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Name: Doreen
Status: other
Grade: other
Location: NV
Country: N/A
Date: N/A


Question:
May husband and I are having a slight disagreement in the size of the moon in different parts of the US at the same time. He says depending where you are the moon could be a full moon and I say it would have to be the same size no matter where you are in the US. Is the moon different sizes at the same time depending on where you are?


Replies:
Not as far as I am aware--

The phase of the Moon is the same anywhere you are. IF the moon is rising or setting or near the horizon, it may appear larger but it is not. If it is quarter moon in Tucson, a few hours earlier, when the Moon is up, it is quarter Moon in NY.

David Levy


Howdy,

Essentially you are correct. The portion of the moon illuminated by the sun does not depend upon the location of the observer on the earth. Posit the following response to your husband: Think about how the phase of the moon would appear to a group of people standing on the north pole during the summer. now have each of them walk slightly away from the pole along different lines of longitude. Do they begin observing different phases? No.

here are a few minor, and I do mean minor, corrections to this. However, I do not think these will be enough for you husband to get around this.

The minor corrections include the following:

But what about the fact that two different observers at the same time (meaning the same universal time) observe the moon, would it not appear to have a different phase? Not to the naked eye. The earth-moon distance roughly averages to 385,000 km away, while the average radius of the earth is only around 6,400 km. Therefore, suppose two observers on opposite (or nearly opposite) sides of the earth had an unobstructed view of the moon. One would see the moon just rising, while the other would see the moon just setting. Therefore the difference between the two observed parts of the moon would be less than 2 degrees. Moreover, those 2 degree would vary over the edges of the moon which would be the most difficult places to see any variation.

The next version would be this: What about two different observers, on different sides of the earth, that each viewed the earth at the same local time. So person 1 measures it at 8pm and person 2 measures it 12 hours later at their own 8pm. Would they observe different phases? Not really. Here the question becomes one of "How far does the moon orbit in 12 hours?" The apparent period of the moon's orbit is around 29.5 days. Therefore, 1/2 day would reveal only 6 degrees. Again, that's probably beyond the scope of human eyes (certainly mine).

Neither of those two differences mentioned above should be enough of a caveat for your spouse to squeeze out of it! You can play the same game with observers on mountains and at sea-level or in airplanes, but the results will all be similar.

I used "apparent" above as it is the illuminated portion relative to how it is seen on earth. The actually period is a little less. The difference comes from the fact that the earth and moon move together earth, it is not illuminated in quite the same way. Look up "sidereal orbit" vs. "synodic orbit" if you'd like a bit more information on that.

Michael S. Pierce
Materials Science Division
Argonne National Laboratory


Doreen,

First off, the moon does not change size at all, only the lit portion of the moon changes ;) Since the lit portion of the moon is determined by the moon's position, the Earth's position and the sun's position all relative to one another, one might think that changing your position on Earth would result in seeing a different phase of the moon. While in theory this is true, let us put in actual number to see what kind of a difference it actually makes. Basically what we are going to do is form a triangle between the moon the Earth and the sun. It will be an almost perfect isosolese triangle. That is one that has two equal sides and a third unequal side if it has been too many years :) So draw out two little circles close to each other (put E and M in the middles) and then draw and "s" circle far away from those two so that you can draw two equal length lines between S and E and S and M. The distance between the Earth and the moon is 384,400 km. The distance between the Earth/moon and the sun is 149,597,887 km. These are average distances, not apapsis (furthest position) or periapsis (closest position). As you see, the distance to the sun is much much larger than the distance to the moon, when you are on Earth.

Now that the picture is drawn, what two are arguing over is being on one side of the Earth, versus the other. You can draw two little dots on opposite sides of your Earth circle, so that you can make another triangle between those two dots and the center of the moon. The two lines going to the center of the moon make up an angle. It is this specific angle about which you are debating. So just as we did with the sun, you already have two of the three distances--both lines from the Earth to the moon are 384,400 km long. The diameter of the Earth (on average) is 6,372 km. I am sure on your picture it looks as if the angle is pretty large, but if you would draw the distances in proportion, you would find that the angle is very small because 6,372 into 384,400 is only 1.66 percent! The actual angle is just under 1 degree and the other two angles (the ones on Earth) are almost right angles at 89.5 degrees each. Since this is as far apart on the Earth as you can get, debating just the US matters even less.

Even though we are dealing with the moon in a "frozen" phase (i.e. the comparison is being made at one instance in time), the reason I had you draw the first triangle is to also appreciate the distance to the sun as well. The internal angle of the two lines drawn to the sun is only 0.14 degrees!

So while for distances that are closer you would see a shift, the distances to the moon are so much larger than the diameter of the Earth that it does not matter. You should also know that when these distances are closer the term for the shift is called parallax. This can be easily demonstrated with your hand and your two eyes. Put your hand in front of your face, then close one eye. While starring off into the distance, alternate opening one eye and closing the other and you will see your hand shift. Parallax is important in measuring the distances to stars and you can learn more about parallax here: http://en.wikipedia.org/wiki/Parallax

Matt Voss



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