ASTR430 HW#6 (due 12/12/05)

Your work should be handed to me (or placed under my door) by 5 pm Monday, December 12. I will have office hours as usual that day, so you could hand it in then (and discuss your oral presentation from the previous week if you like).

1. The Maxwell-Boltzmann distribution.

From the kinetic theory of gases, the fraction of particles with speeds between and in an ideal gas at thermal equilibrium is given by the Maxwell-Boltzmann distribution function,

where is the molecular mass and is the temperature ( is the Boltzmann constant).

1. Verify that this distribution is normalized (i.e., show that ). What are the units of ?

2. Derive expressions for the most probable speed (i.e., the speed corresponding to the peak in the distribution), the mean speed , and the root-mean-square speed . Show that . Evaluate at each of these values.

3. Plot the distribution functions for hydrogen and oxygen (O) atoms at 900 K, for between 0 and 25 km/s. For what is in each case? Express your answers in km/s, and also in terms of , , and for both species.

2. Atmospheres.

1. Do problem #9 from Ch. 11 (p. 347).

2. Also do problem #10.

3. Infrared observations of 90377 Sedna show a peak at 88 m. What is the temperature of Sedna? At that temperature, familiar gases like N and CO are frozen ices. Helium (He) and neon (Ne) would still be gaseous. Assuming Sedna has a radius of 800 km and a bulk density of 3000 kg/m, can this body retain an atmosphere of He? What about Ne? Comment.

3. Habitable zones. Do problem #9 from Ch. 12 (p. 369).