physics question #4511



Cheryl, a 51 year old female from Chesapeake, VA asks on January 11, 2009,

Q:

I teach moon phases to my third graders. On posters, in textbooks, and online, I have seen differing depictions. When looking at the moon from the northern hemisphere, does the lighted portion on the waxing phases appear on the right or the left? How about the waning phases? Thank you for your help.

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the answer

Donald J. Barry answered on January 11, 2009, A:
First let me point out that "left" or "right" are terms indicating the relationship between two objects with respect to a third reference frame -- actually a reference plane. If you hang upside down in a room, left and right reverse their usual order. And if two things are adjacent directly overhead, then there is no "left" or "right" without providing another reference.

When we consider the waxing phases, though, we can remove the ambiguity by realizing that the crescent moon just after new moon is seen low in the western evening sky, so there is a clear reference frame. If we lived at the equator and if the moon's and the sun's orbit were perfectly aligned with our equator, then we would see the moon directly above the sun at sunset, and the points of the crescent would face directly upwards, and the arc of the crescent downwards.

We can adjust these assumptions one by one and determine their effect on the appearance of the moon at sunset. As we move to more northerly latitudes, still assuming an equatorially orbiting moon, we see the sky at sunset rotate, with the north star rising from the horizon where it rests at the equator, and we see the plane of the moon's orbit similarly tilt from a vertical above the setting sun to a line now arcing to the left. The moon's illumination still faces, the sun, so the crescent image leans to the left, rotating slightly counterclockwise.

In fact, both the sun's and the moon's orbital planes are tilted with respect to our equator, by about 23.44 degrees for the Sun, and by a varying amount (in the 19-29 degree range) for the moon. Thus at various times of the year and at various stages of the moon's orbital evolution, from the equator the sun and the waxing moon at sunset will appear offset from one another and various tilts will be seen.

But as we move to larger and larger latitudes, ultimately the latitude trumps these effects. At a sufficiently high latitude, we will always see the waxing moon at sunset appear tilted to the left.

I suggest using the wonderful free software stellarium to explore the evening sky at sunset. You can choose a site of a given latitude, see the western sunset sky, and then step forward month by month to see how each subsequent crescent moon appears a little differently -- and if you are sufficiently far north, how all of them tilt to the left.  And if you are close to the equator, how each one is uniquely different as the sun and the moon move in their separate paths in the sky.
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