Observing Techniques: exercises and assignments
Exercises will be assigned in class, to be
handed in one week later.
You may be asked to elucidate
your answer and you may be asked to give a short presentation
at one week's notice.
All of this contributes to your grade.
If you feel more information is needed to answer the question,
say so in your answer and explain why.
Where you can, use
sensible values to complete the answer.
THE ELECTROMAGNETIC SPECTRUM
and associated objects.
Problem set 1:
Problem set 2:
- Kitchin 1.1.1, 1.1.4
- Photometry 1 and Photometry 2 on this page
TELESCOPES and PHOTOMETRY
Problem set 3:
Work out the field of view, plate scale, and
the sampling limit (smallest features which can be
properly imaged) for the WHT1
Cassegrain focus (Primary mirror D=4200mm, f/11 focus),
with a 2000x2000 CCD chip having square 15 micron pixels).
Also work out the size of the diffraction-limited spot and the
image size corresponding to typical atmospheric turbulence. Do the same
for the Prime Focus and finally for the Nasmyth focus of the telescope.
- A camera is attached to the WHT cassegrain. The telescope
beam is "collimated" (each point-like source forms a set of
parallel rays) and then focussed on the detector. The final
focal ratio is f/3. The chip is the same as before. What is now the
field of view, plate scale, and
the sampling limit?
- What is the distance of 61 Cygni? Could we detect it's proper
motion in the duration of this lecture course, with the equipment available?
(see below for details)
The night sky at La Palma on a particular day has a V-band brightness
of 21.8 mag arcsec-2. What is the flux
from a square area of sky of size 10 arcmin x 10 arcmin?
In the section "adaptive optics"
on the web page, mention is made of real-time "tip-tilt"
image correction. How might you do this post-hoc
rather than in real-time,
and without the mechanical device to correct the x-y error?
enable us to determine the absolute magnitudes of stars? Describe
What is the Julian date at the start of the
first lecture (to the nearest minute).
- To what stellar magnitude can you just
detect a star with a 1m telescope of 70% overall efficiency in 1 hour of
exposure time? Assume S/N of 5 is adequate or justify a different
choice. "Efficiency" includes the camera etc. How long would you need
to expose to obtain a flux measurement with 99% accuracy?
The sky background is 21.4 mag
arcsec-2. Assume a V-band filter is in use.
After working this out, run this iraf script
to experiment with the integration time.
- Look at the table of Photometric bands (Bradt 8.2).
This gives the central wavelength
and effective width of each band. The table also gives the
flux that a star with magnitude 0 would have (in that band).
In fact this defines m=0 for this photometric system.
Is this consistent with the rule-of-thumb for the V-band zero point
the photometry page, i.e.
cm-2 s-1 Angstrom-1
and if so
does it hold for all the other photometric bands listed?
2pt bonus Is the flux density given in the Bradt
table consistent with the
other expression given on
the photometry page, i.e.
10-26erg cm-2 s-1
Hz-1 for m=16.4, and does this hold for
all bands? If not, what is the magnitude scale based on?
Look up the term "AB magnitude" (e.g. on the web)
and connect it with the foregoing.
PHOTOMETRY and intro to SPECTROSCOPY
Problem set 4:
What does the term "airmass" (AM) refer to, and how is it defined?
What is "extinction" and explain the units in which it is expressed
(Kitchin from p 306).
Look up the typical values of extinction at an observatory
such as La Palma and calculate it's effect at AM=2 for various
wavelengths (such as those of Bradt's photometric bands),
expressing the answer in magnitudes and linear units.
What is the largest meaningful value of airmass?
Note: you may find
useful information at
A grating with 600 grooves/mm is illuminated by collimated light
at an angle of 10o from the normal. What is the angular dispersion
at a wavelength 500nm in the m=+2 order? At 800nm? For 800nm wavelength, which
Problem set 5:
Consider a grating with 600 grooves/mm
which is illuminated at 10 degrees from the normal -
the blaze gives the grating high efficiency over a
large wavelength range in this
You decide to make a spectrograph using this arrangement,
i.e. fixing the input angle at 10 degrees.
Which orders propagate at 500nm?
In the m=+2 order, work out the focal length of the camera you
would need to have a linear dispersion such that a wavelength
increment of 0.1nm corresponds to two pixels (pixel size 20 micron)
at the detector.
2pt bonus How would you
set up the collimator? Let us say you want the
spectrograph to be "fed" by light from a D=4m telescope
at the f/8 focus of the telescope. In principle you
want the spectrograph to accept all the light in the
seeing spot (also called the seeing disk) without
degrading the spectrum quality.
It is said that most spectrographs require a collimated beam. But the beam
from a star is perfectly collimated... Give as many reasons as you can
for the formation of a focus followed by recollimation. The main exception
to the rule is the "objective prism spectrograph", in which the
starlight indeed is allowed to fall on the dispersing element.
What is it about this application that makes this viable?
Calculate the line-of-sight velocity with respect to the Earth of a
star when the Balmer H-alpha line in its spectrum is observed to be at
a wavelength of 655.2 nm. Present the answer with
the appropriate level of precision. In this calculation
should you use the rest wavelength of the line
in air or in vacuum? The observation was made at La Palma Observatory
on a certain date. Using the iraf task rvcorrect, or any other tool or
formula, convert the line-of-sight velocity you have calculated
to one of the standard systems, such as Heliocentric.
You will need
the following data:
date of observation: 1/1/2003
time of observation: UT=0
coordinates of object: RA 7h, Dec +3o
observatory: lapalma (this will be recognised by rvcorrect,
for other programs you may need the observatory latitude and longitude,
28:46 N, 17:53 W). Describe why this correction is necessary.
What is today's date? What was the Julian date at 2:00 am this morning?
What is the Julian date and why is it used in astronomy?
What is the time at this instant and what is the UT at this instant?
What is the sidereal time now?
ASSIGNMENTS (We will work on these together)
Write and defend an
observing proposal for the 2m INT telescope at La Palma.
The winning proposal will be carried out.
Be prepared to criticise your peers, and to defend
your own proposal.
directly measure the rotation speed of the sun in km/s.
we have a 20cm f/10 reflector
with a CCD detector having 600x600 square pixels of size 9 microns
1 William Herschel Telescope, a 4.2m
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