# Physics-Using the C11 telescope at the Hutton-Westfold Observatory we observe Tycho 8167:1799, which has an R-band apparent magnitude of 8.327. In a 5 second R- band exposure of this star, we record a ux of 155507 ADU

Physics-Using the C11 telescope at the Hutton-Westfold Observatory we observe Tycho 8167:1799, which has an R-band apparent magnitude of 8.327. In a 5 second R- band exposure of this star, we record a ux of 155507 ADU 150 150 Affordable Capstone Projects Written from Scratch

Question 1 (12 marks)
Using the C11 telescope at the Hutton-Westfold Observatory we observe Tycho
8167:1799, which has an R-band apparent magnitude of 8.327. In a 5 second R-
band exposure of this star, we record a ux of 155507 ADU.
(a) (2 marks) If our CCD has a gain of 2.6 electrons per ADU, how many photons
have we detected in this exposure?
(b) (4 marks) If photon counting statistics dominate the uncertainties, what uncer-
tainty would we expect in our measurement of the ux (in units of ADU)?
(c) (6 marks) What (approximate) magnitude corresponds to 1 ADU per second,
also known as the zeropoint?

Question 2
The C11 telescope at Monash University’s Hutton-Westfold Observatory has an aper-
ture of 280 mm and a focal length of 2800 mm. A potential upgrade of the telescope
is to equip it with an SBIG Aluma 8300 CCD. The CCD is 17.96 mm by 13.52 mm
with 3326 pixels by 2504 pixels, with each pixel being 5.4 microns on a side.
(a) (5 marks) On the focal plane of the telescope, a distance in mm corresponds to
an angle on the sky (the plate scale). What angle does one mm correspond to
(b) (6 marks) Each pixel on the Aluma 8300 CCD is 5.4 microns on a side. What
angular size does an individual pixel correspond to?
(c) (6 marks) What is the rectangular eld-of-view (in arcseconds) that this tele-
scope and CCD can image (in a single exposure)?
(d) (5 marks) What is the diraction limited angular resolution that could be achieved
with this telescope at a wavelength of 0.6 microns?
(e) (2 marks) From Melbourne, would you expect to achieve diraction limited
(f) (3 marks) With a 28 mm aperture telescope, would you achieve diraction lim-
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Useful information
Physical Constants:
G = gravitational constant = 6:673 1011 m3 kg1 s2 = 6:673 108 cm3 g1 s2
< = universal gas constant = 8:314 107 ergK1 g1
k = Boltzmann’s constant = mu< = 1:38 1016 ergK1
a = radiation density constant =
4
c
= 7:56 1016 Jm3 K4
= Stefan-Boltzmann constant = 5:67 108 Wm2 K4
c = speed of light = 2:998 1010 cm s1
h = Planck’s constant = 6:62 1034 J s = 2~
mu = atomic mass unit (amu) = 1:66054 1024 g 931:5 MeV
R = solar radius = 6:96 1010 cm
M = solar mass = 1:989 1033 g
L = solar luminosity = 3:86 1033 erg s1
1 eV = 1:602 1019 J
1 J = 107 erg
1 AU = 1:50 1011 m
Physical Formulae:
E = h = hc=
gravitational potential energy: U =
GMm
r
blackbody (Planck) function: B(T) =
2h3=c2
eh=kT 1
redshift: z =
obs
emitted
1
Doppler shift: v
c = z =
0
if v c, otherwise v
c = (1+z)21
1+(1+z)2
ideal gas equation of state: P = kT
mH
gravitational time dilation: t1 = t0

1 2GM
Rc2
1=2
& redshift 1 = 0

1 2GM
Rc2
1=2
Astronomical Formulae:
Flux of an object of luminosity L (radiating photons isotropically) at distance d: F = L
4d2
Stefan-Boltzmann law for luminosity of an object with radius R and temperature T : L = 4R2T4
Stefan-Boltzmann law for surface ux of an object with temperature T : F = T4
Wien’s law (with T in units of K): max = 0:002897755 T1 m or alternatively, max = 5:88 1010 T Hz
Rayleigh-Jeans approximation: B = 22kT
c2 = 2kT
2
m1 m2 = 2:5 log10

F1
F2

= 2:5 log10

B1
B2

m M = 5 log10

d
10 pc

M = 4
Z r0
0
(r) r2 dr
circular speed of a particle orbiting a mass M at a distance r: V =
q
GM
r
velocity of the Earth around the Sun: VE = 30kms1
Binary stars (units of years, AU and Solar masses): P2 = a3
M1+M2
Statistics Formulae:
Gaussian distribution: f(x) =
1
p
22
exp

(x )2
22

Poisson distribution: Px = mxexp(m)
x!
Signal-to-noise ratio: SNR = p S
S+B(1+AS=AB)

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