Download Moon

Moon
Combining some observations with some geometry we can get a theory for the behavior
of the moon.
> What are the places from which you can see the light bulb in the light station?
> Although the previous question has a perfectly definite answer, it
isn’t obvious, just looking at the light station: you can’t see the region, and have to go
look for it. Discuss what this tells you about light, and about what things you can see.
> A small light bulb hanging from the ceiling is shining on a table. Indicate on the
diagram which regions are in shadow..
10/14/15
19- 1
A model to explain the phases of the moon
It seems like the sun and moon move across the sky, but it is a better interpretation that
they are standing still and we are on a rotating earth. This was more obvious before the
invention of the light bulb, because the stars “move” across the sky together, maintaining
an unvarying pattern. One star – the North Star – stays in constant direction and all the
others seem to rotate around it. It is simpler to assume that the stars are standing still and
the earth is rotating.
These three pictures show the northern part of the sky at 8 PM, 10 PM, and midnight on
Nov. 7, 2009. The Big Dipper is at the bottom of the 8 PM picture (it would only be
visible somewhere away from buildings and trees, because it is very low in the sky). But
by midnight (the picture on the right), the Big Dipper has rotated into view. The North
Star is marked on the 8 PM picture.
The sun and the moon do move relative to the stars, because the earth is moving around
the sun and the moon is orbiting the earth. While it only takes a day for the earth to
rotate, it takes a month for the moon to go around the earth and a year for the earth to go
around the sun. So the angle between the sun and the moon does not change much in a
day, but does change over several days. We can understand these changes in a model in
which the sun doesn’t move and the moon slowly goes around the earth.
Here is a drawing showing the earth
and moon (not to scale!), as seen
from "above" the earth. From this
viewpoint, one can see the northern
hemisphere of the earth, but not the
southern hemisphere. The sun is
very far away, in the direction
indicated.
2. In this drawing, what part of the
moon is illuminated by sunlight?
Shade the part that is not
illuminated.
10/14/15
19- 2
3. What does a person on earth see? Give a "moon observation" for the case shown,
reporting the appearance of the moon and the angle between the sun and moon.
4. We went outside once and compared the appearance of the moon to the appearance of
a Styrofoam ball. How did that activity support this theory for the moon?
5. How did the Styrofoam ball activity support the claim that the sun is very far away?
6. The sun rises in the east and sets in the west. Then
which way is the earth turning in this picture (this is a view
from above the North Pole, which is the black dot)?
7. For the case shown in the drawing on the previous page, will the moon set a few hours
before the sun or a few hours after the sun sets?
8. For the day shown in the diagram on the previous page, when is the moon visible?
Approximately when does it rise and set? When would be the best time to determine the
moon angle? What is the moon angle for the day shown?
10/14/15
19- 3
9. September 27, 2015 was a full moon (and eclipse); it was the 270th day of the year .
January 4, 2015 (the 4th day of the year!) was also a full moon. Then how many days
(including fractions of a day) is it between new moons? (There usually is one full moon
per month, but both July 1 and July 31 were full moons).
10. What does the moon look like today?
the same (assuming it was visible)?
On what other days this semester did it look
Check: How well does this theory of the moon agree with your observations of the moon?
10/14/15
19- 4
11. Every 29.5 days, the moon
gets back to its same position.
In between, it goes around the
earth once. This means that the
moon will be in a slightly
different place around its orbit a
day later. How much does the
angle between the sun and moon
change in a day?
12. Use your observations of the moon to figure out whether the moon goes around
clockwise or counterclockwise in the diagram above. There are several clues:
how the shape changes from day to day,
how the angle between sun and moon changes from day to day,
and how the time of moonrise changes from day to day.
Show that these are all consistent with your answer to Q. 12
10/14/15
19- 5
Moon phases
Back when people were outside more of the time, the moon served as a calendar. The
original month was the time between new moons (the name gives this away). New
moon, full moon, and the two half-moons broke the month into four parts, each about a
week long.
The phases of the moon have names. When the moon is less than half-lit, it is called a
crescent moon; when it is more than half-lit, it is a gibbous moon. During the two
weeks after new moon, the lit part gets larger every day, which is called a “waxing
moon”; then for two weeks it gets smaller again, and this is a “waning moon.” The word
“crescent” comes from the Latin that means “growing” but somehow the name became
attached to the shape; “wax” is from a German word that means “grow” (and has nothing
to do with the stuff that bees make).
Eclipses
New moon means that the moon is almost directly between the sun and the earth, so that
we are looking at the unlit side of the moon. And full moon means that the earth is
almost directly between the moon and the sun, so that we are looking at the lit side of the
moon. According to the picture, it seems that the moon should make a shadow on the
earth every new moon, giving an eclipse of the sun, and the earth should make a shadow
on the moon every month, giving an eclipse of the moon.
Eclipses are less common that this, because the orbit of the moon is tilted slightly relative
to the orbit of the earth around the sun. Then most months the moon is slightly above or
below the direct path from earth to sun. The moon’s shadow misses the earth, and the
earth’s shadow misses the moon. The sun and moon are only ½ degree wide, so it’s
pretty easy for one to slide past the other in the sky without our noticing.
Because the sun is a lot larger than the moon, the moon’s shadow
on the earth is rather fuzzy. The region that is in total shadow is
small (about 50 miles wide). So when there is an eclipse of the
sun, only a few people along a narrow path get to see it. There
will be a total eclipse of the sun visible in parts of Western
Kentucky on August 21, 2017 (around 1:15 PM CDT).
When the moon enters the shadow of the earth during an eclipse of the moon, everyone
on the night-time side of the earth gets to see it (they may have to stay up rather late).
Here is a photograph of the beginning of an eclipse of the moon. Note that this is
very different in appearance from a gibbous moon. The curved edge of the dark
zone is the shadow of the edge of the earth; it gives you an idea how large the
earth is compared to the moon.
10/14/15
19- 6
Each group should hand in one copy of this page at the end of class
Group:
Names of group members present:
11. Some cultures use a lunar calendar, so that each month starts with a new moon.
How many lunar months are there in a year?
12. Catherine thought the full moon was so pretty that she telephoned her boyfriend in
Arizona to tell him about it. Can they watch the moon at the same time? [Hint: when
does the full moon rise?]
10/14/15
19- 7
Checks
The side of the earth and the moon that are opposite the sun are dark.
A person on earth would measure
the angle between the sun and the
moon; it is about 45 degrees.
A person on earth would be mostly
looking at the unlit side of the
moon, which is not visible. In the
northern hemisphere a little bit on
the right side would be lit: a
crescent moon.
A Styrofoam ball right next to the moon would look just like the moon. This tells us that the
moon is also a ball, and that it is being lit by sunlight the same way as the ball in our hand. If
the sun were not far away (at the same distance as the moon), the moon would be lit from a
different direction and would look different.
The earth is turning counterclockwise (viewed from above the north pole). A person on the
earth is being carried into the dark area at sunset, and last sees the sun in the west.
In the diagram above, when a person is standing at the edge between light and dark (so that it is
sunset for that person), the moon is still 45 degrees above the horizon. So the moon will set
later, by several hours (the earth turns all the way around in 24 hours, so 45 degrees (1/8 of a
circle) is a three hour difference: the moon sets at 9 PM if sunset is at 6 PM, and the moon rose
about 9 AM.
10/14/15
19- 8
Yellow sheet questions
> Some cultures use a lunar calendar, so that each month starts with a new moon. How
many lunar months are there in a year?
We found that there are 29.5 days between full moons. Unlike the length of a day, this
does not change appreciably from month to month. Note that it is just a bit shorter than
most months (which are 30 or 31 days long), so the date of full moon creeps a day or two
earlier almost every month, and occasionally we get a month that contains two full moons
(right at the beginning and the end – the “blue moon”).
Yet 29.5 days is just over 4 weeks, so the day of the week for a full moon creeps in the
other direction!
Finally, 29.5 days for the moon’s schedule divides into 365.25 (the sun’s schedule)
twelve times with a third of a month left over. Then the lunar calendar people have 12
“months” in some years, and a “leap month” about every third year. Iran, for example,
starts its calendar on the new moon in March, and every so often has a thirteenth month
which (in Iranian) is called “Second February.”
Using astronomical events as calendar markers seems convenient because you can just
look at the sky and know when it is, but the time intervals are all different, so many
cultures gave up on it.
> Catherine thought the full moon was so pretty that she telephoned her boyfriend in
Arizona to tell him about it. Can they watch the moon at the same time?
The moon is full when it is exactly opposite the sun. So it rises near sunset, and sets near
dawn. Arizona is pretty far west, and the sun sets two hours later there. So Catherine
can’t call him right at moonrise in Kentucky. About two hours later, the moon will be
rising in Arizona. By then the moon seen from Kentucky will be well above the horizon,
and no longer a big-looking orange ball, but she can call and talk about it.
(The moon is actually the same size all the time. You can always cover it up with your
little finger. But when it is just rising, you tend to compare it with objects on the horizon
– trees and buildings – and it looks large compared to them.).
10/14/15
19- 9