Fall 2003 **Special Topics:
Astrophysics (Phys 493)**

Dr. I. Fernini

**Homework
# 1**

** **

**Due Monday
– October 04 - Late
HW won't be accepted. **

**Problem
1:**

What are the perihelion and
aphelion speeds of Mercury? What are the perihelion
and aphelion distances of this planet? Compute the product (vr)
at each of these two points and interpret your result physically.

**Problem
2:**

Find the relative position
of the center of mass for:

(a)
the
Sun-Jupiter system, and

(b)
the
Earth-Moon system

**Problem
3:**

Using astronomical units as the unit of length, years as
the time, and the mass of the Sun as the unit of mass, the value for k in Kepler's third law (P^{2} = k a^{3}) is
1.0. In these units, what is the value of

**Problem
4:**

How far from the star would we have to be (in astronomical
units) to find a substellar temperature comparable to
that of the Earth for:

(a)
Rigel (surface temperature T=12,000 K, radius
R = 35 R_{8})

(b)
Barbard's star (t=3000 K, R =0.5 R_{8})

**Problem 5:**

Formaldehyde (H_{2}CO) has
been discovered in interstellar space.

(a)
Calculate its "mean" molecular speed for T =
280 K. Would our Moon retain this gas for billion of years?

(b)
Would Saturn's satellite Titan retain formaldehyde?
(For Titan, radius » 2600 km, mass » 10^{23}
kg).