A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Bob Crawley
Date: 2021 Jan 12, 01:43 -0800
I hope this is not too much off topic as it's not really navigation. I've been worrying away at this for the last few days and would be interested to know if my understanding is along the right lines. I'm well aware that the more mathematically talented could resolve the issue easily but I wanted to get an understanding of what was physically happening. At least I think I now understand eclipses better than before. Any views appreciated.
BobC 52N 1E
The BBC In Our Time episode on Eclipses is a good listen. In the extra material at the end one of the speakers mentions the 04DEC21 0735 eclipse, which occurs over the Antarctic Peninsula. It is unusual because the shadow travels east to west rather than west to east as per normal.
Mathematical Theory of Eclipses by Buchanan seemed a sensible place to start but whilst it helped it didn't help me to understand what was happening.
Trying to work out the east to west movement took a little time. Although I was aware of the Moon creeping east while it moved across the sky to the west, I realised that I was not really sure why a normal eclipse shadow moves west to east (See Why Does the Eclipse Move From West to East? Is the Eclipse Going Backward? FreeSchool) .
There are several websites that show the ground path but I wanted to understand what was behind this. Mentally simplifiying the problem by ignoring axial tilt, stopping the Earth's rotation and considering the relative velocites helped. As both the Earth and Moon travel around the Sun in the same orbit then the Earth's orbital velocity can be ignored. That leaves the Moon moving across the Earth's surface west to east at about 3680kph. At the equator the shadow should pass across from west to east in about 3.5 hrs. However, the observer on the surface is moving in the same direction at 1668kph which slows the movement of the shadow to around 2000kph across the surface but still leaves it moving west to east.
Visualising what is happening in 3D is tricky. Being in the southern hemisphere made it a bit harder at first. This simulator was useful in verifying the eclipse tracks as was this alternative one. There is also an explanation here.
The Moon - Earth system should revolve about an axis through the Barycentre, inside the Earth about 1700km beneath the surface, and perpendicular to the Earth-Moon axis.
The width of the cone of the Moon's shadow on the Earth varies between 100km and about 240km.The ellipticity of the shadow will vary according to the angle between the Earth's surface and the Sun-Moon line i.e. at noon nearly circular but a thin ellipse if the angle is small.
The direction of the axis of the cone of shadow is along the Sun-Moon axis which is determined by the difference in their declinations. This should be almost parallel to the Earth-Moon axis and rotate around the axis through the Barycentre although offset from it.
The Barycentre - Moon line is not necessarily co-incident with the Sun-Moon axis: the cone of shadow should be parallel to this, or nearly so.
For the 04DEC21 eclipse we can consider an observer at, say, 80S 60W at about 0740UTC. The Sun does not set and it is near to the Southern Summer Solstice. The Declination of both the Sun and Moon are around 25S with that of the Sun edging northwards and of the Moon southwards. This would move the shadow cone from north to south while the rotation of the Moon would move it from west to east. The eclipse has a durarion of less than an hour so the movement of the Earth's surface at 80S would not be very significant at something like 250kph. At 0740UTC at 60W the local time will be 0340 and the Sun+Moon will be the other side of the Pole.
The track of the eclipse shadow starts around Latitude 55S and initially moves south west turning southwards then, in the region of the antarctic circle, its starts to move from east to west finishing up at the Antarctic Circle moving north. The track is wholly on what would be the dark hemisphere were it not for the tilt of the earth. The way the track behaves illustrates quite nicely how the shadow cone is intersecting with the Earth as a sphere unlike an eclipse in lower latitudes which appears to move across the surface.
This all got me wondering if an eclipse could pass over the Poles and it can. There is one in 2094 by which time I'll be very old.
I also wonder what the implications would be for a navigator, say Nansen who forgot to wind his watch, who wanted to find the time from a Lunar observation.
Websites found useful: