RE: Equatorial Ceiling Dial

[Andrew James]

John, Fer, and others,

John asked : 
> Let's say you have a spherical room, built like a planetarium, where the
> walls curve up into the ceiling and you locate your mirror in 
> the center. ... Would the sunspot be perfectly round all the time?  

I think that the image of the sun coming from any part of the mirror (I'm
assuming it is a horizontal mirror for simplicity) is always circular, so
that if the mirror is very small compared with the room the sunspot will
approximate to a circle.  

However the circular image of the sun is blurred or enlarged by the apparent
size of the mirror (as seen from the sunspot, more or less) and this
enlargement will only be equal in all directions when the sun and its
reflection are both at the zenith.  From the sunspot, the mirror appears as
an ellipse and from the zenith it is the special circular case.  At sunrise
and sunset it appears almost as a line so the enlargement is almost purely
horizontal, and at intermediate altitudes the vertical enlargement of the
circle is less than the horizontal.  (The elliptical appearance of the
mirror varies slightly as you move up and down the image of the sun, hence I
write "almost".)

Regards
Andrew James

Re: Equatorial Ceiling Dial

[John Carmichael]

Hi Andrew

I agree with most of what you said, however I think that the most important
factor in determining the shape of the sunspot on the receiving surface is
principally determined by the angle of the sphere's surface to the mirror.
If the sunbeam hits the sphere's surface perpendicular to the tangent of the
sphere, then the sunspot will be circular.  Because the surface is
spherical, the sunbeam will always be tangent no matter where it hits.

Sounds like it time to experiment!

John

John L. Carmichael Jr.
Sundial Sculptures
925 E. Foothills Dr.
Tucson Arizona 85718
USA

Tel: 520-696-1709
Email: [EMAIL PROTECTED]
Website: <http://www.sundialsculptures.com>
- Original Message -
From: "Andrew James" <[EMAIL PROTECTED]>
To: "'John Carmichael'" <[EMAIL PROTECTED]>; "fer j. de vries"
<[EMAIL PROTECTED]>
Cc: "Sundial List" 
Sent: Monday, January 14, 2002 5:41 AM
Subject: RE: Equatorial Ceiling Dial


> John, Fer, and others,
>
> John asked :
> > Let's say you have a spherical room, built like a planetarium, where the
> > walls curve up into the ceiling and you locate your mirror in
> > the center. ... Would the sunspot be perfectly round all the time?
>
> I think that the image of the sun coming from any part of the mirror (I'm
> assuming it is a horizontal mirror for simplicity) is always circular, so
> that if the mirror is very small compared with the room the sunspot will
> approximate to a circle.
>
> However the circular image of the sun is blurred or enlarged by the
apparent
> size of the mirror (as seen from the sunspot, more or less) and this
> enlargement will only be equal in all directions when the sun and its
> reflection are both at the zenith.  From the sunspot, the mirror appears
as
> an ellipse and from the zenith it is the special circular case.  At
sunrise
> and sunset it appears almost as a line so the enlargement is almost purely
> horizontal, and at intermediate altitudes the vertical enlargement of the
> circle is less than the horizontal.  (The elliptical appearance of the
> mirror varies slightly as you move up and down the image of the sun, hence
I
> write "almost".)
>
> Regards
> Andrew James