Moon duration

Silent Shrill

Hi, can anyone tell me why the moon has been up in the sky now for 15hrs? It came up around 1am, and it's still out at 2pm with another 2-3 hrs left before it goes from view. Date.....today, 26/08/16

SOPHIE THE DOG

Its not an unusual happening.
its unusual to see it from here - because of our grey skies (and because people don't look up enough).

Silent Shrill

SOPHIE THE DOG wrote: »

Its not an unusual happening.
its unusual to see it from here - because of our grey skies (and because people don't look up enough).

Thanks. There's only 24 hrs in a day, and we can only see the moon until it goes beyond the curvature of earth from our view. So if I can see the moon when it's directly over Mexico, (according to day&night), nearly on the equator, how is this possible?

SOPHIE THE DOG

Have read at this:
www (dot) earthsky.org/space/when-can-you-see-a-daytime-moon

ps200306

Silent Shrill wrote: »

Hi, can anyone tell me why the moon has been up in the sky now for 15hrs? It came up around 1am, and it's still out at 2pm with another 2-3 hrs left before it goes from view. Date.....today, 26/08/16

We can think about this by using the Sun as a proxy for the Moon. You're familiar with how the length of the day changes with the seasons, as the Earth tilts toward the Sun, right? The Sun is over the equator at the equinoxes and at a maximum declination of 23.5 degrees at the solstices. The Moon doesn't orbit in the Earth's equatorial plane but also varies in declination, up to a maximum of just over 5 degrees north or south of the equator.

Let's do an extremely rough and ready calculation. Let's suppose there are 360 days in the year and the Earth moves one degree around the Sun per day. This is close enough for our purposes. When will the Sun be five degrees north of the equator? It's simply the arcsine of 5/23.5 in degrees. The answer is just over 12, so we look up the length of the day for our latitude at 12 days before the autumnal equinox, i.e. on September 10th. Hey presto! ... it's 15 hours.

So when the Moon is at its maximum declination of 5 degrees above the equator, that's how long we expect it to remain above the horizon too!

EDIT: just realised these numbers are all wrong. I'll see if I can fix them up shortly.

ps200306

Silent Shrill wrote: »

Hi, can anyone tell me why the moon has been up in the sky now for 15hrs? It came up around 1am, and it's still out at 2pm with another 2-3 hrs left before it goes from view. Date.....today, 26/08/16

My last attempt at this was embarrassingly wrong, so I'll try another stab.

The orbit of the Moon around the Earth is close to the plane of the ecliptic, i.e. the plane of the Earth's orbit round the Sun. That means when the Sun is high in the sky in summer, the Moon is high also -- not necessarily at the same time of day of course, but whenever it crosses the meridian directly south.

In fact the Moon's orbit varies up to more than five degrees from the ecliptic, so it may be even higher than the summer Sun. Whereas the Sun moves a maximum of 23.5 degrees (the angle of the Earth's tilt) in declination north or south of the equator, the Moon may be up to 28.5 degrees in declination.

There's a formula that we can use to calculate the Sun's angle of elevation which will be useful. I've taken it from the Wikipedia page on the Solar Zenith Angle. The zenith angle is simply related to the elevation of the Sun above the horizon, so we'll use the version that uses elevation angle:



... where:

• is the solar elevation angle (how far above the horizon)
• is the latitude of the observer
• is the declination of the Sun (how far north of the equator)
• h is the hour angle of the Sun

Now, at sunrise the solar elevation is zero degrees, so we rearrange the above formula to calculate the hour angle of sunrise. We need to make one little adjustment. The formula is for the geometric position of the Sun. That means the centre of the Sun is on the horizon when its elevation is zero. But sunrise is conventionally defined as the point where the top limb of the sun touches the horizon and, what's more, this combines with the refraction of the Earth's atmosphere to make sunrise appear when the geometric centre of the Sun is nearly a full degree below the horizon.

So now we can rearrange our formula and fill in the values for the latitude of Dublin (53°) and the declination of the Sun for August 26th (10.3°, which I looked up in Stellarium). We are looking for the hour angle when the Sun is 1° below the horizon. Thus:



Microsoft Excel gives an answer of almost exactly 105°. This is the hour angle of sunrise relative to local solar noon. Since the earth rotates 360° in a day, or 15° in an hour, we divide 105° by 15° to get 7 hours. That's half a day (from sunrise to noon), so the full day is 14 hours. I looked up the length of the day on Aug 26th on timeanddate.com and it was just under 14 hours and 3 minutes -- pretty close considering that our simple formula doesn't take into account the variable day length due to the Earth's orbital eccentricity!

We should be able to use the same formula for the Moon as well as the Sun. We just swap out the declination of the Sun and swap in the declination of the Moon. If the Moon is at a higher declination than the Sun we should find that it spends more time above the horizon than the Sun does. To my puzzlement*, when I looked up the Moon's declination in Stellarium I found it was a full 6° higher than the Sun, whereas Wikipedia implies it should never be more than 5.14°. Nevertheless I ran the calculation and found the hour angle of moonrise to be 114.6°.

On the face of it, this looks like the Moon should be up for less time than the Sun, but there is a catch. The Moon is orbiting in the same direction as the Earth is rotating, and it's orbital period of 27 days means on average it moves 0.55° per hour in its orbit. As the sky rotates with the Earth's diurnal movement, the Moon moves slower by this amount. In fact, because the Moon's orbit around the Earth is quite eccentric the Moon's hourly motion in its orbit can be faster or slower than the average by about 10%.

Anyway, to cut a long story short we divide 114.6° by 14.4° and get a whisker under 8 hours. The Moon is above the horizon for twice that, or just under 16 hours. When we check the value on timeanddate.com we see it was 15 hours and 56 minutes. Bingo!

One final calculation shows that if the moon was at it's maximum angle to the ecliptic on our summer solstice, then our longest possible Moon at the latitude of Dublin would be in the sky for over 19 hours!


* EDIT: I discovered that lunar parallax can change the apparent declination of the Moon by up to a degree depending on the observer's position on Earth compared to the geocentric calculation, so the Moon can indeed be more than 5.14 degrees different in declination to the Sun.