Transcript The motions of the Earth

BASICS FOR
ASTRONOMICAL
OBSERVATIONS
Jean-Pierre Rivet
CNRS, OCA,
Dept. Lagrange
[email protected]
© C2PU, Observatoire de la Cote d’Azur,
Université de Nice Sophia-Antipolis
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.
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Where is my target ?
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 !
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Earth’s motions
and reference planes/directions
Polar (spherical) coordinates:
(r, , )
Polar axis
Coordinate systems

Origin

PROBLEM:
finding “good” reference
plane and zero direction.
Reference plane
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The motions of the Earth (I):
orbital motion
NOT TO SCALE !
Ecliptic plane
Earth orbit
Earth
Sun
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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
a.e
(e = eccentricity)
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Aphelion
a
(a = semi-major axis)
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… 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)
…
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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
… but in
… but what is a “year” ?
real life, things are a bit more
complicated
depends
the reference…
direction chosen to start/stop
a.e
a
the chronometer !
(e = eccentricity) (a = semi-major axis)
Center
Aphelion
•
•
•
•
•
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anomalistic year (365.25964 d)
sidereal year (365.25637 d)
tropical year (365.24219 d)
draconic year (346.62008 d)
…
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The motions of the Earth (II):
secular motions
NOT TO SCALE !
Earth’s orbit now
Perihelion
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Aphelion
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The motions of the Earth (II):
secular motions
NOT TO SCALE !
Earth’s orbit in 3000 years
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The motions of the Earth (II):
secular motions
NOT TO SCALE !
Earth’s orbit in 6000 years
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The motions of the Earth (II):
secular motions
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 !
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The motions of the Earth (III):
proper motion
North ecliptic pole
North equatorial pole
 : Obliquity  23° 27’
Ecliptic plane
… but what is a “day” ?
depends the reference
direction chosen to start/stop
the chronometer !
P = 1 “day”
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• mean solar day (24 h)
• sidereal day (23h 56m 04.09s)
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The motions of the Earth (III):
proper motion
NOT TO SCALE !
Spring
equinox
Ecliptic plane
Summer
solstice

Sun

vernal direction
Winter
solstice
Earth orbit

vernal direction
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
vernal direction
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Reference directions and planes
Ecliptic
North
pole
Ecliptic plane

Earth
North
pole
Orbital and proper motions
of the Earth provide for
2 reference planes
and
2 polar directions

vernal direction
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Reference directions and planes
Ecliptic
North
pole
Ecliptic plane

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 …

vernal direction
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The motions of the Earth (IV):
precession
Ecliptic
North
pole
Ecliptic plane
Earth
North
pole
P  26 000 years


Jan. 2000
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The motions of the Earth (IV):
precession
Ecliptic
North
pole
Ecliptic plane
Earth
North
pole
P  26 000 years

Jan. 2010
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The motions of the Earth (IV):
precession
Ecliptic
North
pole
Ecliptic plane
Earth
North
pole

Jan. 2020
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P  26 000 years
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The motions of the Earth (IV):
nutation
Ecliptic
North
pole
Earth
North
pole
P  18.6 years
Ecliptic plane


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The motions of the Earth (V):
nutation
Ecliptic
North
pole
Earth
North
pole
P  18.6 years
Ecliptic plane

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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
Nutation
(P  18.6 years)
Precession
(P  26 000 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
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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 !
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About light...
Light takes its time !
NOT TO SCALE !
Moving object
(asteroid, comet)
Real position
at time T0
Photon sent
at time T0
T = T0
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Earth
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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
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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
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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 
This is “atmospheric refraction”.
Star’s
apparent
position
Star’s
actual
position
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Light doesn’t go straight !
NOT TO SCALE !
Atmospheric refraction depends on:
- star elevation
- atmospheric pressure
- temperature
- relative humidity
- air composition
- wavelength
Star’s
apparent
position
Star’s
actual
position
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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)
Airmass   turbulence and absorption 
Rule of thumb:
Avoid airmass > 2
Star close
to the horizon
Airmass > 1.0
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Conclusion
Light propagation is complex !!!
Must be taken into account
to find an astronomical object in the sky !
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Space coordinates
Coordinate systems
(r, , )
Polar axis
Polar (spherical) coordinates:

Origin

Fundamental plane
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A reference system =
- Origin point
- Fundamental plane (or polar axis)
- Zero direction
A reference frame =
- Reference system
- Definition of time
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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
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A fancy angular unit :
the “hour”
1 turn = 360o = 24 hours
1
24
turn = 15o = 1 hour
Format for angles expressed
in hours, minutes and seconds:
5h 02m 01s
Format for angles expressed
in degrees, minutes and seconds:
75° 30’ 15’’
¼ turn = 90o = 6 hours
½ turn = 180o = 12 hours
¾ turn = 270o = 18 hours
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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
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Ecliptic North
Ecliptic coordinates
e
Sun
• 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
le
Ecliptic plane
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several variants depending on which
 direction is chosen…
 J2000 coordinates
 EOD coordinates
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North pole
Equatorial coordinates

Sun
• 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

Equatorial plane
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several variants depending on which
 and polar directions are chosen…
 J2000 coordinates
 EOD coordinates
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North pole
Mount coordinates

Sun
• 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
H
Equatorial plane
These are the natural coordinates
for a telescope equatorial mount,
delivered by its angular encoders !!!
Beware !
H angle defined from star meridian to local meridian !
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Equatorial vs Mount
coordinates
North pole
Earth’s rotation
Obs.
Star
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 - 
Equatorial
plane

H
Ts
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Equatorial vs Mount
coordinates
Star
Earth’s rotation
H

Obs.
Ts
H = Ts - 
 vernal direction
(fixed, more or less)
North pole
Ts : True Local Sidereal “Time” =
the angle of rotation of the Earth
 : Right ascension of the star
H : Hour angle of the star
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Equatorial vs Mount
coordinates
H(t) = Ts(t) - 
Thus,
time-dependent
(stars rise and set)
Constant
(more or less)
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)
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Zenith
Horizontal coordinates
East
h
Sun
•
•
•
•
•
•
•
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
West
a
Horizontal plane
Convention:
North: a = 0°
East: a = 90°
South: a = 180°
West: a = 270°
Beware !
a angle defined from star vertical plane to local North !
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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
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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
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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 ....
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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)
Subtract delay
from observation
date
Compute target-telescope distance
and the associated delay “distance/C0”
Correct for Bradley effect
Correct for atmospheric refraction
Send to telescope
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Do we need to care ?
NO !
our software does it for you !
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Time coordinates
What time is it ?
• Several ways to DEFINE the current date/time (time scales)
•
•
•
•
•
•
•
•
•
•
•
•
•
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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)
LT = UTC
Ephemeris Time (ET)
Terrestrial Time (TT)
Terrestrial Dynamic Time (TDT)
Barycentric Dynamic Time (BDT)
GPS time
LORAN time
…
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+ 1 hour ( + 1 hour)
Time zone
DST
summer time
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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)
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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):
•
•
•
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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
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Do we need to care ?
NO !
our software does it for you !
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Magnitudes
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.
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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”.
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Magnitudes of brightest stars
Name
V Magnitude
Name
V Magnitude
Sirius
-1.46
Achernar
0.50
Canopus
-0.72
Adar
0.60
Rigil Kentaurus
-0.27
Altair
0.77
Arcturus
-0.04
Aldebaran
0.85
Vega
0.00
Spica
1.04
Capella
0.08
Antares
1.09
Rigel
0.12
Pollux
1.15
Procyon
0.34
Fomalhaut
1.16
Betelgeuse
0.42
Deneb
1.25
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For more informations
Lecture notes on general astronomy:
https://www-n.oca.eu/rivet/00Francais/IntroAstro.html
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