**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).*

- 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,

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

- Verify that this distribution is normalized (i.e., show that
). What are the units of ?
- Atmospheres.
- Do problem #9 from Ch. 11 (p. 347).
- Also do problem #10.
- 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.

- Do problem #9 from Ch. 11 (p. 347).
- Habitable zones. Do problem #9 from Ch. 12 (p. 369).