Re: Longest day of year?

Ken Starks wrote:
> Charlie wrote:
>
> > It is sometimes said that in the northern hemisphere,
> > the longest day of the year occurs around the summer solstice.
> >
> > Can anyone turn that into a simple, valid math statement?
> >
> > Can assume spherical earth and sun,
> > and the earth has fixed rotation and fixed Keplerian elements,
> > and anything else that seems reasonable.
> >
> > Enjoy.
>
> Relating to a nearby thread, there seems to be a lack of geometrical
> insight or visualisation in most of the replies so far.

I hope you include me among the exceptions; however, I
admit that it didn't help matters when I described things
rather poorly at first. Your clear presentation (along
with some others) is a welcome remedy.

Nevertheless, it remains true that, no matter how you
make your idealizations, there will be a so-called "time
equation" induced by the continuous change in the angle
of the earth's axis wrt the sun. (Or any other fixed
star, for that matter.) The date of earliest sunrise
always comes before the date of latest sunset. Since
the *changes* in the times of sunrise and sunset are
always out of phase, it does seem possible that subtle
effects can occur near the equator, where *all* effects
are small. Certainly the effect that Charles Bernier
mentioned, i.e. the one caused by orbital eccentricity,
must occur very near the equator. (But it's the *only*
effect of this nature, I think.)

This is why I expressed some doubt, in the face of
Astucias's expressions of certainty. However, he
spoiled his argument by linking it all to the tropics
and to the fact of the sun's passing overhead, neither
of which are relevant per se.

.

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