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

(give your answer in arcseconds)?

(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

imaging with a C11 telescope? (Explain your answer.)

(f) (3 marks) With a 28 mm aperture telescope, would you achieve diraction lim-

ited angular resolution when viewing from Melbourne? (Explain your answer.)

Page 4 of 5

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

erg cm2 s1 Hz1 steradian1

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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