ASTR 306 - HW #1

Note: 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). Star 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) separation?

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?