A Guide to Supermoons and Mini-Moons through 2030

This webpage describes why some full Moons appear larger than others do. While not a large effect (about 6.5% larger and 13% brighter than average; you gain another 1.5% in diameter and 3% in brightness by observing it overhead as opposed to when it rises), it may be noticable to you. These `large' full Moons are not rare; in fact, each year has a supermoon season that lasts a couple of months as you will see below. By the way, NO, IT IS NOT 14% LARGER AND 30% BRIGHTER THAN AVERAGE...

What is a Supermoon?
A Supermoon is a term that has arisen relatively recently in the popular press, and refers to a full Moon that appears significantly larger than normal.

What equipment do I need to see it?
None. Just look up. In fact, the full Moon isn't all that great to look at in a telescope because the shadows that make structures like craters and mountains easiest to see are shortest when the Moon is full. Your unaided eye, or at most, binoculars, is probably best for these events.

Why are some full Moons larger and brighter than others? How big is the effect?
The orbit of the Moon around the Earth is elliptical, so sometimes the Moon is closer and sometimes further away. The distance between the center of the Earth and the center of the Moon averages about 383,000 km, and ranges from about 356,000 km to about 407,000 km, or about +/- 6.5%. As a result, the angular diameter of the Moon as it rises ranges between about 29.5 and 33.5 arcminutes (60 arcminutes equals one degree). The closest approach of the Moon to the Earth is called perigee, and its location at maximum distance is called apogee. The amount that an ellipse is non-circular is given by its eccentricity. The eccentricity e = 0 for a circle, and averages 0.054, but ranges from 0.026 to 0.077 for the Moon. Because the diameter is about 6.5% larger, the area is about 13% larger than average, and so is the overall brightness. That is a rather small effect, easily outdone if the weather happens to have produced a cold front that clears out all clouds and haze in the atmosphere. It will be difficult, but perhaps not impossible, to notice a 10% increase in brightness. You'll have to decide for yourself.

Note you can find claims that the Supermoon will be 14% larger and 30% brighter than average. As is typical for internet sensationalism, these estimates are misleading: they compare the Supermoon with the smallest possible Minimoon and not the average Moon. As a result, the numbers appear twice as large as they should be. The percentages also look a little bigger when you compare with the smallest value and not the average. For example, a typical Minimoon has a distance of 407000 km from the Earth's center (also the distance when the Moon is rising or setting), compared with, say, 356761 km for the Feb 2019 supermoon. The respective angular diameters in arcminutes are mini = 29.3433 and super = 33.4754. Computing super/mini = 1.141, it looks like the supermoon is 14.1% bigger than the minimoon. Square super/mini to get an area and you have 1.301, or 30.1% brighter. These are the sources of the 14% and 30% numbers. However, if we take the average, avg = (super+mini)/2 = 31.409 and compute super/avg = 1.066, or 6.6% larger and (super/avg)^2 = 13.6% brighter than average. Similarly, for the minimoon, mini/avg = 0.934 = 6.6% smaller, and (mini/avg)^2 = 0.873 or 12.7% fainter than average. I find using the average to be a more honest comparison. No matter how you might try to spin this, it is a small effect.

It is also possible to pad the numbers with the 1.5% in distance you get when the Moon is overhead. With the eccentricity as high as 0.077, you'd think it should be 7.7% larger than average, but that eccentricity changes during the orbit so the effect is a bit smaller. The best way to tell what is going on is simply to plot values, which I do below.

Does the shape of the ellipse change with time?
Yes indeed! The Moon's orbit is quite complex
(Fig 4.6 in Espenak and Meeus, 2009), and varies in shape as the Moon responds to gravitational perturbations caused by the shape of the Earth and the location of the Sun. Perigee is smaller than the average distance by a factor (1-e), so the Moon ends up ranging between about 1.065 and 0.935 of its average angular diameter. According to Espenak and Meeus, over a 5000 year time interval there were 33,138 perigees, and they ranged from 356,355 km to 370,399 km. Similarly, apogees (maximum Earth-Moon distance) ranged from 404,042 to 406,725 km. There is a nice on-line calculator by John Walker that allows you to calculate the perigee and apogee distances for any year.

How big does it have to be to qualify as a Supermoon?
There are no set criteria. Greater than a 5% increase above normal seems like a reasonable definition, and that's what I adopt here.

What about when the Moon appears smaller than normal?
Yes, this occurs just as frequently as the Supermoon. Someone appears to have coined the term `Mini-Moon' (or `micro-Moon') to refer to such a case.

Can we tell the difference by looking at it?
If you were to put a normal-sized Moon next to a Supermoon or a Minimoon you could tell which one was larger. Alone in the sky that determination is a more difficult task. Have a look and see what you think. I've looked at these enough that usually I can tell, without remembering if it is supposed to be a supermoon or not.

Is there anything else interesting to look for during a Supermoon or Minimoon?
Actually, yes. In addition to the ~12% difference in diameter between these extremes, you will always see a bit more of the right side of the Moon (`Man in the Moon' is looking left) during a Supermoon and more of the left side ('Man in the Moon' looking right) during a Minimoon. The Minimoon is especially interesting that way because just around the left side of the Moon there is a huge basin, Mare Orientale (for the 'Eastern Sea') that just starts to come into view during a Minimoon. There isn't anything too exciting on the right side that a Supermoon reveals. Still, it is fun to think about being able to see around to the back side of the Moon that we normally never see (sometimes the press calls this the `dark' side of the Moon, though the Sun rises and sets there just like it does on the side that faces the Earth).

The side-to-side effect is about +/- 8 degrees in the angle where the Moon is pointed, and is called libration. The Moon's spin is, on average, synchronized with its rotation, which is why we see only one side of it. But during a supermoon the orbital motion is faster than normal so we begin to see around the right side during a full Moon as the Moon moves from right to left. The opposite happens with the minimoon. Putting pictures side-by-side that you might take of a rising Supermoon and a rising Minimoon will show both the size difference and that the Supermoon is looking more to the right. Would be a nice project to involve the kids in, but requires 6 months of planning.

The Moon goes through the extremes of eastern and western libration every month. These extremes line up with the full Moon phases during Minimoons and Supermoons.

How special was the November 13, 2016 Supermoon?
The 2016 Supermoon was noteworthy in that the center of the Moon will not come as close to the center of the Earth again until November of 2034 (see below). However, a closer examination of the data show that the 2016 Supermoon wasn't really any more special than other Supermoon. Let's look at the numbers.

The Walker calculator mentioned above shows that the extremes of the perigees and apogees aren't rare: in the twenty year period that spans 2011 - 2030, every year had an apogee within 400 km (i.e. within 0.1%) of the maximum value achieved in the entire 5000 year span, and 15 out of 20 years had two such apogees. Close perigees are a bit more rare, but not that unusual either. Between Jan 1, 2011 and Dec 31, 2030, seven years had a perigee within 0.1% of the minimum possible perigee, and 17 out of the 20 years had perigees within 0.2% of the minimum possible value. Apogees and perigees shift around relative to the lunar phase with a period of about 13.5 months. If perigee and the full Moon are lined up today, in 13.5 months there will have been nearly exactly 14 full Moons and nearly exactly 15 perigees, so the full Moon and perigee will again align. Hence, lining up a perigee with a full Moon is a common occurrence. As a result, maximum apogee and minimum perigee are nearly achieved most years for some full Moon, and often for several full Moons.

You can see this in the plot below, and in the following table, where I tabluate the data for a few Supermoons.

                  Perigee        Time Delay         
        DATE      Distance   Perigee to Full Moon  Perigee/Record
    Dec 4, 2017: 357,495 km       16h54m            1.0032            |
   Jan 21, 2019: 357,344 km       14h42m            1.0028            |
   May 26, 2021: 357,309 km        9h22m            1.0027            |
   Jan 21, 2027: 357,284 km       14h28m            1.0026            |
   Jul 13, 2022: 357,263 km        9h29m            1.0025            |
   Aug 30, 2023: 357,181 km        9h45m            1.0023            |
   Oct 17, 2024: 357,172 km       10h41m            1.0023            |
   May 17, 2030: 357,017 km        2h27m            1.0019            |
    Apr 7, 2020: 356,908 km        8h26m            1.0016            |
   Sep 27, 2015: 356,876 km        1h05m            1.0014            |
    Nov 5, 2025: 356,832 km        9h10m            1.0013            |
   Feb 19, 2019: 356,761 km        6h47m            1.0011            |
   Feb 10, 2028: 356,677 km        4h40m            1.0009            |
   Mar 30, 2029: 356,664 km        3h13m            1.0009            |
   Dec 24, 2026: 356,649 km        7h01m            1.0008            | FROM THE STANDPOINT OF AN OBSERVER,
    Jan 1, 2018: 356,565 km        4h29m            1.0006            |  THESE, AND ALL OTHER SUPERMOONS ARE
   Nov 13, 2016: 356,511 km        2h30m            1.0004            |     ESSENTIALLY EQUIVALENT                             
   Nov 25, 2034: 356,447 km        0h26m            1.0003            |
   Jan 14, 1930: 356,399 km        2h04m            1.0001            | ...AND YOU GET A COUPLE EVERY YEAR
    Jan 1, 2257: 356,372 km        0h26m            1.0000            |
5000-yr Record : 356,355 km          -              1.0000            |
Remember your position on the surface of the Earth can affect the distance to the Moon by several thousand km, larger than the distance differences between these Supermoons.

The Moon always looks larger to the eye when it is rising or setting because when it is high in the sky there are no reference points and it appears rather lonely up there surrounded by blank sky and a few stars. In actuality, the Moon is closer to you when it is overhead because you are standing right underneath it. Because the full Moon looks most impressive when it is near the horizon - and that's kind of the point of all of this, to look at the Moon and think `Wow, that looks big!' - let's see how it's angular diameter varies from month to month just after the full Moon has risen.

The red points on the above graph show the angular diameter of every full Moon between 2010 and 2025 at a time soon after it has risen so that it is still low in the eastern sky. To construct this graph I chose Houston as the location, but the results won't change by more than the thickness of the points for other locations in the continental US. Technically, the full Moon only occurs at a single time, so I picked the moonrise closest to the actual time of full Moon, and determined (from the planetarium program Stellarium) the angular diameter of the Moon when it was about 5 degrees above the horizon. A graph extending to 2040 that also shows eclipses is here:

The graphs show:

If you look very carefully at the first graph, it looks as if the Supermoon on 1/1/18 appears a tiny bit larger than the one on 11/13/16, even though the table shows that the 11/13/16 moon should have been closer. There are a couple of reasons for this. Consider the following graph, which depicts how the angular diameter of the Moon varies on the Supermoon nights of 11/13/16 (black curve) and 1/1/18 (red curve), and one night before and after the Supermoon on 1/1/18 (blue and green curves, respectively). By the way, the dates can be a bit confusing because the date changes at midnight. The dates in tables usually refer to the Universal Time (Greenwich England) of the time of full Moon or perigee. Perigee occurs at 11:24 11/14/16 UT and 21:56 1/1/18 UT and full Moon at 13:54 11/14/16 UT and 2:25 1/2/18 UT for these two events. Exact times are denoted with the letters 'P' and 'F' respectively on the graph (the time of perigee on 1/1/18 is just off the graph to the left at -8.5, ; CST is 6 hours earlier than UT).

For observers in North America the closest approaches occur on the nights of 11/13/16 - 11/14/16 (Sunday/Monday), and 1/1/18 - 1/2/18 (Monday/Tuesday), respectively. However, adjacent nights are essentially the same because the Moon's orbit isn't all that different from a circle, so it has to move a ways from perigee before the distance changes very much. This is why supermoons are relatively common - it is not as if it matters much to the distance if the timing between perigee and full Moon is a bit off. You'll notice that both perigee and full Moon precede transit on 1/1-1/2 (red curve), so by the next night (green curve) the distance increases a bit from the minimum value, while on the previous night (New Years Eve, blue curve), the distance starts to approach what it will be on the best night. But these differences are all tiny: it is highly doubtful you will be able to tell a change in the lunar diameter of less than 1% just by looking at it.

On all nights, notice the Moon becomes about 1.5% larger as it rises in the sky as we rotate underneath it. Perigee (P) occurs closer to moonrise on 1/1/18, and closer to moonset on the morning of 11/14/16, with both perigees nearly identical in distance. F denotes the actual time of the full Moon. If you were to watch the Moon rise and measure its size when it transits (and is closest to you), it turns out that the Moon is actually about 50 km closer when it transits the middle of the sky on the night of Jan 1-2, 2018 than it is on the night of Nov 13-14, 2016. You would never be able to tell this with your eye, and it would be extraordinarily difficult to measure this difference even with high-precision imaging cameras. It turns out that Moon is a bit higher in the sky (and therefore closer) when viewed from North America in early-January than it is in mid-November. At the level of a few hundred km, these tiny effects come into play.

Oh no! I missed it, or it was cloudy on that night!
No problem. Supermoons are not rare. In fact, just look the next night (or the night before it was supposed to happen); the Moon won't look any different to you. Compare the green and blue curves with the red one in the above graph. The difference in angular size over the 24 hour interval is less than 0.5%, not something you'll notice. Although it was technically a day past full, you likely to not notice that either, because the Moon looks more or less full for at least a day either side of the time of official full Moon.

Have fun with this. An easy connection to the cycles of our natural world.

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Patrick Hartigan