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AST 3722C  Spring 2008
Homework #5 – solutions.
Instructions: Solve each part of each problem below. Where math is involved, and unless
otherwise indicated, show your work.
•
1.
[2 points]
You want to study the double star 32 Eridani. Star A has J2000
coordinates
α
A
= 03
h
54
m
17
.
47
s
and
δ
A
=
−
02
◦
57
′
14
.
5
′′
. Star B has J2000 coordinates
α
B
= 03
h
54
m
17
.
28
s
and
δ
B
=
−
02
◦
57
′
09
.
9
′′
. You want to start an observing campaign where
you observe these two stars at many wavelengths across the EM spectrum, from ultraviolet
to radio, with the following telescopes:
wavelength
telescope
wavelength
primary mirror
regime
range
diameter (m)
ultraviolet
GALEX
135 nm to 280 nm
0.5
visible
Hubble
3000
˚
A to 9000
˚
A
2.4
infrared (near)
Keck
0.9
μ
m to 2.5
μ
m
10
infrared (mid)
Subaru
5
μ
m to 23
μ
m
8
infrared (far)
Spitzer
24
μ
m to 160
μ
m
0.85
radio (submillimeter)
JCMT
0.35 mm to 0.85 mm
15
radio (millimeter)
ARO
1 mm to 3 mm
12
radio (microwave)
GBT
0.7 cm to 21 cm
100
(a) Calculate the separation of star A and star B, in arcseconds.
The stars are close together so we can use the smalltriangle formula:
separation =
r
(Δ
δ
)
2
+ (Δ
α
)
2
.
The tricky part is that Δ
α
must have the same units as Δ
δ
. The separation in R.A. is
Δ
α
=
α
A
−
α
B
= 0
.
19
s
= (0
.
19
×
15
×
cos
δ
m
) in arcsec
= (0
.
19
×
15
×
cos(
−
02
◦
57
′
12
.
2
′′
)) in arcsec
= 2
.
85
′′
.
I used
δ
m
=
1
2
(
δ
A
+
δ
B
) here.
The separation in Dec. is easy, just Δ
δ
=
δ
A
−
δ
B
=
−
4
.
6
′′
.
So that means
separation =
r
(
−
4
.
6
′′
)
2
+ (2
.
85
′′
)
2
=
5
.
4
′′
.
1
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View Full Document (b) For each telescope, calculate the Rayleigh criterion at both the short and long wave
length boundaries. Express your answers in arcseconds.
The Rayleigh criterion is 1
.
22
×
λ/D
. So we have to do this for all 8 rows in the above
table and at 2 wavelengths each. Note that you want to have
λ
have the same units as
D
.
Then the answer comes out in radians which you can then change to arcsec.
wavelength
telescope
wavelength
Rayleigh criterion
Rayleigh criterion
regime
in radians
in arcsec
ultraviolet
GALEX
135 nm
3
.
29
×
10
−
7
0.068
ultraviolet
GALEX
280 nm
6
.
83
×
10
−
7
0.141
visible
Hubble
3000
˚
A
1
.
52
×
10
−
7
0.031
visible
Hubble
9000
˚
A
4
.
57
×
10
−
7
0.094
infrared (near)
Keck
0.9
μ
m
1
.
10
×
10
−
7
0.023
infrared (near)
Keck
2.5
μ
m
3
.
05
×
10
−
7
0.063
infrared (mid)
Subaru
5
μ
m
7
.
63
×
10
−
7
0.157
infrared (mid)
Subaru
23
μ
m
3
.
51
×
10
−
6
0.723
infrared (far)
Spitzer
24
μ
m
3
.
44
×
10
−
5
7.105
infrared (far)
Spitzer
160
μ
m
2
.
30
×
10
−
4
47.368
radio (submm)
JCMT
0.35 mm
2
.
85
×
10
−
5
5.872
radio (submm)
JCMT
0.85 mm
6
.
91
×
10
−
5
14.260
radio (millimeter)
ARO
1 mm
1
.
02
×
10
−
4
20.970
radio (millimeter)
ARO
3 mm
3
.
05
×
10
−
4
62.911
radio (microwave)
GBT
0.7 cm
8
.
54
×
10
−
5
17.615
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This note was uploaded on 11/09/2009 for the course AST 4700 taught by Professor Fernandez during the Spring '09 term at University of Central Florida.
 Spring '09
 Fernandez
 Astronomy

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