ASTR 306 - HW #1
Many times problems will have information missing. This is intentional,
and meant to get you in the habit of using online sources to find the
data you need. You must cite your sources, and the data must come from
professional scientific sources (journal articles, observatory
websites, data archives, NED, etc), not Wikipedia or amateur astronomy
sources (ie SEDS, non-academic/professional websites, and the like).
1. Star A has coordinates (alpha,dec) = (45.58o, +21.5o).
B has coordinates (88.2o, +19.6o) From
Cleveland, what the altitude (in degrees) of Star A when it
transits? About how long after Star A transits will Star B transit?
What time of the year is the best for observing Star A? Do this problem from first principles (ie geometry and the definitions of RA and dec) without using online
calculators or looking up coordinates, etc.
For the rest of the problems, it's
okay to use online calculators when necessary. In particular
2. When I observe, to minimize problems with the atmosphere, I won't
observe my objects at airmasses greater than 1.5. How low in altitude
is this? I will admit, though, having been desperate enough to chase
something down to 2 airmasses. How low (in altitude) is that? Now go
outside and point to where objects transiting at an airmass of 1.5 and
2.0 would be, both in altitude and azimuth. (Yes, really. Do this. If you don't, I have ways of
knowing you didn't, and I'll be crabby at you.)
3. Track down and report values for extinction coefficients for KPNO
broadband imaging. Make a plot of how much a star is extincted (in V
magnitudes) as you go from sec(z)=1 to sec(z)=3. Make another plot
showing how much its B-V color is changed by atmospheric extinction
over this same range of airmass. In terms of flux (not magnitudes) how
much fainter is the star at 3 airmasses than at 1 airmass? If there
were no atmosphere at all, how much brighter would the star be compared
to its sec(z)=1 brightness?
4. We want to observe the galaxy pair NGC 4038/4039 using the 4m
telescope at Kitt Peak (KPNO). When is the best time of the year (to within a few weeks) to observe
it, and at that time how long is it above 1.5 airmasses each night? How does your answer change if we used the
4m telescope at Cerro Tololo instead?
5. What are the J2000 coordinates of the galaxies M81 and M82? What time of the year are they best visible? How
far apart are these two galaxies on the sky? At their distance, what does this
separation translate to in terms of a physical (projected)
6. What is the Crab Nebula's B1950 coordinate? Its J2000 coordinate?
Its coordinate today? You're observing this fall using the KPNO 4m
mosaic imager. If you mistakenly pointed your telescope at the Crab
tonight using its B1950 coordinate, how far off would your pointing
be? Would you see it in your image?
7. I am using the KPNO 4m to do a spectroscopic survey of Ap stars.
If each observation takes an hour, and I don't want to observe below
1.5 airmasses, what is the declination limit of my sample? Think
about both the northern and southern declination limits.
8. Data analysis check: Here is a simple dataset of standard star photometry. It has several observations of one star (of known apparent magnitude mV=12.40),
taken at different airmasses (column1=airmass, column2=instrumental
magnitude). Read and plot the data, and do a linear fit to work out the
airmass term and photometric zeropoint (i.e, do a fit to the
relationship truemag = instmag - K*secz + zp, and give the values of K and zp AS WELL AS THEIR UNCERTAINTIES!). Show a plot of the data, with your fit overplotted.
ASTR 406 extras:
11. We will be observing the galaxy M101 this spring from Kitt Peak.
We need to be observing it at airmass<1.5 and with the Moon down,
and we want to be able to observe at least 4 hours per night. In
March, April, and May, what are the range of usable dates?
12. Use astropy's Coordinate functionality (explained here) to work out how fast the small angle Cartesian assumption for calculating angular separations breaks down. Here is a dataset
of SDSS stars within a few degrees of the spiral galaxy M101. Work out
the angular distance of each star from the center of M101, using both
the small angle approximation and the true angular distance via
astropy. Make a plot of the log of the difference between the two
methods (y-axis) versus the true separation (x-axis). If you wanted to
keep your calculated distances accurate to 1 arcsecond or better, at
what point should you not be using the small angle approximation?