Re: [Phys-L] saros

[John Denker <jsd@av8n.com>]

On 10/7/19 11:58 AM, Anthony Lapinski asked:

> Is the Moon's precession
> related to the saros and predicting eclipse dates?
1) Some links to the physics of the saros were given in a
previous note.

2) As for the specific question that was asked above: The
answer is basically no;  precession of perigee is not
relevant to the saros (although it is still interesting
for other reasons) as discussed below.

For starters, consider a circular orbit (zero eccentricity).
The concept of precession is is undefined ... but there
will still be eclipse seasons and a saros, for the usual
reasons;  see item (1) above.

Next, consider a slightly elliptical orbit.  
  2a) It may be that the a-axis lies in the plane of the ecliptic,
   while the b-axis is inclined to the ecliptic.
  2b) Or it may be that the b-axis is lies in the plane of the
   ecliptic, while the a-axis is inclined.

To a good first approximation, lunar eclipses don't care about (2a)
versus (2b).  The moon still crosses the ecliptic twice a month,
and if this happens at full moon you get an eclipse.

  2c) Precession converts (2a) to (2b), but the lunar eclipses
   still don't care.

Now, to a second approximation, if we look more closely, and in
particular if we look at solar eclipses, phase with respect to
the a-axis determines whether you will get a total versus annular
solar eclipse.

So precession is irrelevant to the /date/ of the eclipse but
is relevant (indirectly) to the /type/ of the eclipse.