Download + cos - Astronomia

AGA5802
Astrofísica Observacional
Astronomical coordinates
& planning observations II
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
Spherical triangle
A
Is the region of
the sphere
limited by the
intersection of 3
planes passing
by the center of
the sphere
c
b
O
C
A, B, C = vertices
a
B
a,b,c = sides
Spherical triangle
A
c
r
b
r
O
B
r
a
C
a , b , c : sides of the spherical triangle = measurements of the central angles
Sin & cosine
formula in a
spherical triangle
A
Important relations for
Spherical Trigonometry
c
B
b
a
Co-seno
cos a = cos b . cos c + sen b . sen c . cos A
C
Seno sen a sen b sen c
---- = ---- = ---sen A sen B sen C
Seno & Co-seno
sen a . cos B = cos b . sen c - sen b . cos c . cos A
Sin & Cosine of (900- x)
sin x
Sine
90-x
sin (900-x) = cos x
x
cos x
CoSine
cos (900-x) = sin x
Angle between 2 cities
PN
cos a = cos b . cos c + sen b . sen c . cos A
Greenwich
90o- j'
q
Co-seno
cos q = cos (90- j) . cos (90- j' ) +
sen (90- j) . sen (90- j' ) . cos ( l' - l )
j l
j'
N
L
l'
cos q = sen j . sen j' + cos j . cos j' . cos ( l' - l )
Se |l`- l| >1800
q` = 3600 - q
PS
Angle between 2 stars
PN
cos a = cos b . cos c + sen b . sen c . cos A
Co-seno
Dados:
90o- d'
a ,d
a' , d'
q
a'
g
Se |a`- a| >1800
q` = 3600 - q
a
d'
N
d
L
cos q = cos (90- d) . cos (90- d' ) +
sen (90- d) . sen (90- d' ) . cos ( a' - a )
cos q = sen d . sen d' + cos d . cos d' . cos ( a' - a )
PS
What is the condition for the rise or
set of an astronomical object?
Z
Passagem
meridiana
PS
E
h=0
or
z = 90o
Rise
N
S
W
Set
Y
Z
Passagem
meridiana
PS
E
N
AN
Rise
AO
AN
Azimuth at rise & set
in the North & South
hemispheres
S
Z
Passagem
meridiana
PN
W
Set
Rise
Y
AN: Azimuth at Rise
AN
N
AO
AN
AO : Azimuth at Set
ASet = 360o - ARise
E
Set
W
S
Z
Passagem
meridiana
SP
Rise
E
HN
N
HO
S
Simmetry of the
rise & set in
relation to the
local meridian
W
Meridian
crossing
Z
NP
Set
E
Rise
HN
Y
HO
N
HOcaso = - HNascer
Set
W
S
Azimuth & Hour of
rise & set of an
astronomical object
Z
360-A
PN
Spherical triangle at
set
H
Z
j
PN
H
90o - d
90o
90o
N
d
W
Y
Azimuth at rise and set
cos a = cos b . cos c + sen b . sen c . cos A
Z
H
a = 90 – d
b = z = 90 (zenital distance)
c = 90 – j
A = 360 – A
PN
Q
cos (90-d) = cos z. cos(90-j) + sen (90-j) . sen z . cos (360-A)
cos (90-d) = sen (90-j) . cos (360-A)
sen d = cos j . cos A
cos A = sen d / cos j  0  A  180o
No Nascer: A = A
No Ocaso: A = 360o - A
Hour angle at
rise and set
Z
H
PN
cos a = cos b . cos c + sen b . sen c . cos A
Q
cos z = cos (90-j) . cos (90-d) + sen (90-j) . sen (90-d) . cos H
0 = sen j . sen d + cos j . cos d . cos H
cos H = - sen j . sen d / cos j . cos d
cos H = - tan j . tan d
 0  H  1800
At set: Ho = H
At rise: Hn = - H
Zenital distance of an
extended object at rise & set
z = 900 + s
Zenith
s(SOL) ~ s(LUA) ~ 16’
z
Horizon
Observer
s
Terra
s:
angular semi-diameter
Dispersion,
refraction
and
twilights
Twinkling: brightness fluctuations
Seeing: blurring + twinkling
Star
Zenith: short path
 less twinkle
Horizon: long path 
more twinkle
Atmosphere
Binary system
(without
correction)
With adaptive
optics
Adaptive optics
Center of the Milky Way
Light
dispersion in
the atmosphere
Dispersion
D
n: refraction index
N: density of molecules
Rayleigh formula for dispersion
In Earth’s atmosphere
D = k / l4
0
Color of radiation
l
Refraction
Light
Medium 1
Medium 2
Change in direction
due to the change
from one medium to
other
Refraction index n
c : light speed in
vacuum (n = 1) c vacuum
n
nc/v
v
Medium
n 1
Snell
Descartes
Snell-Descartes Law
Medium 2
n2 = c/v2
Normal
Medium 1
n1 = c/v1
Normal
n1 . sen i = n2 . sen r
i
i
r

n2 > n1
 : change in
angle due to
refraction
=i-r
r

n2 < n1
Atmospheric refraction
Normal to the
surface at
incidence point
One spherical layer
Incident ray
Atmosphere
Earth
Real
Tangent to the
surface at
incident point
Refraction
in layers
Real
position
Atmosphere
Earth
Atmospheric refraction
Apparent position
Zenith
The object seems
always higher than
at its real position
Real position
Atmosphere
Horizon
O
Earth
Color dependence
of the observed
position
‘Upper atmosphere limit’
Earth atmosphere
Ground
Position of the star on the CCD
depends on color
Angle of refractional change (arc minutes)
Angle of refractional change as a
function of star’s altitude
D
36´
900
80
70
60
50
40
30
20
10
0 Zen. Dist.
30
h
Horizonte
24
18
hD
12
6
0
Zenith
Horizon
0
Ground
10
20
30
40
50
60
70
80
900 Altitude (h)
Zenith
Rise and set including refraction
Zenith
Apparent
Real
Horizon
Observer
34’
Earth
r: angular change due
to refraction
z = 900 + r
Twilight
solar light before sunrise or after sunset
Dispersion & Twilight
Twilight is the result of the
dispersion of solar light at high
layers of the atmosphere
Zenith
Light dispersion in
the high atmosphere
Horizon
< 18o
Earth
Ilumination during twilights
Illumination on horizontal plate [lux]
1000
Civil
twilight
100
Nautical
twilight
Day
10
Night
Astronomical
twilight
Full moon
at zenith
1
0,1
Contribution
of stellar
light is more
than solar
light
0,01
Horizon
0,001
0,0001
Plate
-080
-000
50´
-060
-120
-180
Altitude of
Sun’s center
Z
Zenital distance z at start and end
of each twilight
Z
Sun
Horizon
West
90o 50’
Civil
96o
Nautical
East
6o
6o
6o
6o
6o
6o
102o
Evening
96o
Nautical
102o
Astronomical
Astronomical
108o
90o 50’
Civil
Night
108o
Morning
Sunrise, Meridian Crossing and Sunset
A.R. & Dec
de Mintaka?
Declination
How to
obtain the
coordinates?
How bright is
my target?
Magnitude?
R.A.
37
Planning observations
Coordinates : Simbad
http://simbad.u-strasbg.fr/simbad/sim-fid
Simbad
Epoch 2000
magnitudes
R.A. (α) dec (δ)
OPD format
-0.081
-0.024
OPD: proper motion in “/ano:
Divide SIMBAD’s value by 1000
Observing tools
https://www.eso.org/sci/observing/tools/calendar.html
41
https://www.eso.org/sci/observing/to
ols/calendar/skycalc.html
42
43
Astronomical Sky Calendar
http://www.briancasey.org/artifacts/astro/skycalendar.cgi
44
45
Object visibility
http://catserver.ing.iac.es/staralt/
Airmass
Altitude
Airmass = sec z = 1/cos z
z : zenital distance
Limits of 1.6m at OPD
zenital distance <= 60
(could be larger, but be careful)
48
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Useful hours
Altitude above horizon
Altitude of Middle-Dark-Time
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Airmass
Finding charts: important for weak
objects or crowded fields
http://catserver.ing.iac.es/dss1/
What about moving objects?
http://ssd.jpl.nasa.gov/horizons.cgi
51
Asteroid Ceres
La Silla
1 – 10 august 2014
one per hour
52
53
Sidereal time
Trip to OPD
http://www.lna.br/distempo/17i/intro.html
Trip to OPD
•
•
•
•
•
Do you have a laptop ? Linux ? IRAF ?
Warm clothes ?
Sunglasses ?
Flashlight (light from cell phone is OK) ?
Good tennis or trekking shoes, as you have to walk
many stairs at night, and perhaps you may want to
walk around the observatory
56