Eclipses of the Sun by the Earth, seen from the Moon

1. ECLIPSES OF THE SUN SEEN FROM EARTH

The Moon's shadow is much smaller than the Earth, and because the apparent sizes of the Sun and Moon are so similar, the Moon's umbra (the dark, inner part of the shadow, corresponding to when the Moon covers the Sun completely during totality) is very small - never more than 269 km (167 mile) wide, and usually much smaller. (Sometimes it doesn't touch the Earth at all.) Total eclipses of the Sun happen about twice every three years, but any given place on the Earth experiences a total eclipse only once every few hundred years.

The Moon's orbital period is 27.3 days, corresponding to an orbital speed of 1.03 km/s, or 3697 km/hr. However, there are two effects that cause the Moon to cross the Sun more slowly than this speed would suggest. Firstly, rotation moves the Earth's surface eastwards away from the shadow, so the shadow's speed across the ground is slower than its space velocity by an amount that depends on latitude [rotation is zero at the poles]. Secondly, the Earth is moving round the Sun, which causes the Sun to move eastward -against the background stars- at just under 1 deg/day. As it moves eastwards in its orbit, therefore, the Moon must "catch the Sun up": the space velocity of its shadow relative to the centre of the Earth is about 8% lower than we naively think it is, so it takes longer for the Moon to cross the Sun. Using the Moon's synodic (new to new) period of 29.5 days will take this lag into account.

During a total eclipse the Moon moves in front of the Sun from west to east. Equivalently, the inner shadow, or umbra, of the Moon approaches you from the west at a speed of between 1700 and 3400 km/hr, depending on your latitude. The Moon appears to move very slowly as it creeps across the Sun - it takes around an hour to cover it completely. But watching the umbra rush towards you from the west at a speed of around 3000 km/hr provides a dramatic demonstration of how fast the Moon is really moving. You are actually seeing its motion as it hurtles round the Earth.

Both Moon and Sun subtend approximately 0.5 deg on the sky. (The Sun's apparent diameter is 0.533 deg at the Earth's mean distance of one astronomical unit) To go from first contact (Moon touching the western -right- limb of the Sun) to fourth contact (Moon touching the eastern -left- edge of the Sun) the Moon must move by twice its own diameter, or a full degree.


Earth's equatorial rotation speed	12756 * 3.142 / 23.93 = 1675 km/hr
	= 0.465 km/s
Moon's synodic period is 29.53 days
Space velocity of shadow is	384400 * 2 * 3.142 / 29.53 / 23.93 = 3418 km/hr
	= 0.949 km/s
=> Ground speed of moon's shadow at equator	3418 - 1675 = 1743 km/hr
Ground speed of moon's shadow at poles	3418 km/hr
Moon's angular speed across our sky is	360 / 29.53 = 12.2 deg/day
hence moon moves 1 deg in	1 / 12.2 = 0.082 day = 1.96 hr
and 0.5 deg in	1 / 12.2 * 0.5 = 0.041 day = 0.98 hr
Time from 1st contact to 2nd contact	1 hr
Time from 3rd contact to 4th contact	1 hr
Time from 2nd contact to 3rd contact	a few minutes only
=> Total duration of eclipse	~2 hr
Maximum duration of totality	7.5 minutes

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2. ECLIPSES OF THE SUN SEEN FROM THE MOON

The time between new moons is 29.5 days, so this is the length of the lunar day. The Sun rises once a month and sets ~15 days later, to rise again after a night of ~15 days. The daytime sky is black (because there is no air to scatter light and make the sky blue) and away from the Sun and Earth you can see the stars and other planets easily. The only real difference between day and night sky is that during the night the most brilliant star is nowhere to be seen.

The tilt of the Moon's axis with respect to the ecliptic is close to zero (compared with 23.5 deg for the Earth; notes), so there is almost no seasonal change in day length. The Sun is always close to the celestial equator, so no matter where you are (except at the poles) or what time of year it is, it rises due east and sets due west. At high latitude it simply describes a lower arc across the sky.

Earth can be seen from only one hemisphere of the Moon, known as "Earthside". At any given location, Earth is always in approximately the same position in the sky; it doesn't rise or set. Lunar observers find it difficult to convince themselves that anything is moving, least of all that the Moon is in orbit around the Earth. On the Moon's equator at longitude zero Earth is overhead; at high latitudes it is lower in the sky and at the "terminators" (the extremes of Earthside, longitude +90 and -90 degrees) it is on the horizon. Observers in the southern hemisphere have the disturbing experience of seeing the Earth upside down, i.e., with its north pole downwards. Night is never very dark on Earthside because the mother planet is always hanging there, waxing from half to full, then back to half again over the 353 hours of the lunar night.

Just as the Moon does here, the Earth goes through its phases once every 29.5 days. When the Sun crosses the meridian (the zenith for observers on the lunar equator), the Earth is "new", i.e., dark. When the Earth is full the Sun is directly behind the Moon and it is night. Sometimes, when the Earth is new, the Sun passes behind it and observers see a solar eclipse.

During a solar eclipse the Sun moves behind the Earth at the same speed as the Moon moves in front of the Sun during a solar eclipse on Earth. But the Earth isn't orbiting the Moon and doesn't move across the sky; rather, Earth's shadow is hanging there in space and the Moon blunders into it. Lunar observers, though, see the shadow rushing towards them across the ground, providing dramatic proof that the Moon is moving relative to the Earth.

As the Sun disappears, it grows fainter and redder, and observers see a glowing, reddish arc, or even a complete ring, lluminating the rim of the Earth. These rare and beautiful sunsets, which persist throughout the total eclipse, are caused by scattering and bending of light in the Earth's atmosphere. (The Moon looks coppery during a total lunar eclipse because it is bathed in sunset colours.) Occasionally, though, if there has been a major volcanic eruption on Earth, dust in the atmosphere will absorb most of the light, and the Sun will disappear abruptly into eclipse with no colourful phase.

Some solar eclipses are partial but, for any given point on lunar Earthside, total eclipses are more frequent here than there are on Earth, and last longer, because the Earth's shadow is bigger than the Moon. The maximum total eclipse occurs when the Sun crosses a full Earth diameter (termed a "central" eclipse).

Note that a total solar eclipse viewed from some point on the Moon is not exactly analogous to a total lunar eclipse seen from Earth (notes). When there is a central total solar eclipse, it is visible from anywhere on Earthside. Meanwhile, on Earth, observers everywhere on the night side see a total lunar eclipse, because the whole Moon is in the Earth's shadow. But if the solar eclipse is not sufficiently central, it is total only if you're in the right place on the Moon, and back on Earth, night-side observers see only a partial lunar eclipse.

For a lunar observer, the total phase of a deep solar eclipse lasts longer than the corresponding total lunar eclipse seen from Earth. This is because the latter phenomenon requires the whole Moon to be in Earth's umbra, whereas the former requires only the observer's location to be in Earth's inner shadow.

The ("stationary") Earth subtends 2 deg on sky, and the Sun 0.5 deg.


Sun's angular speed across the lunar sky is	360 / 29.53 = 12.2 deg/day
hence sun moves 1 deg in	1 / 12.2 = 0.082 day = 2 hr
sun moves 0.5 deg in	1 / 12.2 * 0.5 = 0.123 day = 1 hr
sun moves 1.5 deg in	1 / 12.2 * 1.5 = 0.123 day = 3 hr
sun moves 2.5 deg in	1 / 12.2 * 2.5 = 0.205 day = 5 hr

Eclipses can last much longer than they do on Earth, because the Earth is 4 times larger than the Sun on the sky. How long exactly depends on how "central" the eclipse is, i.e., whether the Sun passes behind the Earth near the equator or near a pole. During a maximum eclipse, to go from first contact (Sun touching the eastern -left- edge of the Earth) to fourth contact (Sun touching the western -right- edge of the Earth) the Sun must move by 2.5 degrees, so such an eclipse lasts ~5 hr. From second to third contact takes 1.5 degrees, so the total phase lasts 3 hours. Less deep eclipses are correspondingly shorter.

From time to time, when the Sun is down and the Earth is full, watchers on the Moon can see a fuzzy dark blob moving slowly across the Earth - the Moon's shadow. When this happens, people on that small patch of Earth are seeing a solar eclipse.

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Notes

We cannot directly compare eclipses of the Sun by the Moon (solar eclipses seen from Earth) and eclipses of the Moon by the Earth's shadow (lunar eclipses seen from Earth) because they are reciprocal aspects of the same phenomenon - a lineup of Earth, Moon and Sun - but necessarily seen from a fixed viewpoint. The counterpart of a solar eclipse on Earth is not a lunar eclipse, but a solar eclipse on the Moon. And the counterpart of a lunar eclipse on Earth is an "Earth eclipse" on the Moon. However, there is no such thing as an Earth eclipse, because the Moon is too small; its shadow can never cover more than a small fraction of the Earth. Using the terminology of lunar eclipses, all "Earth eclipses" are partial. (A total solar eclipse on Earth is just a "partial eclipse of Earth" when viewed from the Moon.)

(An interesting aside.) Relative to spring insolation, the Earth's axial tilt effectively moves one to a latitude that is 23.5 degrees higher in winter and 23.5 degrees lower in summer - a total latitude excursion of 46 degrees. This explains why continental winters and summers are judged to be harsh. In spring a place gets the climate it "should have" for its latitude, and would have if the Earth's axial tilt was very small, like the Moon's. A simple comparison shows this idea works surprisingly well, at least for mid-latitudes.

For a particular latitude, compare its weather in midsummer and midwinter (when it's at its minimum and maximum "effective latitudes") with spring weather at latitudes -/+ 23.5 deg. Example: In spring, a location at 31.5 N is experiencing its "true" latitude. However, in northern summer, land at 55 N is tilted 23.5 deg towards the Sun, and has an effective latitude that is also 31.5 deg. So summer weather at 55 N should be like spring weather at 31.5 N - and it is.

Similarly, winter weather at 55 N should be like spring weather at 78.5 N, and summer at 78.5 N like spring at 55 N - and they are.

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