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AST 3003S: Galactic and Extragalactic Astronomy
Tutorial 1:
Due: Aug 7
Question 1:
Show that the law of sines in spherical trigonometry reduces to the planar
formula when we use the small angle approximations. Do the same for the law
of cosines for angles (ignore all quadratic and higher-order terms).
Question 2:
Star A has coordinates a1 = 10h, d1 = 70° and Star B has coordinates a2 = 11h,
d2 = 80°.
Calculate their angular separation if we treat them as points on a planar triangle.
Now calculate their separation treating them as points on a sphere. Under which
conditions would the two answers be closest?
Question 3:
Derive the transformation equations for converting from Galactic to
Supergalactic coordinates and vice-versa. The north SG pole (SGB=90º) lies at
Galactic coordinates (l=47.37º, b=+6.32º). The zero point (SGB=0º, SGL=0º)
lies at (l=137.37º, b=0º). Make a sketch of the 2 coordinate systems and
clearly mark the spherical triangle and any angles or sides you use for your
derivations of the transformation equations.
Determine the Supergalactic coordinates for the Galactic coordinates of M87 (l,b
= 283.78, 74.49), the central galaxy of the Virgo cluster) using your equations.
Question 4:
The Sun has an apparent magnitude of -26. What is the optical thickness, tau, of
a layer of fog if the Sun seen through it appears as bright as the full Moon
(apparent magnitude of -12.5)?
Question 5:
The apparent magnitudes of two stars in binary system are 7 and 11
respectively. What is the apparent magnitude of the system?
Question 6:
Two open clusters, which are seen near each other in the Galactic plane, have
angular diameters a and 3a, and distance moduli 16.0 and 11.0, respectively.
Assuming their actual diameters are equal, find their distances and the
interstellar extinction coefficient a.
Question 7:
The V magnitude of a star is 15.1, B-V = 1.6 and Mv = 1.3. The extinction in the
direction of the star (in the visual band) is Av = 1 mag kpc-1. What is the intrinsic
colour of the star?
Question 8: Determine the foreground and internal extinction towards a galaxy
Go to NED, the NASA/IPAC Extragalactic Database
(http://ned.ipac.caltech.edu/) and find the coordinates of 3 galaxies, one far from
the Galactic Plane, i.e. M87, the central galaxy of the Virgo cluster; , one deep in
the extinction layer of the Milky Way, i.e. HIPASS J0836-43, the most HImassive galaxy in the nearby Universe (fully obscured in optical) and your
favorite galaxy, as well as the B-band magnitude, morphological type and axis
ratio.
Determine the total foreground extinction in the B- and K-bands towards these
objects using the methods discussed in class (partially available through the
extinction calculator on same (NED) website, i.e. the
(a) the cosecant law by Sandage based on galaxy counts
(b) The Galactic HI-column density (use the HI-column density calculator on
http://www.astro.uni-bonn.de/hisurvey/profile)
(c) the NED Extinction calculator which is based on the DIRBE/COBE extinction
maps.
What are the values? How do the respective determinations compare?
(d) Do any of the magnitudes of these 3 galaxies need correction for internal
extinction as well. If so, how large would that correction be (use the Sandage
and Tammann 1981) approximations listed in course notes?)