More Solstice Astronomy

In my last blog post, I skipped a bunch of steps in explaining why the Midnight Solstice Lunar Eclipse was such a rare thing. My friends were asking for clarification, so I thought I'd post it here, too.

[The whole shebang. The height of the sun and moon is what we're trying to figure out.]

This is the diagram from yesterday's blog post. We're looking for the answer that the moon at its highest point is 20 degrees from the zenith and the sun at its lowest point is 24 degrees from the horizon. The questions I want to answer are: How do the 43 degrees and the 23 degrees fit into this? Where do those numbers come from?

[The Earth and how Wolf Creek's sky fits into the picture.]

This diagram shows where the 43 degrees comes from.

It's a simple set of geometry that makes the number of degrees in the altitude of Polaris the same as the latitude of the place where you're standing. When we point a stick directly at Polaris, that stick is parallel with the Earth's axis, 43 degrees above the horizon. That's because Wolf Creek is located at a latitude of 43 degrees North. Perpendicular to that stick is the equator.

[On the Winter Solstice, the North Pole points 23 degrees away from the sun, giving us short days and a sun that's low in the sky.]

Once we know where the equator is, we can make use of another bit of geometry - the tilt of the Earth's axis compared to the plane of its orbit around the sun. This is 23 degrees.

At the Winter Solstice, the North Pole is pointing away from the sun. In the sky, this puts the sun 23 degrees below the line of the equator, which it crosses at the equinoxes. That's 90 (the zenith) minus 43 degrees latitude minus 23 degrees axial tilt, giving a final answer that the sun will rise to only 24 degrees above the horizon on the Winter Solstice. This is the lowest solar noon we will see all year.

With a full moon on the Solstice, we know that the moon is directly opposite the sun in the sky. That's why it's full. This means that the moon will be the same number of degrees above the equator as the sun is below it. The gives us 90 degrees (zenith) minus 43 degrees latitude plus 23 degrees axial tilt for a final answer of 20 degrees below the zenith or 70 degrees above the horizon. While the sun is at its lowest, the moon is at its highest. While we measure the sun at solar noon, we measure the moon at lunar midnight.

And that's what all those angles and mumbo-jumbo in the last blog post meant. Once we get a look at the whole picture piece-by-piece, it all makes sense. We can get an idea of just how rare it is to have a lunar eclipse at lunar midnight on the winter solstice. It won't happen again in our lifetimes.