Astronomy 10 Spring 2000

Homework #4

Due in one week.

Be careful of units and use appropriate precision. Be sure to explain your reasoning on each problem, so you can get partial credit for your work. Answers without explanations are not acceptable. You are encouraged to work together, but please write this up yourself.

1) When a new star is forming, a cold molecular cloud (10K) collapses to form a warm circumstellar disk (1000K) and a new star (10000K). The star produces magnetic activity that makes a corona (10⁶K) . Describe the type of radiation each of these produces (eg. "X-rays"). Describe the sort of instrument that might be used to observe it, and whether it can be done from the ground or in space.

2) Suppose the starship Enterprise has running lights which are very violet (400 nm). How rapidly does it have to travel relative to you in order that you see those lights as very red (700 nm)? Express your answer first as a fraction of the speed of light, then as km/s, then as mph. Does the starship have to move towards or away from you to produce this effect? (Note: the Doppler formula will actually start to break down at these speeds because of relativity, but don't worry about that now.)

3) Astra's Son is cooler and fainter than the Sun. If it is two-thirds as hot (4000K), at what wavelength does its radiation peak? If it is also half as big, how much less total energy than our Sun does it radiate (ie. what is its luminosity compared to the Sun)?

4) If the distance of Astra from its Son is half an AU (our units), how much energy does Astra receive compared to us (per cm² at its surface), i.e. how much brighter/fainter does the Son look compared to our Sun? How big does the Son look from Astra, compared to our Sun from here (compare their angular diameters)?

Useful Formulae:

Wien's Law for blackbody radiation (p. 102)

Doppler Formula (p.112, p.367)

Angular Diameter (p. 40)

Inverse Square Law (p.358)

Stellar Luminosity Relation (p. 359,360)