### Homework #9

Size and Time Scales [10 pts]
Due 11am (in class) Monday Nov 10

DISTANCE SCALES

Speed of light: 3.0 x 105 km/s
Radius of the Earth: 6380 km
Distance to the Moon: 383,000 km
Distance to the Sun: 1.5 x 108 km
Radius of Sun: 7.0 x 105 km
Distance Sun - Mercury: 0.39 AU
Distance Sun - Venus: 0.72 AU
Distance Sun - Earth: 1.00 AU
Distance Sun - Mars: 1.52 AU
Distance Sun - Jupiter: 5.20 AU
Distance Sun - Saturn: 9.54 AU
Distance Sun - Uranus: 19.2 AU
Distance Sun - Neptune: 30.0 AU
Distance Sun - Pluto: 39.4 AU
1 parsec = 1 pc = 3.09 x 1013 km
1 kpc = 1,000 pc
1 Mpc = 1,000,000 pc
Distance to nearest star: 1.3 pc
Distance to the Orion Nebula: 450 pc
Thickness of Milky Way's stellar disk: 1 kpc
Distance to center of our Galaxy: 8.5 kpc
Distance to Magellanic clouds (satellite galaxies): 55 kpc
Distance to Andromeda galaxy : 0.66 Mpc
Distance to Virgo cluster of galaxies : 19 Mpc
Distance to edge of observable universe : 3000 Mpc

Scale 1: The Earth-Moon system on a table

Suppose the Earth has a diameter of a quarter (radius 1 cm). Calculate:

1. The radius of the Moon:
2. The distance to the Moon:
3. The distance light travels in one second:
4. The radius of the Sun:
5. Distance to the Sun:
8. Lay out a scaled model of the Earth-Moon system for the instructor/TAs to see.
• Now step back and take at least 30 seconds and try to actually visualize these size scales.
That is, I want you to think of an object of the size you found for the Sun, Jupiter, etc. and
imagine it at the right distance. Write `OK' here when you have done so:

Scale 2: The Solar System on a Football Field

Set the distance from the Earth to the Sun to be 3 yards. Place the Sun on the goal line. Find

1. The correct yard line to place each of the 9 planets:
Mercury:
Venus:
Earth:
Mars:
Jupiter:
Saturn:
Uranus:
Neptune:
Pluto:

2. Mark the position of each planet on a drawing of a football field

3. The distance to the nearest star:

4. Relate the distance to found for the nearest star to something familiar; i.e., is the distance comparable to the size of campus? Of Houston's inner Loop? The distance to Dallas?

• Again, take at least 30 seconds and try to actually visualize these size scales.
Write `OK' here when you have done so:

Scale 3: Our Galaxy and the Universe

Now let the distance to the nearest star equal 1 cm. Find the following distances, and relate them to something familiar. For example, if your answer is 3x104 cm, this is 300 meters or 0.3 km. This distance is slightly less than one lap around a running track, probably comparable to the distance you had to walk to come to class. Do NOT simply write down a number!

1. Distance to the Orion Nebula:
2. Thickness of Milky Way's stellar disk:
3. Distance to the Galactic Center:
4. Distance to the Magellanic Clouds:
5. Distance to the Andromeda Galaxy:
6. Distance to the Virgo cluster of galaxies:
7. Distance to the Edge of the Observable Universe:

TIME SCALES

1 year = 3.15x107 seconds
Age of the Earth: 4.5 billion years
Primitive life in the seas: 4.0 billion years ago
Complex life in the seas (Cambrian Period): 600 million years ago
Dinosaurs die out: 65 million years ago
Primitive humans evolve: 4 million years ago
AC/BC boundary: 2000 years ago
Duration of WWII: 5 years
Human population doubles every 30 years
Recorded history is about 4000 years old
The last ice age was about 15,000 years ago
Galileo lived in the early 1600's

Imagine a scale where five years go by every second. On this scale, the Earth, which is 4.5 billion years old, would be (4.5x109)/5 seconds old, or 28.6 years old. That is, the Earth would be a bit older than most of you are.

So pretend that you are the Earth on this scale. When in the Earth's life did the following happen, or how long do the following last from the Earth's `point of view'.

• How old was the Earth when primitive life formed in the seas?

• How old was the Earth when complex life deveolped in the seas?

• When did the dinosaurs die out?

• How long ago did primitive humans evolve?

• How long ago was the AC/BC boundary?

• How long do most humans live?

• How long did WWII last?

• How frequently does the Human population double?

• How long ago did Galileo live?