It is not that I ignored that ignored the Ds-m, but that Ds-m does not enter into the logic of my claim.
Which is your problem, not mine.
No, not my problem at all! Omitting the sun to moon distance,
Ds-m was not an accidental omission at all. So long as flat earthers insist on a
close sun and moon the actual distance does no enter into the logic of what I was claiming.
Have the radius of the moon be larger than the Sun, you get total eclipses just fine. Have the altitude of the Sun not be fixed, you get an annular eclipse just fine. You aren't explaining your problem with this, you're just insisting it won't work. I don't want you to 'spell it out in such painful detail,' I want you to spell it out in any detail.
Sure "
Have the radius of the moon be larger than the Sun, you get total eclipses just fine" but
do what you like with the "
altitude of the Sun" will not "get an annular eclipse".
I would have thought that anyone could see that at a glance from any of the diagrams, mine or Wikipedia's.
That is the crux of what I have been asserting all along.
Annular eclipses do occur and eclipses with quite wide
umbras occur.
Solar eclipse, Path
The width of the track of a central eclipse varies according to the relative apparent diameters of the Sun and Moon. In the most favourable circumstances, when a total eclipse occurs very close to perigee, the track can be up to 267 km (166 mi) wide and the duration of totality may be over 7 minutes.
Repeating part of the earlier post.
Eclipse, Umbra, penumbra and antumbra
For spherical bodies, when the occulting object (the moon) is smaller1 than the star (the sun), the length (L) of the umbra's cone-shaped shadow is given by:
L = (Ds-m . Rmoon)/(Rsun - Rmoon)
where Rsun is the radius of the sun, Rmoon is the moon's radius, and Ds-m is the distance from the sun to the moon.
Modified from: Eclipse, Umbra, penumbra and antumbra
From this
if
(Rsun - Rmoon) > 0 then
L > 0, the umbral cone is
converging and the
umbral width is less than the moon's diameter.
and
if
(Rsun - Rmoon) < 0 then
L < 0, the umbral cone is
diverging and the
umbral width is greater than the moon's diameter.
Ds-m does not enter into it!
So please check exactly what I say!
| | Sun-moon configurations that produce a total (A), annular (B), and partial (C) solar eclipse |
Summarising!
For an
annular eclipse (Rmoon < Rsun) and
For an
umbral width greater than the moon's diameter
(Rmoon > Rsun).
Which are contradictory statements.To my simple mind, it would appear that the sun and moon sizes and heights usually accepted simply cannot come close to explaining what is observed. The sun to moon distance,
Ds-m does enter into calculating the size uf the umbra, but simply does not enter into the above discussion.
The only possibility that I can see is for the sun and moon to be much larger than 267 km (166 mi) and correspondingly much higher.
But then, you are changing the whole model of sun and moon sizes and heights, which changes the observed elevation angles of the sun and moon -
but so what! They are wrong anyway
.
You cannot simply change part of a model to fit one set of observation, but then find that it does not fit others.
Now, instead of just saying it
might be this and it
might be that, present something constructive and show some sizes and distances that could work.
I keep trying to hammer out the message that there is no coherent flat earth model - none "hang together".