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AGA5802 Astrofísica Observacional
Astronomical coordinates and planning observations I
Bibliography: Any book (or chapter) on coordinates.
Some basic astrometry in slides from Prof. Roberto Boczko + myself (Elementos de Astronomia):
http://www.astro.iag.usp.br/~jorge/aga205_2011/
Prof. Jorge Meléndez 1
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Iguazu falls http://www.twanight.org
http://apod.nasa.gov/apod/ap100514.html
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Finding the South
-50 -55 -60 -65 -70 -75 -80 -85 -90
14h
15h
16h
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Finding the South
-50 -55 -60 -65 -70 -75 -80 -85 -90
14h
15h
16h
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Local coordinates
Linha do
Horizonte
Zenith
Nadir
Vert
ical
Slide adapted from Prof. Boczko
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Local Meridian
Zenith
N S
E
W
Nadir
Horizon
Is the semicircle
passing through
the points
zenith, N and S.
Slide adapted from Prof. Boczko
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Altazimutal System Azimuth (A): N E S O(W)
Fig. 3.2 from Astronomy Methods
Altitude (h):
-90o a +90o
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Altitude & zenith distance
Horizon
Zenith
Nadir
S
W
E h = altitude z = zenith distance
z
N h
Altitude is the angle between the local horizon and the object
Zenith distance is the angle between the object and the zenith
h + z = 90o
Slide adapted from Prof. Boczko
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l
j < 0
j
NP
SP
Greenwich
North
East
(S) -900 j +900 (N)
0 l +1800 (E, W) (W) -1800 l +1800 (E)
Longitude l
Geographic system
Latitude j
Slide adapted from Prof. Boczko
Sampa? 23.55° S 46.63° W
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How to find the Latitude
j
hPole
Slide adapted from Prof. Boczko
The altitude of the pole is the latitude of the observer
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La Silla/ESO (3,6m telescope) 29.2612° S, 70.7313° W on 2014/01/12 © J. Meléndez
j
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Equatorial
system NP
SP
g a
d
(a , d ) p
a = right ascension
d = declination
p = polar distance
p + d = 900 N
E
Slide adapted from Prof. Boczko
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Zero point
for R.A. :
intersection
of ecliptic &
equator
Polo
Celeste
Norte
Sun
Equatorial
system
g Vernal equinox
Obliquity of the ecliptic
23o 27' 08"
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Equatorial
coordinates
Fig. 3.1 from Astronomy Methods
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Units
1 hour 150
0h a < 24h
00 a < 3600
Right Ascension Declination
(S) -900 d +900 (N)
(N) 00 p +1800 (S)
Polar distance
Slide adapted from Prof. Boczko
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Example: equatorial coordinates for
the Sun
g
W
1
2
NP
PNE
a = 6h
d = +
a = 18h
d = -
4 a = 0h
d = 00
a = 12h
d = 00
3
a = 6h a = 18h
SP Slide adapted from Prof. Boczko
Zero point is the Vernal equinox, about March 21
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Horizontal & Equatorial system for
observer in the NH Z
NP
E
W
N S
Slide adapted from Prof. Boczko
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Provinha 2 4. Plot both horizontal + equatorial system for an
observer in São Paulo. Show the horizontal and
equatorial planes, the zenith, the cardinal points and the
position of the Celestial South Pole
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Local Meridian and Projection Z
SP
N S
E
W
Nadir
Horizon
Zenith
Nadir
Horizonte E W
SP
S N
Projection on the meridian plane
Slide adapted from Prof. Boczko
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Hour circle: the great circle passing
through the object and the celestial poles NP
SP
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Z
H d
( H , d )
H = hour angle
d = declination
p = polar distance
W
N S
E
p NP
SP
Observer in the
Northern H.
Slide adapted from Prof. Boczko
Hour angle H: the angle measured (on the
equator’s plane) from the local meridian to the object’s
hour circle
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Units
(E) -1800 H +1800 (W)
1 hour 150
(E) -12h H +12h (W)
(S) -900 d +900 (N)
00 p +1800
Hour angle Declination
1 h = 15° 1 m = 15' 1 s = 15"
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Provinha oral
3h 20m = 0 ‘ “? -300,5 = h m s ?
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Culmination or Meridian crossing
NP
Horizon
W
S
At lower meridian crossing: H = 180o
L
SP
Z At upper meridian crossing H = 0.
M
N
Slide adapted from Prof. Boczko
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Horizon
S
12
At lower
meridian
crossing
H = 12h
E
W
6
Z
0
At upper meridan crossing:
H = 0.
M
N
Example of hour angles
Ñ
1
2
3
4
5
11 10 9 8
7
SP
NP
Slide adapted from Prof. Boczko
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Sidereal time: the hour angle of g
g
ST Hg
Horizon
W
S ST
Z
NP
M
SP
N
Slide adapted from Prof. Boczko
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Sidereal day Z
SP
N
Interval for 2 succesive local meridian crossings
of g
Sidereal day 23h56m04s
E
W
Sidereal day 24h*00m*00s* * : sidereals
Sidereal
Midnight
Sidereal
Noon
Slide adapted from Prof. Boczko
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Measuring the right ascension
at meridian crossing
NP
d
g
a
ST = Hg ST = a + H
At upper meridian crossing: H = 0
Then:
a = STMer.crossing
Horizon
W
H S
M
Z
SP Slide adapted from Prof. Boczko
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Prof. Rama
Meridian
Circle at
Valinhos
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Do it yourself: star in London with hour angle H = 3h & declination d = 15o?
PN
d Horizon
W
H S
M
Z
PS Slide adapted from Prof. Boczko
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Do it yourself: star in London with H=3h, d=15o & a=1h30m, draw a
PN
d
g a
What is the sidereal time ST? Horizon
W
H S
M
Z
PS Slide adapted from Prof. Boczko
ST = 4h30m
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Do it yourself: draw Orion as seen from São Paulo
(23.5° S, 46.6° W) at the meridian passage
32
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-90
-80
-70
-60
-50
12
h
http://www.stellarium.org/
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The Sky at OPD observatory
2013/03/22 18h
R.A. of the Sun? What time is it?
Which date?
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Sky at OPD: altazimutal
2013/03/22 18h
+90
+80
+70 +60 +50
0
+40
+30
+20
+10
0
What are the coordinates
(A, h) of the Moon?
Where is the
celestial South Pole?
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Sky at OPD: altazimutal + equatorial
2013/03/22 18h
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Sky at OPD: equatorial
2013/03/22 18h
-20
-30
-40
-50 -60
-70
-80 -90
-10
0
6h
7h
8h
9h
10
h
11
h
12
h
1h
0h
Latitude = -22°30’
P.S.
Which are the coordinates (α, δ) of
the Sun & Moon ?
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-90
-80
-70
-60
-50
12
h
h (pole) = |latitude|
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Sky at OPD: equatorial
2013/03/22 19h
-20
-30
-40
-50 -60
-70
-80 -90
-10
0
6h
7h
8h
9h
10
h
11
h
12
h
1h
Latitude = -22°30’
P.S.
13
h
Which are the coordinates (α, δ) of
the Orion belt?
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Sky at OPD: equatorial
2013/03/22 20h
-20
-30
-40
-50 -60
-70
-80 -90
-10
0
6h
7h
8h
9h
10
h
11
h
12
h
Latitude = -22°30’
P.S.
13
h
What is the hour angle (H) of Sirius?
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Sky at OPD: equatorial
2013/03/22 22h
-20
-30
-40
-50 -60
-70
-80 -90
-10
0
6h
7h
8h
9h
10
h
11
h
12
h
Latitude = -22°30’
P.S.
14
h
13
h 15
h
At what time would be the meridian crossing of
the Southern Cross?
What is the R.A. and declination of Crux & a Cen?
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Sky at OPD: equatorial
2013/03/23 0h
-20
-30
-40
-50 -60
-70
-80 -90
-10
0
6h
7
h
8h
9h
10
h
11
h
12
h
Latitude = -22°30’
P.S. 1
4h
13
h
15
h
16
h 1
7h
What is the sideral time?
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Sky at OPD: equatorial
2013/03/23 2h
-20
-30
-40
-50 -60
-70
-80 -90
-10
0
8h
9
h
10
h
11
h
12
h
Latitude = -22°30’
P.S.
14
h
13
h
15
h
16
h
17
h
18
h
19
h
What is the R.A. of Scorpius' tail?
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Sky at OPD: equatorial
2013/03/23 4h
-20
-30
-40
-50 -60
-70
-80 -90
-10
0 10
h
11
h
12
h
Latitude = -22°30’
P.S.
14
h
13
h
15
h
16
h
17
h
18
h
19
h
20
h
21
h
22
h
What would be the hour angle (H) of Arcturus at
05:00 in the morning?
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Sky at OPD: equatorial
2013/03/23 6h
-20
-30
-40
-50 -60
-70
-80 -90
-10
0
12
h
Latitude = -22°30’
P.S.
14
h
13
h
15
h
16
h
17
h
18
h
19
h
20
h
21
h
22
h 23
h
What is the R.A. of the East point?
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Campos dos Goytacazes, RJ http://www.twanight.org
http://apod.nasa.gov/apod/ap090509.html
Imagine the equatorial system on the sky!
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Ecliptic system
PNE
W
N
L
b
( ℓ , b ) 00 ℓ < 3600
(S) -900 b +900 (N)
ℓ : ecliptic longitude
b : ecliptic latitude
g
ℓ
Slide adapted from Prof. Boczko
![Page 48: Astronomical coordinates and planning observations Ijorge/aga5802_2017/2017_05_coordenadas1.… · AGA5802 Astrofísica Observacional Astronomical coordinates and planning observations](https://reader034.vdocuments.mx/reader034/viewer/2022051605/6014768d89e83f067f4ba04b/html5/thumbnails/48.jpg)
Equatorial & Ecliptic System
NP
EPN
W
NP EPN
g
N
E
g
W
Slide adapted from Prof. Boczko
![Page 49: Astronomical coordinates and planning observations Ijorge/aga5802_2017/2017_05_coordenadas1.… · AGA5802 Astrofísica Observacional Astronomical coordinates and planning observations](https://reader034.vdocuments.mx/reader034/viewer/2022051605/6014768d89e83f067f4ba04b/html5/thumbnails/49.jpg)
Galactic system ( ℓ , b )
© Astronomy Methods
ℓ b
![Page 50: Astronomical coordinates and planning observations Ijorge/aga5802_2017/2017_05_coordenadas1.… · AGA5802 Astrofísica Observacional Astronomical coordinates and planning observations](https://reader034.vdocuments.mx/reader034/viewer/2022051605/6014768d89e83f067f4ba04b/html5/thumbnails/50.jpg)
Exemple drawing
50
Dec = lat
Zenith
Horizon