of the Earth (III):proper motion


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


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


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


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


Ecliptic plane

Equ

ator

ial p

lane

Jan. 2000

EclipticNorthpole

EarthNorthpole

P 26 000 years



Ecliptic plane

Equ

ator

ial p

lane

Jan. 2010

EclipticNorthpole

EarthNorthpole

P 26 000 years



Ecliptic plane

Equ

ator

ial p

lane

Jan. 2020

EclipticNorthpole

EarthNorthpole

P 26 000 years

The motions of the Earth (IV):nutation


Ecliptic plane

Equ

ator

ial p

lane

EclipticNorthpole

EarthNorthpole

P 18.6 years

The motions of the Earth (V):nutation


Ecliptic plane

Equ

ator

ial p

lane

EclipticNorthpole

EarthNorthpole

P 18.6 years

The motions of the Earth (V):precession-nutation


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


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 !


NOT TO SCALE !

T = T0

Real position

at time T0

Moving object(asteroid, comet)

Earth

Photon sent

at time T0

Light takes its time !


NOT TO SCALE !

T = T0 + distance / c0

Apparent position at

time T0 + distance / c0

Real position at


Photon received at


Earth’s velocity changes light’s direction


Rain falls tilted on a running man... Photons falls tilted on a running planet...

Bradley effect

apparentposition

realposition

Light doesn’t go straight !


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 !



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”


e 0

10

km


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


Light propagation is complex !!!

Must be taken into accountto find an astronomical object in the sky !

Space coordinates

Coordinate systems


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


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”


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


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


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


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



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



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


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 ?


• 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 ?


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 :


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


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 ?


NO !

our software does it for you !

Time coordinates

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

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)

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

Do we need to care ?


NO !

our software does it for you !

Magnitudes

Star brightness


• 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


• 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


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


https://www-n.oca.eu/rivet/00Francais/IntroAstro.html

Lecture notes on general astronomy:

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