ASTRONOMY 9: HISTORY OF COSMOLOGY

Assignment #11

2000 March 1

Journal Assignment

Due: Tuesday, March 7, 5:00 pm, in my mailbox (6th floor Campbell, across from elevators, OR you may turn it in Monday in class)

1.

Why was the Newtonian cosmos required to be infinite?

2.

Astronauts typically orbit the Earth about 100 miles above its surface. Explain carefully why they are ``weightless''.

3.

If Aristotle could drive, he would say that you have to keep your foot on the accelerator because you need a steady force to keep an object in motion. How would Newton respond?

4.

Fun with surface gravity (the gravitational acceleration g at the surface of a planet or star).

(a): The Sun's surface gravity is about 28 times stronger than Earth's. If you were on the Sun, how much would you weigh (lbs)? What would your mass be (kg)?
(b): The radius of the Sun is now about $7\times 10^5$ km. In about 5 billion years, it will expand all the way out to the Earth's orbit, becoming a ``red giant'' star! At that point, how much stronger will the Sun's surface gravity be than Earth's? (Hint: you don't need to use the value of G, just use ratios!)
(c): Earth is 81 times more massive than the Moon, and Earth's radius is 3.7 times larger than the Moon's. What is the ratio of Moon's surface gravity to Earth's?
(d): Why can astronauts on the Moon jump around like superman?

5.

Suppose you are sitting on Earth's equator, rotating at constant speed.

(a): Explain why the rotation of the Earth is causing you to accelerate. (Hint: what is the difference between speed and velocity?)
(b): Compute this acceleration (in meters per second squared, m/s²). (Hint: see assignment #8 for useful numbers!)
(c): How short would a ``day'' (one rotation) have to be in order for you to be in danger of being thrown off into space?

6.

Tides.

(a): According to Galileo, what did the tides prove?
(b): What was wrong with Galileo's ideas about the tides?
(c): It turns out that tidal forces decrease with the cube of the distance: $F_{\mathrm{tidal}} \propto M/r^3$ . The Sun is 390 times farther than the Moon, and 27 million times more massive. What is the ratio of tidal forces on Earth due to the Moon and Sun?
(d): Does the Sun have a significant effect on the tides?

7.

You are floating slowly through space, and notice you are about to collide with a classmate! Fortunately, you are holding your Astro 9 reader. Explain how you might use it to avoid this calamity.

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jonathan baker
2000-03-01