ASTR 1040                                                                      Spring, 2005

HOMEWORK NO. 1

Due date:  Thursday, January 27

1. How much less would you weigh on the summit of Mt. Everest (altitude 8.84 km).  Give your answer as a fraction of your sea-level weight; no need to tell me what you actually weigh!

2. A binary star system is observed.  The orbital period is P = 17.28 years, and the semimajor axis, in angular units, is 0.44".  The distance to the system is 22 pc (recall that 1 pc = 206,265 AU).  The distance from star 1 to the center of mass of the system is 0.273 of the total distance between the two stars.  What are the masses of the individual stars?  Solar units are fine.  (Hint:  You'll have to use the small-angle approximation to convert the semimajor axis into linear units.  Also, note that the ratio of distances from the center of mass gives you the ratio of the masses of the two stars.)

3. Suppose a star has a luminosity of 780 times the solar luminosity, and its spectrum shows a wavelength of maximum emission of 1074Å.  What is the radius of the star, in both basic units (meters) and in solar units?

4. The energy needed to ionize a hydrogen atom (from its ground state) is 2.18 X10^-18 J.  What wavelength of photon does this energy correspond to?  What kind of telescope is needed to observe at that wavelength?  How fast would an electron have to be moving to have this much kinetic energy, so that it could cause collisional ionization?

5. The Rydberg formula for the spectral lines of hydrogen is

1/lambda = R(1/n^2 - 1/m^2), n = 1, 2, 3, ...; m = n+1, n+2, ...∞.

The value of R is R = 1.097 X 10^5 cm-1.  Calculate the wavelengths of the first three lines and the ionization limit (m = ∞) for the Paschen (n = 3) and the Brackett (n = 4) series. Express all wavelengths in Å.