Eclipse Reality

Here's the geometry of the March 14, 2025 lunar eclipse, from Wikipedia:

The gray-filled circle in the center is the umbra, the part of the Earth's shadow where the sun is fully hidden behind the Earth. Initially, I used this chart to position the moon shots in the composite picture, but I wasn't sure how accurate Wikipedia's diagram was, so I set about caculating the size of the umbra myself.

Here's how I did it:

The umbra is smaller than the Earth by the amount marked as c in the diagram. This can be calculated by noting that the ratio a/b = c/d. The amount a is the sun's radius minus the Earth's radius, b and d are the Earth-Sun and Earth-Moon distances, so c can be calculated as da/b. Plugging values into APL, I get:



So, according to my calculations, the umbra is about 2.6x larger than the apparent diameter of the moon. (The Wikipedia diagram is close, with the umbra being shown as 2.7x larger than the moon.)


To create the composite picture, I first overlaid the partial phase shots atop the totality picture and rotated them as necessary to make lunar features align. Then I drew a circle 2.6x larger than the eclipsed moon and moved the partial shots to where they fit on the circle. Finally, I moved the eclipsed moon so its top edge kissed a line drawn between the tops of the partial shots. The totality picture was taken about 4 minutes past the midpoint of the eclipse, so I placed the moon a little to the left of the center point. Here's the result, with the full umbral circle shown:

And here's how the composite compares with the Wikipedia diagram, with its 4% larger umbral circle:

Pretty good agreement.


Originally, I thought I could position the images by lining up the stars visible to the right of the moon in each image. But look what happens when you do that:

Whoa—the shadow is all cockeyed! What's going on??? (The partial-phase shots above were snapped at different times than those in the nice composite picture, but that isn't what causes the shadow misalignment.)

The problem is the Earth is rotating between exposures. Due to the rotation, each exposure was taken from a different location in space, and as you move around, the location of the Earth's shadow (at the moon's distance) changes amongst the stars. The first frame, on the right, was taken at 2:15 AM. By the time I took the totality picture in the middle, at 3:03, the rotation of the Earth had carried me about 600 miles to the east, and by the time the leftmost frame was taken, at 3:51 AM, I had moved another 600 miles further east. The rotation of the Earth causes the shadow to move towards the right over time, bringing the shadow edges on the moon closer together. And the inclination of the Earth's axis causes the movement to be downward to the right, resulting in the asymmetrical angle of the edges. (An animation of the complex twisting involved can be seen here: Time and Date Lunar Eclipse March 14, 2025.)

The umbra center moved from A to B in the hour and a half between the first and last exposures.

So the idealized picture is what you would capture if the Earth wasn't rotating—or if you were at the north or south pole, or were photographing the eclipse from a jet plane traveling westward at about 766 mph at 42° latitude. (Or if there were three moons right next to each other in space!)

Though it's simulated, the idealized picture is still an accurate depiction of what the Earth's shadow looks like—and what a lunar eclipse looks like over time, minus the Earth's rotation.