1. of Montgomery College Planetarium
Geometry in Astronomy
By Dr. Harold Williams
of Montgomery College Planetarium
Title slide

2. Lunar Eclipse for Lunatics

3. Why do we see phases of the Moon?
Lunar phases are a consequence of the Moon’s 27.3-day orbit around Earth, relative to the fixed stars, the siders, so the sidereal month is 27.3 days. But the synodic month a cycle of phases is
29.53 days.
You may want to do an in-class demonstration of phases by darkening the room, using a lamp to represent the Sun, and giving each student a Styrofoam ball to represent the Moon. If your lamp is bright enough, the students can remain in their seats and watch the phases as they move the ball around their heads.

4. } } Phases of the Moon: 29.53-day cycle waxing waning new crescent
first quarter
gibbous
full
last quarter }
waxing
Moon visible in afternoon/evening.
Gets “fuller” and rises later each day. }
waning
Moon visible in late night/morning.
Gets “less” and sets later each day.

5. What causes eclipses? The Earth and Moon cast shadows.
When either passes through the other’s shadow, we have an eclipse.
This slide starts our discussion of eclipses. Use the figure to explain the umbra/penumbra shadows.

6. When can eclipses occur?
Lunar eclipses can occur only at full moon.
Lunar eclipses can be penumbral, partial, or total.
Use the interactive figure to show the conditions for the 3 types of lunar eclipse.

7. How come we don’t we have an eclipse at every new and full moon?
The Moon’s orbit is tilted 5° to ecliptic plane…
So we have about two eclipse seasons each year, with a lunar eclipse at new moon and solar eclipse at full moon.
Use this pond analogy to explain what we mean by nodes and how we get 2 eclipse seasons each year (roughly).
Note: You may wish to demonstrate the Moon’s orbit and eclipse conditions as follows. Keep a model “Sun” on a table in the center of the lecture area; have your left fist represent the Earth, and hold a ball in the other hand to represent the Moon. Then you can show how the Moon orbits your “fist” at an inclination to the ecliptic plane, explaining the meaning of the nodes. You can also show eclipse seasons by “doing” the Moon’s orbit (with fixed nodes) as you walk around your model Sun: the students will see that eclipses are possible only during two periods each year. If you then add in precession of the nodes, students can see why eclipse seasons occur slightly more often than every 6 months.

8. An ellipse looks like an elongated circle
What is an ellipse?
Use this slide to review ellipses and the definition of eccentricity.
An ellipse looks like an elongated circle

9. What are Kepler’s three laws of planetary motion?
Kepler’s First Law: The orbit of each planet around the Sun is an ellipse with the Sun at one focus.

10. Kepler’s Second Law: As a planet moves around its orbit, it sweeps out equal areas in equal times.
means that a planet travels faster when it is nearer to the Sun and slower when it is farther from the Sun.

11. Kepler’s Third Law p = orbital period in years
More distant planets orbit the Sun at slower average speeds, obeying the relationship
p2 = a3
p = orbital period in years
a = avg. distance from Sun in AU
Actually Kepler’s daughters law statement.

12. How did Kepler state his third Law?
2 log(p) = 3log(a)
p = orbital period in years
a = avg. distance from Sun in AU

13. Colors of Light White light is made up of many different colors
Newton showed that white light is composed of all the colors of the rainbow.
White light is made up of many different colors

14. I know noting about the stars without looking at their spectral lines
I know noting about the stars without looking at their spectral lines. Light and Matter: Reading Messages from the Cosmos
Spectra of a G2V our Sun, Sol or Helios.

15. Three Types of Spectra

16. Special Topic: Polarized Sunglasses
Polarization describes the direction in which a light wave is vibrating
Reflection can change the polarization of light
Polarized sunglasses block light that reflects off of horizontal surfaces
Demonstrate Polarization and optical activity to rotate polarization!