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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 (P2 = k a3) is 1.0. In these units, what is the value of Newton's constant of gravitation G.

 

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 R8)

(b)               Barbard's star (t=3000 K, R =0.5 R8)

 

Problem 5:

 

Formaldehyde (H2CO) 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 1023 kg).