Astronomy 1L (Lab Class) Information
Moon Project: Finding the Moon
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For a discussion of the total lunar eclipse of Sep 27/28, 2015, see here
To find the direction of the Moon at a given time of day, see below

 Most people know that the Moon orbits the Earth, but unfortunately not everyone realizes that because of this, it is not up at the same time every day. Like the Sun, the Moon is up about half the time and down about half the time, but that time changes from day to day throughout a period of about a month. The Moon orbits the Earth once every 27 1/3 days, and gains one full "lap" on the Sun every 29 1/2 days. It moves eastward in the sky about 13 degrees per day relative to the stars, and about 12 degrees per day relative to the Sun (the difference of 1 degree per day is a result of our orbital motion around the Sun, which makes the Sun appear to move 1 degree per day relative to the stars). As a result of this change in position the Moon rises, crosses the sky, and sets nearly an hour later each day than the day before. Because of this, it is in a different place in the sky each night, and cannot be seen at the same time every day. There may be a period of a couple of weeks when it is visible at some place in the sky at a given time, but during the next two weeks it wouldn't be up at that time. Obviously, if you went outside to look at the Moon when it wasn't up, you could get quite frustrated -- and especially if that happened every night for nearly two weeks. So if you want to see the Moon, you must learn how to estimate when it is up, or how to look up when it rises and sets, so you don't waste your time in a futile effort to find it.
 Finding the Moon is fairly easy, if you know when it rises and sets. Just after moonrise it will be somewhere in the east, low in the sky (and perhaps even too low to see if it is just after moonrise, and there are buildings, trees or mountains in the way). Similarly, just before moonset it will be low in the western sky. Halfway between moonrise and moonset it would be in the southern part of the sky; a little earlier than that, it would be somewhere in the southeast; and a little later, it would be somewhere in the southwest (this discussion assumes that the observer is in the Northern Hemisphere; observers in the Southern Hemisphere should replace southeast with northeast, and southwest with northwest). In other words, all you have to do to find the moon is find out when it rises and sets, then compare those times to the time when you actually want to look for it. The closer it is to moonrise, the further east you would look for the Moon, and the closer it is to moonset, the further west you would look for it.

The Lazy Person's Guide to Finding the Times of Moonrise and Moonset
 If you take a daily newspaper, you can usually find the times of moonset and moonrise on the weather page. Soon after moonrise the Moon will be somewhere in the East; not long before moonset it will be somewhere in the West, and at in between times, it will be somewhere in the South, Southeast, or Southwest, depending upon how close to moonrise or moonset it happens to be.
 If you don't take a paper, you can find the times of moonrise and moonset on the Internet. One convenient site has an interactive map of the United States which you can click on to find the times for moonrise and moonset nearest today (there is also an entry form, for other locations and dates). Once you have done so, you can estimate the position of the Moon at various times of the day in the same way as if you had looked up the times in a newspaper.

The Inquiring Person's Guide to Finding the Times of Moonrise and Moonset
 If you want to actually understand what is going on, you can use the table of lunar phases in Chapter 8 of the lab text to find out when the Moon is at a given phase, and the table below to see how this affects the times of moonrise and moonset, and where to look for the Moon. There will also be, at a later date, a detailed discussion of the motion of the Moon, its appearance, and its location in the sky, posted on this web site. In the meantime, you can refer to a textbook on astronomy, or if you bought the supplementary text for the lab course, The Stars, by H. A. Rey, you can refer to the discussion of the Moon's phases in that book for a fuller understanding.
When the Moon is in Various Directions (Table)
Phase East
Southeast South Southwest West
New Moon Not observable
Waxing crescent Not observable Just after sunset
First Quarter Noon Afternoon Dusk Evening Midnight
Waxing gibbous Afternoon Dusk Evening Midnight Pre-dawn
Full Moon Dusk Evening Midnight Pre-dawn Dawn
Waning gibbous Evening Midnight Pre-dawn Dawn Morning
Last Quarter Midnight Pre-dawn Dawn Morning Noon
Waning crescent Just before dawn Not observable
New Moon Not observable

When the Moon is in Various Directions (Explanation)
 New Moon is not observable, because it is up when the Sun is up, and in the same direction as the Sun.

 A waxing crescent Moon will rise a little after Sunrise, but be too close to the Sun to see during the day. After the Sun goes down, it will be visible low in the West, for an hour or so, depending upon how long it has been since New Moon. Each day after New Moon will cause the crescent Moon to stay up for almost an hour longer after sunset. Usually, the first day after New Moon, the crescent is too close to the Sun, and up too short a time, to be visible during twilight, and goes down before the sky gets dark enough to see it. But the second and third days after New Moon, the crescent is fatter and brighter, and further from the Sun, and up a little longer, and easy to see, if you think to go out early in the evening.

 A fat waxing crescent Moon, just a day or two before first quarter, is far enough from the Sun that you can see it rising in the East a little before noon, in the South not long before sunset, and is easily visible throughout most of the early evening, in the Southwest and West.

 A First Quarter Moon rises in the East at noon, is in the South near dusk, and sets in the West around midnight, and is easily visible at all those times, if you remember where to look.

 As the Quarter Moon turns into a waxing gibbous Moon, it rises later and later, not coming up until sometime in the afternoon, but then it stays up later and later in the evening, as well, which makes it quite easy to find, as well.

 A Full Moon rises as the Sun goes down, or within half an hour of sunset, is in the South near midnight, and sets in the West within half an hour of sunrise. The fact that the Full Moon rises and sets very close to sunrise and sunset is the easiest way to tell that it is full. A day before and after Full Moon, the Moon looks just as round and full as on the day of Full Moon, but if it is a day before Full Moon, it rises and sets about an hour before the Sun sets and rises, and if it is a day after Full Moon, it rises and sets about an hour after the Sun sets and rises. It is only on the day of Full Moon that its rising and setting times almost exactly match the setting and rising times for the Sun.

 During all of the phases discussed above, the Moon would be visible, if at all, sometime in the evening, and perhaps, when far from the Sun, also during part of the day, and after midnight. But as the Moon moves past Full phase, the fact that it rises later and later means that it will not be up until after sunset, and in some phases, it won't be up until well after sunset. For most students, this makes it more and more difficult to observe. To encourage you to continue to observe the Moon even when it is in a phase which is less convenient to observe, observations of those phases which require you to go out at inconvenient times will generally be worth more points than observations of those phases which are easy to see.

 After Full Moon, a waning gibbous Moon will rise later and later each day, not coming up until sometime well after sunset, passing due South in the early predawn hours, and setting in the West sometime after dawn. It is still fairly easy to observe the waning gibbous Moon when it comes up fairly early in the evening, but as it rises closer to midnight, it becomes less convenient to observe it in the evening. However, since it is then visible after dawn the next morning, it can still be easily observed, if you remember to look for it.

 The Last Quarter Moon doesn't come up until midnight, is due South at dawn, and sets in the West around noon. Since it doesn't come up until late, it may be difficult to observe at night, but you can still observe it the next morning, in the Southwest or West.

 A waning crescent Moon won't come until sometime well after midnight, and will be more and more difficult to observe, unless you get up before dawn, or watch for it in the morning, in the South or West. The first two or three days after last quarter, you can see it at any of these times, providing that you know where to look, but the last two or three days before the next New Moon, it will be too close to the Sun to see during the day, and you will only be able to observe it during the last hour or so before sunrise. Because of the difficulty of seeing it in this phase, observations of thin crescent Moons visible only before sunrise count more than any other type of observation.