[chris (OP)]

Robert came to the talk I did at Madingley Hall's open day on April 1st (April Fool's Day, no less!); he's since been in touch with this question. Hopefully everyone here can help:

At times when you can see both Sun and Moon I have noticed that a line bisecting the illuminated section of the Moon does not pass through the Sun, as I had expected that it would. Years ago I asked for an explanation from another "we answer any questions" programme. The scientists gave the answer that it is "all to do with the Celestial Sphere," which I found not illuminating at all! Sorry.

I have wondered if it has something to do with light bending due to gravity, but the effect seems too pronounced for that, and Arthur Eddington would have gone to a lot of trouble unneccesarily when the phenomenon was under his nose and had been apparent since time immemorial. Is it an optical illusion?

What do you think?

[Colin2B]

No, not due to the bending of light, that's too small to notice and the reply "all to do with the Celestial Sphere," sounds like a cop out considering the explanation isn't complex.

The earth orbits the sun on a plane (known as the ecliptic). If the moon orbited the earth on that same plane then the centre of the moon, earth and sun would be aligned. However, the moon orbits the earth at an angle of about 5° to that plane. So the moon will sometimes be above, below or aligned with the plane depending on its position relative to the earth.
You can have great fun with a desk lamp and 2 balls to work out how the shadows look for various positions, on the other hand you can have even more fun in many other ways.

[jeffreyH]

I remember going into a lot of aspects of the moon's orbit when I was studying the Thomas Harriot papers. At one time I had a copy of the microfilm of the papers which I had transferred to CD. Both his moon and sunspot drawings were included. He is a bit forgotten to history which is a pity. I personally believe it was the correspondence between Harriot and Kepler that resulted in the laws of planetary motion.

[RD]

At times when you can see both Sun and Moon I have noticed that a line bisecting the illuminated section of the Moon does not pass through the Sun, as I had expected that it would...

The illuminated part of the moon you can see from Earth is not all of the moon which is illuminated.
If you included the illuminated part of the far-side of the moon, (wrongly called the dark-side),
then a plane bisecting the entire illuminated part would pass through the Sun.


https://wikipedia.org/wiki/Lunar_phase#Phases_of_the_moon

[evan_au]

a plane bisecting the entire illuminated part would pass through the Sun

This is almost a geometric definition - 3 points define a plane. If you make those 3 points the observer, the center of the Moon and the point on the Moons surface which is the center of the illuminated side (ie the subsolar point) then the plane will pass through the Sun. After all, the subsolar point points straight towards the Sun.

the moon orbits the earth at an angle of about 5° to (the ecliptic)

Wikipedia lists this characteristic of the Moon's orbit as "Inclination: 5.145° to the ecliptic".

To add to this, there are two points on Earth's orbit where the plane of the Earth's orbit around the Sun intersects the plane of the Moon's orbit around the Sun, and there is an opportunity for an eclipse on the two dates where the Earth reaches these points in its orbit in a given year.

We do not get two eclipses per year, because the Moon must also be at the right point in its orbit to lie on a straight line between Sun and Earth).

The actual date of this (potential) alignment drifts slowly over an 18 year cycle; the angle of inclination of the Moon's orbit remains roughly the same over this period, but its orientation in space precesses (like a spinning gyroscope).
See: https://en.wikipedia.org/wiki/Lunar_node