Problem Set #3

Problem set due in class, Jan 29. Show your work.

1) Sirius has a proper motion of -0.037 sec/yr in Right Ascension and -1.12 arcsec/yr in Declination (Sirius is at Declination -17). The parallax of Sirius is 0.375 arcsec and radial velocity -8 km/sec. What is the total proper motion? [1.26 arcsec/yr] What the tangential and total velocities? [15.9 km/sec and 17.8 km/sec] When will Sirius be closest to the Sun? (Draw a diagram) (8 points)

2) If a star has an apparent magnitude of -0.4 and a parallax of 0.3 arcsecs, what is its distance modulus and absolute magnitude? [-2.39 and 1.99] (4 points)

3) What are the absolute magnitudes of the following (5 points):

4) The Sun has an apparent visual magnitude of -26.75. Calculate its absolute visual magnitude. [4.82] Calculate its magnitude at the distance of Alpha Centauri (1.3 pc). [0.46] The Palomar Sky Survey is complete to magnitudes as faint as +21, how far away would a star identical to the Sun have to be in order to be visible on a Sky Survey image. (6 points)

5) The total magnitude of a triple star is 0.0. Two of its components have magnitudes 1.0 and 2.0. What is the magnitude of the third component? [0.88] (4 points)

6) The absolute magnitude of a star in the Andromeda galaxy (distance 690 kpc) is M=5. It explodes as a supernova, becoming one billion times brighter. What is its apparent magnitude? [6.69] (4 points)

7) A globular cluster has a total of 10^4 stars. 100 of them have absolute mags = 0.0, the rest have absolute mags = +5.0. What is the integrated visual mag of the cluster? [-5.75] (4 points)