## Homework 1.

1. Review question 1., p.37. = a) equator; b) northern half

2. Review question 4., p.37. = see quiz 1, solutions, question 1.

3. Does Venus ever cross the sky at Earth? Explain. Harder: Does venus exhibit retrograde motion? Why or why not?

I should have asked if Venus can be seen crossing the sky. When Venus is on the near side of the Sun, it does cross the sky, but only during the day, meaning it's not visible. Venus does not cross the night sky like the outer planets do, since its orbit is closer to the Sun than ours. (This is why Venus is the Evening Star or the Morning Star, but not the midnight star!)

Since Venus' orbit is inside ours, it orbits the Sun more quickly, meaning it catches up and then passes us. (At some point, we'd see apparent retrograde [E to W] motion; exactly when depends on the relative positions of the two planets.)

4. Does Jupiter go through phases (like Venus) when viewed from Earth? Explain.

The big point here is that Jupiter always appears more than half lit, or can never appear dark to us. Venus, on the other hand, can be "new," or wholly dark.

5. Proxima Centauri is the star system most near to our Sun, only about 4 ly away. A very fast rocket might travel 100 km/s through interstellar space. How long would such a rocket take to get from here to there?

1) If your speed's in km/s, but your distance is in ly, you're computing with apples and oranges. Convert everything to the same units! Since km are easiest for me, I'll convert ly --> km. In Lecture 1 notes, I have a table where you can find:

• 1 ly = 1013 km

• then 4.1 ly = 4.1 x 1013 km

2) Everybody knows this equation (whether they know they know it or not!) --

time = distance/velocity.

(You go through this calculation every time you go driving around the state. Example: how long does it take to drive to Billings? Well, it's 150 miles from Bozeman, and most folks drive 75 m.p.h., so it'll take 2 hours.)

Using this equation, one gets

time = (4.1 x 1013 km)/(100 km/s) = 4.1 x 1011 s.

(Note that I cancelled the km on top with the km on bottom, and seconds [s] was "downstairs twice," so I moved it "upstairs.") This answer was good enough for full credit.

3) How many years are in 1011 s? In one year, there are

(60 sec/min)x(60 min/hour)x(24 hr/day)x(365 day) = 3.2 x 107 s (approx.).

Dividing the number of seconds by the amount of seconds in each year gives the number of years,

(4.1 x 1011 s)/(3.2 x 107 s/yr) = 1.3 x 104 yr = 13,000 yr (approx.),

which is a very long time. So forget about a round trip to the Centauri system for your 50th birthday!

6. Problem 18, parts a) & c), p. 38.

a) you must have walked from the pole to the equator, or 90o of the planet's 360o circumference. Multiply by four, and you've got the full circumference.

c) 8,000 miles x 4 = 32,000 miles

7. Review question 3., p. 56.

b) feathers