Download 7. When should I observe my target? How long can

7. When should I observe my
target?
•  Rough answer: estimate the date when it
transits the meridian at midnight.
•  Sun is at RA = 0h on March 21 (spring
equinox)
•  So objects are best observed around:
– 
– 
– 
– 
Sept 21 for RA = 0h
Dec 21 for RA = 6h
Mar 21 for RA = 12h
Jun 21 for RA = 18h
•  Add 2 hours per month.
•  Also make sure itʼs in the right hemisphere!
How long can I observe my
target?
•  This depends on the targetʼs declination.
•  Seeing and transparency degrade rapidly at
sec z > 2.
•  Wait till star has risen to z = 60 degrees, i.e.
altitude 30 degrees.
•  How much longer does it take to reach the
meridian? •  It will take the same time again from
meridian crossing to setting below 30
degrees.
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The Meridian
•  A great circle divides the sky exactly into 2
hemispheres.
•  The meridian is the great circle that runs
overhead through the zenith Z and the
celestial pole P.
–  Angle PZ = 90 - latitude φ
Z
90
-φ
P
Right Ascension and Declination
•  The equivalent of longitude on the sky
•  Line of constant RA is a great circle
running through star S and pole P.
–  Angle SP = 90 - declination, δ
Z
90
δ
90-
-φ
P
S
2
Hour Angle
•  The meridian intersects with a line of
constant RA through the star, at the pole.
•  The angle H = ZPS is the hour angle of the
star.
–  Negative when star is east of the meridian
–  Positive when star is west of the meridian
–  Increases with time.
Z
90
-φ
H
δ
90-
P
S
Altitude and zenith distance
•  Draw a third great circle through zenith Z
and star S.
•  Angle ZS is the zenith distance z of the
star.
–  Altitude = 90 - z
–  Airmass = sec z
Z
90
z
-φ
H
δ
90-
P
S
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Spherical triangles: the
essentials
•  All three sides are great circles.
sin a sin b sin c
•  Sine rule:
=
=
sin A sin B sin C
•  Cosine rule: cos c = cos a cos b + sin a sin bcos C
B
€
a
€
c
C
b
A
When is star at a given zenith
distance?
•  We know the angles ZP, PS and ZS –  need to know the hour angle H.
–  So use cosine formula:
cos z = cos(90 − φ )cos(90 − δ ) + sin(90 − φ )sin(90 − δ )cos H
⇒ cos z = sin φ sin δ + cos φ cos δ cos H.
Z
90
z
€
-φ
H
δ
90-
P
S
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How many hours above 2
airmasses?
•  Cosine formula gives H in degrees:
cos H =
cos z − sin φ sin δ
cos φ cos δ
•  Divide by 15 to convert to hours.
•  Object rises above 2 airmasses when z=60
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deg.
•  H gives time until meridian crossing
•  Object is observable for twice this duration Question
Latitude @ St Andrews=56.34 deg.
1) Above what declination will stars never set
from St Andrews
2) Ra=12.0, dec=0.0 How long does field
spend above Airmass=2
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Answer 1
•  Lowest point of star is when H=180, i.e., ZPS are
points on the same great circle.
•  In this case we have the condition:
Z
90=90-φ+90-δ, δ=90-φ=33.66
90
z
-φ
H
δ
90-
P
S
•  Stars above 33.66 deg never set in St Andrews sky
Answer 2
Use:
cos H =
Sub in values:
cosH =
cos z − sin φ sin δ
cos φ cos δ
cos(60) − sin(56)sin(0)
cos(56)cos(0)
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Evaluate:
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H = 26.77deg
H = 1h47m
Total time above 60deg = 3h34m
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What time does the star rise/
set?
•  Youʼve already worked out the hour angle H
when the star rises above z = 60 deg.
–  H is negative when star rises, positive when it sets.
•  H = Local Sidereal Time (LST) - RA of target
–  So LST = RA - |H| when star rises
–  And LST = RA + |H| when star sets.
•  Local Sidereal Time = GMST - (West
longitude)
–  So GMST = LST when star rises + West Longitude
•  Look up the UT (GMT) at this Greenwich
Mean Sidereal time on the date concerned.
–  http://www.roman-britain.org/astronomy/astro.htm
–  The Astronomical Almanac
For 12h 0dec field
•  LST field rises = 10h13m
•  LST field sets =1h47m
•  On 1st Dec RA overhead at midnight is ~:
0+
71
24 = 4h40m
365.25
•  Hence my field rises at: midnight
+(10h13m-4h40m)=5h34m am
•  And sets at: 5h34m+3h34m=9h8m am
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•  Will rise and set at same local time in Australia etc.
•  Note slight modification due to longitude offset.
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