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Geoff Butt wrote, inter alia

>...The magnitudes of these theoretical free ocean tides are calculated in the
>Admiralty Manual of Tides (1941) as a range of 1.76ft due to the Moon and
>0.80ft due to the Sun (each calculated for zero zenith distance and average
>lunar parallax).
>
>I find students who have been brought up on the notion that "the tides are
>caused by the Moon" find the magnitude of the solar component surprisingly
>large. However, picturing these influences coming into and out of alignment
>every 14 days or so makes the understanding of spring and neap tides easy to
>grasp. And also, if you picture the vectors, why the interval between high
>tides alters according to the phase of the Moon.
>
>.. only leaving the question of why there are two tides per day rather than
>one to be explained!
>
>Geoff Butt

========================

George Huxtable responds-

The tidal force on Earth from a body turns out to be proportional to its
mass and inversely proportional to the cube of its distance; which has an
interesting consequence.

By chance, the Moon and the Sun happen to subtend almost exactly the same
angle in the sky, seen from Earth. This implies that the ratio of the
volumes of Sun and Moon is almost equal to the cube of the ratio of their
distances. If Sun and Moon were made up of the same stuff (which they
aren't) so that their masses were in the same proportion, then the tidal
forces generated by Sun and Moon would be exactly the same. This would
imply that at neaps their effects would completely cancel, and neap tides
would be zero.

The fact that we observe the Sun component of tide force to be about half
that from the Moon implies immediately that the mean density of the Sun is
about half the mean density of the Moon. It's a cosmological deduction,
that can be made simply by measuring the surface of the sea.

Geoff's reference to the Admiralty Manual of Tides reminds me of my
Liverpool University days of 50 years ago, during which I enjoyed a 1-year
course in Oceanography, when that Manual was the course-book for Prof.
Proudman's lectures on tides. It so happened that my wife took that same
course a few years later.

I understand that the Manual was produced at short notice in the early days
of the 1939-45 war to meet the sudden need to train up thousands of
officer-recruits for the Royal Navy. It's good to see it still being taken
as a reference.

Geoff, tantalisingly, adds-

>.. only leaving the question of why there are two tides per day rather than
>one to be explained!

Geoff's contribution sounds rather authoritative, and I wonder if he would
be prepared to respond to his own suggestion, in explaining the two tides.

Otherwise, perhaps I could recall (or reinvent) some of the arguments I
learned half-a-century ago, if anyone is really interested enough to want
to understand why there are two tides per day. If any listmembers still
find that a puzzle, and seek an explanation, I'm quite prepared to have a
go if requested.

However, it usually needs several diagrams and much waving of hands in the
air, so it would be something of a challenge to do it in words only.

George.

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