1. Today’s topics Phases of the Moon Solar and lunar eclipses
Measuring distances
Reading sections 1.5,

2. Phases of the Moon

3. Phases of the Moon
The phases of the Moon are caused by the orbit of the Moon around the Earth, but how does this work?
Any thoughts?

4. Moon’s Orbit
Relative to the Sun, the Moon orbits the Earth once every 29.5 days (relative to the stars the orbit is 27.3 days)
The orbit of the Moon is tilted by about 5 degrees relative to the ecliptic
The Moon rotates at the same rate that it orbits, so the same face of the Moon always points towards Earth

5. Picture taken by Galileo spacecraft from 4 million miles away
Phases of the Moon
Picture taken by Galileo spacecraft from 4 million miles away

6. Phases of the Moon

8. Does the Earth have phases? (as seen from the Moon)

9. Do the planets have phases?

10. Phases of the Planets

11. Solar and Lunar eclipses
What causes a solar eclipse?
How about a lunar eclipse?

12. A solar eclipse
Earth
Moon
Sun

13. Eclipse

14. Lunar eclipse

15. How can you measure the distance to an object you can’t reach?
Use triangles…

16. Triangles The small triangle has the same shape as the large one.
By measuring the two sides of the small triangle and the short side of the big triangle, we can calculate the length of the long side of the big triangle.

17. Measuring distance a d A D

18. So, how can we measure the distance to stars?p p
Take two telescopes some distance apart and observe the same star.
Measure the tilt between the two telescopes – this sets all the angles for the triangles.
Then we can find the distance to the star from the distance between the telescopes and the angle of the tilt.

19. So, how can we measure the distance to stars?
We want to use the largest distance we can for the short side of the big triangle
What is the largest distance we can get between the two telescopes (if both of them have to be on Earth – no spacecraft).

20. So, how can we measure the distance to stars?
The largest distance is not by placing the two telescopes at opposite ends of the Earth.
Instead, we can use one telescope and just let the earth move.

21. A.U. = Astronomical Unit = distance from Earth to Sun

22. Stellar Parallax
As Earth moves from one side of the Sun to the other, a nearby star will seem to change its position relative to the distant background stars.
d = 1 / p
d = distance to nearby star in parsecs
p = parallax angle of that star in arcseconds

23. Closer star – larger parallax

24. Example: Using parallax to determine distance
The bright star Vega has a measured parallax of 0.1 arcsec (p = 0.1″)
This means that Vega appears to move from +0.1″ to -0.1″ with respect to distant stars over a year’s observation
D(pc) = 1/p(″) = 1/0.1 = 10 pc
Vega is 10 pc (parsec) from Earth
(remember: 1 pc = 3.26 light years)

25. Review questions
Draw a diagram of the positions of the Earth, Sun, and Moon at new moon, first quarter moon, and full moon.
Draw a diagram of the positions of the Earth, Sun, and Moon during a solar eclipse.
Determine the distance to Alpha Centauri which has a parallax of 0.75 arcseconds.