Homework #4

# Homework #4

Due on June 21st at the beginning of class (10:10 AM)

Show All Work and Explain your answers.

100 points total

1. ### What seems to be the problem officer?

You are driving and inadvertently run a red traffic light and a police office pulls you over. You decide to tell the officer that you thought the light was green. You explain the Doppler shift of light to the officer and how since you were moving toward the traffic light the wavelengths of light were getting blueshifted. How fast would you have to have been driving for this to be true? Give your answer in both km/s and miles/hr. Should the officer give you a ticket?

(NOTE: use the wavelength of the red light to be 7000 Å and that of green light to be 5000 Å)

2. ### E = mc-who?

1. Using Einstein's famous equation E = mc2, show that when 4 protons fuse into 1 helium nucleus via the proton-proton cycle, about 4.14 x 10-12 Joules of energy is released. (The mass of one individual proton is about 1.6725 x 10-27kg; the mass of one helium nucleus is about 6.644 x 10-27 kg.)
2. The total luminosity (energy radiated per second) of the sun is about 3.85 x 1026 J/s. How many nuclei of helium are being created per second?
3. What percentage of the hydrogen mass is converted into energy via fusion?
4. How much mass in the Sun is being converted into energy every second?
5. The Sun has a mass of 1.989 x 1030kg. Only 10% of that mass is available for hydrogen fusion in the core. Show that the Sun's lifetime on the main-sequence (how long it burns hydrogen in the core) is 10 Billion years.

3. ### This star won't be telling its life story to Barbara Walters

Suppose Putrix is a main sequence star twice as massive as the Sun.

1. What is Putrix's luminosity relative to the Sun?
2. If Putrix and the Sun each use about 0.1M of gas as thermonuclear fuel during their main sequence lives, and if the Sun's main sequence life is 10 billion years, what is Putrix's lifetime?
3. Actually, Putrix will burn the same fraction of gas (10%) as the Sun during its main sequence lifetime. (The Sun burns about 0.1M, 10% of its mass.) So, how may solar masses of gas will Putrix burn?
4. Knowing this, revise your answer to part (b) accordingly to calculate Putrix's main-sequence lifetime.

4. ### H-R Diagrams

Let us assume that main sequence O, B, A, F, G, K, and M stars live approximately 3 million, 20 million, 300 million, 2 billion, 10 billion, 50 billion, and 200 billion years respectively. Draw and label completely a rough H-R diagram for clusters of stars with ages
1. 2 million years old
2. 300 million years old
3. 10 billion years old
Explain why you have drawn the diagrams as you have.

5. ### They might be Red Giants

Red Giants have proceeded further in the evolutionary sequence than main sequence stars, but is it correct to say that all red giants are older than all main sequence stars? (For example, which star is older, the Sun or a red giant of 10M ?)

6. ### When Stars Explode

Describe the two main types of supernovae, in terms of both their observed characteristics and their probable explosion mechanisms.

7. ### Black Holes Suck

1. If the Sun (1M = 2x1030 kg) were a black hole, its Schwarzchild radius (Rs = 2GM/c2) would be only 3 km. What would the Schwarzchild radius be for the following objects?
1. An 80 kg person
2. Earth (M = 6x1024 kg)
3. A supermassive black hole with a billion times the mass of the Sun.
2. How would the orbit of the Earth change if our Sun suddenly collapsed into a black hole? (Assume the mass stays the same.)
3. Now, a space-goat herder, named Bob, keeps watch over his space-goats by making them wear collars with blue lights that flash in 10 second time intervals. One day one of his flock wanders too close to a black hole and begins to fall toward it. Describe what the fall toward the black hole will look like from Bob's perspective far away from the black hole. Also describe what the fall is like for the poor space-goat.
4. Nothing that falls beneath the surface of a black hole ever emerges, not even light. So how, then, do astronomers go about trying to detect black holes?

8. ### Pair-o-Ducks

Howard the duck and Donald Duck are in separate space ships initially at rest with respect to one another. Howard leaves for home heading away from Donald at 1/2 the speed of light.
1. What is Donald's velocity as measured by Howard?
2. Does Donald find that his own meter stick is longer, shorter or equal to 1 meter? Explain.
3. Does Howard find that his own meter stick is longer, shorter or equal to 1 meter? Explain.
4. Does Howard find that Donald's meter stick is longer shorter or equal to 1 meter? Explain.
5. Does Donald find that Howard's meter stick is longer, shorter or equal to 1 meter? Explain.
6. Does Donald find his watch running faster, slower or the same to Howard's? Explain.
7. Does Howard find his watch is running faster, slower or the same as Donald's? Explain.
8. Howard and Donald were actually twins. If Howard turns around and meets up with Donald again, who will be older? This is the famous "pair-o-ducks paradox".