# The Physics, Astronomy and Mathematics of the Solar System

## CONTENTS OF CURRICULUM UNIT 07.03.06

## Astronomy: The Mathematician's Perspective

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## Appendix B

Geometry Warm-up Worksheet

Put the following events in order:

___ 1. Thales - Proposed the first known model of the universe that did not rely on

supernatural forces.

___ 2. Plato - Asserted that planet motion must be in perfect circles.

___ 3. Eratosthenes - Accurately established the circumference of the Earth.

7/360 * circumference of the Earth = 5,000 stadia (pl. Greek unit of distance)

___ 4. Ptolemy - His Earth-centered model of the universe remained in use for some

1,500 years.

___ 5. Copernicus - His model of the solar system provided a geometric layout for the

Sun-centered solar system.

___ 6. Tycho - His naked-eye observatory worked like a giant protractor.

___ 7. Kepler - His three laws of planetary motion describe the orbits of planets as

being elliptical and not circular.

Perihelion distance = a(1 - e)

Aphelion distance = a(1 + e)

___ 8. Newton - Force = mass * acceleration

F = ma

___ 9. Einstein - E = mc
^{
2
}

Energy = mass of the object * the speed of light squared

The Sun converts mass to energy through a similar process of nuclear

fusion. The reverse of Einstein's equation is also true. Energy can be

transformed into mass.

PQ _|_ QR

Your pen pal calls you on the telephone and tells you to go outside and look at the full moon. It is especially bright tonight. The moon is above your pen pal but it is at an angle for you. How much further are you looking in the distance to see the moon?

(image available in print form)

**
Figure 7
**
The figure above is not
**
**
drawn to scale. The diagram was drawn as such for clarification purposes only. Consider the Earth a globe and that you and your pen pal are not necessarily on the edges of the planet. Source of numerical data: The Cosmic Perspective, Bennett, Donahue, Schneider, Voit, fourth edition, 2007 for noted distances and the figure was drawn by the author.

Teacher discussion notes:

1. What is common for each entry in the list of the geometry warm-up?

2. Tie in the following during class discussion:

- a. Ancient mathematicians were politically sought and valued.
- b. Mathematicians were needed to accurately explain the events of the universe. For example: the eclipse.
- c. Mathematicians worked out the mathematics to predict celestial happenings. ]
- d. Mathematicians needed to invent new mathematics to explain astronomical events.
- e. Planet means "wanderer" and the planets were named after Roman gods.
- For example: Jupiter means the king of the gods.

3. Misconceptions:

Did you know . . .

there are eight planets?

- the Moon wobbles?
- the asteroids in the asteroid belt are great distances apart from each other?
- the hottest planet is not Mercury?