<p style="margin-bottom: 0in; widows: 0; orphans: 0">By Bill Pellerin</p>

<p style="margin-bottom: 0in; widows: 0; orphans: 0">Houston Astronomical Society</p>

<p style="margin-bottom: 0in; widows: 0; orphans: 0"><i>GuideStar </i>Editor</p>

<p style="margin-bottom: 0in; widows: 0; orphans: 0"> </p>

<p style="margin-bottom: 0in; widows: 0; orphans: 0">I was checking the weather forecast earlier this week. The weather web-site that I consulted contained additional information, including sunrise and sunset, and moonrise and moonset. It caught my attention that in a couple of days there would be day without a moonset. Interesting. Probably most of us think of the moon rising and setting on a daily basis, and on most days it does just that. After consulting the US Naval Observatory web site showing moonrise and moonset for my location I realized that there is one day a month without a moonrise and one day a month without a moonset. Actually, there’s one day per lunar cycle without a moonrise and one day per lunar cycle without a moonset.</p>

<p style="margin-bottom: 0in; widows: 0; orphans: 0">Let’s start at the beginning and see if we can figure out why this happens. The objects that are important in this analysis are the moon (obviously), the sun, and the earth. When the moon is at the same RA (right ascension) as the sun we have a new moon and from our point of view on earth we don’t see any illuminated part of the moon. RA is the coordinate system in the sky that corresponds to east/west. Declination is the measure of the distance of an object from the equator, so it measures distance north/south. If the new moon happens to be at the same RA <u>and</u> the same declination as the sun, we have a solar eclipse. When the moon’s RA is 12 hours different from the sun’s RA, we have a full moon. The earth time from new moon to new moon is 29.53 days (29 days, 12 hours, 43 minutes). This time takes into account the apparent movement of the sun over that time.</p>

<p style="margin-bottom: 0in; widows: 0; orphans: 0">These numbers get modified because the moon’s orbit is not circular, it’s elliptical, and keen-eyed observers of the moon will be able to see the difference between the moon at apogee (farthest from earth) and the moon at perigee (closest to earth). This is in part why some solar eclipses are annular and some are total.</p>

<p style="margin-bottom: 0in; widows: 0; orphans: 0">We know enough to figure out why there’s no moonrise on one day per lunar cycle and why there’s no moonset on one day per lunar cycle. Because the moon makes one trip around the earth (relative to the sun) in 29.53 days, we can say that the average angular distance traveled per cycle is 360 (re the sun)/29.53 which equals 12.2 degrees. (Strictly speaking there’s another one-degree due to the movement of the earth on its orbit, but we’re close enough.) Since the earth rotates 15 degrees per hour (360/24) we can easily ask how much later, per day, are lunar events (moonrise and moonsets). The answer is (12.2/15) * 60 = 48.8 clock minutes. This is certainly in the ‘ballpark’; I’ve found some references that say the difference is about 49 minutes per day and other say it’s about 50 minutes per day. To keep it easy, let’s go with a 49 minute per day difference.</p>

<p style="margin-bottom: 0in; widows: 0; orphans: 0">If the moonset on any particular day is more than 49 minutes before midnight, the next moonset will occur on the next day. However, if the moonset on our first day of interest is less than 49 minutes before midnight, there will be no moonset on the next day; the next moonset will be just after midnight on the third day.</p>

<p style="margin-bottom: 0in; widows: 0; orphans: 0">This is what a professional astronomer would call a back-of-the-envelope calculation. It doesn’t take into account a lot of details that would be important if an exact determination of the timing of this phenomenon is needed. I can think of several considerations that were left out – angle of the moon to the horizon, apogee and perigee of the moon, latitude of the observer, and probably a few other things that don’t occur to me.</p>

<p style="margin-bottom: 0in; widows: 0; orphans: 0">How does this fit with real data? To see, I analyzed data from the Naval Observatory moonrise / moonset chart for all of 2012. Based on this calculation I’d expect that the time between successive moonsets is 24 hours 48 minutes and 46 seconds. I looked at the data for 2012 for my hometown (Houston, TX) and found that the average time between moonsets for over 300 moonsets was 24 hours + 50.4 minutes. I’m in the right ballpark. The actual difference in moonset time on any given day can vary quite a bit. At my location the minimum difference in 2012 is 35 minutes and the maximum is 68 minutes.</p>

<p style="margin-bottom: 0in; widows: 0; orphans: 0">If you look at a moonrise / moonset calendar you’ll see that the day with no moonset is near the first quarter and the day of no moonrise is near the last quarter. If you think about the geometry of this, it makes sense.</p>

<p style="margin-bottom: 0in; widows: 0; orphans: 0">It’s fun to say to your astronomy friends, “Guess what? There’s no moonset next Thursday.” You’ll probably get a blank stare back.</p>

<p style="margin-bottom: 0in; widows: 0; orphans: 0">You want to see when you’ll have a day without a moonset (or a moonrise)? Go here:</p>

<p style="margin-bottom: 0in; widows: 0; orphans: 0"><font color="#0000ff"><u><a class="western" href="http://www.usno.navy.mil/USNO/astronomical-applications/data-services/rs-one-year-us">http://www.usno.navy.mil/USNO/astronomical-applications/data-services/rs-one-year-us</a></u></font></p>

<p style="margin-bottom: 0in; widows: 0; orphans: 0">…enter the year, specify that the ‘Type of Table’ is moonrise/moonset, enter your location, and click [compute table] and you’ll get a table of all moonrise and moonset events for your location. For locations outside the US, you can enter the latitude and longitude of the location. Note that the table does not take into account daylight saving time. So, if you observe daylight saving time, or the equivalent, be sure to compensate for that.</p>

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