What is the longest time the Moon can stay in the sky?

Question

It is known that in northern latitudes the Moon, like the sun, can remain in the sky for a long time, a week or more. What is the longest time the Moon can stay in the sky?

Answer 1

In the polar regions, the Moon can be above the horizon for over 14 days, 19 hours. That's ignoring refraction and parallax.

At the north or south pole, the celestial equator is on the horizon, so a celestial body with positive declination is above the horizon at the north pole, and a body with negative declination is above the horizon at the south pole.

The Moon's sidereal period is around 27.32 days, so it takes roughly that long for the Moon to go through one declination cycle, but the exact cycle length varies a little, due to the complex nature of the lunar orbit.

Here's a plot of the Moon's declination, spanning two years, taken from a previous answer of mine on lunar declination.

However, the Moon's orbit is moderately eccentric (mean eccentricity ~0.0549), and it undergoes apsidal precession over a 8.85 year cycle.

In a given declination cycle, the time that the Moon is above the equator is generally not equal to the time that it's below the horizon. The difference is greatest when a lunistice (maximum or minimum declination) occurs near lunar perigee.

Here's a plot spanning from 2021-Jan-02 to 2038-Jun-29 showing the time between points when the Moon has zero declination (i.e., when it crosses the celestial equator).

We can see an extreme point at fortnight 400, which is 2035-Dec-22 06:50:43 TT to 2036-Jan-06 02:41:49 TT. That's a timespan of 14 days, 19h 51m 06s.

Here's a plot of the Moon's (geocentric) declination over that timespan.

So over that timespan, the Moon is above the horizon at the south pole.

Here's a short Horizons query for those dates.

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The time that the Moon is actually visible above the horizon can vary from this value. Firstly, the declination calculated for a point on the Earth's surface is slightly different to the geocentric declination. But more importantly, celestial bodies near the horizon are subject to atmospheric refraction effects. Typically, the Sun and Moon are visible when their centre is ~50' below the horizon. But refraction effects can be much larger, depending on the weather.

We can plot the Moon's elevation at the South Pole using my script in this answer. (The altitude at the South Pole is 2.835 km). Horizons also computes the times of moonrise and moonset. It claims that the Moon is visible when its elevation is ~1.88°; I'm not sure where that extra degree comes from. But anyway, that gives us a moonrise time of 2035-Dec-21 22:06:26 TT and moonset at 2036-Jan-6 11:45:30 TT, which means the Moon is visible for 15 days, 13h 39m 04s.

Here's an elevation plot over that timespan. The plot includes an estimate of refraction effects.