Caption: A diagram for explaining the identities of spherical trigonometry.
We will use this diagram in eplaining how to relate the angular diameter of a telescope field of view (FOV) subtended at the Earth. to the angular diameter the FOV subtends from the celestial equator at the about the same height above the celestial equator as the location of the FOV on the celestial sphere.
Explanation:
Let R be the radius of the sphere.
The azimuthal curve has to be imagined.
We call the the length of this curve inside the FOV be &phi.
The angle &phi is the angular diameter the FOV subtends from the celestial equator at the about same height above the celestial equator as the location of the FOV on the celestial sphere.
We can now find an approximate relation between α and &phi$ that turns out to be 2nd-order good in small α and &phi$
Let the arc length be S. Now S = α*R and S = &phi*R*&sin(θ) = &phi*R*&cos(δ).
Solving for α gives &alpha = &phi*&sin(θ) = &phi*&cos(δ)
For almost all practical cases, this simple relation is all you need.
Now we need spherical trigonometry which is the angle the
UNDER CONSTRUCTION
Credit/Permission:
© Peter Mercator (AKA User:Peter Mercator),
2013 /
CC BY-SA 3.0.
Image link: Wikimedia Commons:
File:Spherical trigonometry vectors.svg.
Local file: local link: field_of_view_declination_2.html.
File: Telescope file:
field_of_view_declination_2.html.