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angular diameter distance

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Fr.: distance angulaire

1) The ratio of an object's → linear size (l)
to its → angular size (δθ, in
→ radians), that is
D_{A} = l/δθ.
It is used to convert observed angular separations into proper separations
at the source.

2) In cosmology, a distance defined as the ratio of an object's physical
transverse size (l) to its angular size (δθ).
It is used to convert angular separations in telescope images into proper
separations at the source. The angular diameter distance
is defined by: D_{A} = l / δθ.
Consider a light source of size l at r = r_{1}
and t = t_{1} subtending an
angle δθ at the origin (r = 0,
t = t_{0}). The proper distance
between the two ends of the object is related to δθ by:
δθ = l / [a(t_{1}). r_{1}],
where a(t_{1}) is the → scale factor
at the present epoch. Therefore,
D_{A} = r_{1} / (1 + z).
The angular diameter distance has the particularity that it does not increase
infinitely with z→ ∞. It gets its maximum value at a
→ redshift of ~ 1 and then decreases for higher z.
Therefore, more distant objects appear larger in angular size. This is explained
by considering the size of the Universe when the light of the object was
emitted. At that time the Universe was smaller and therefore the object
occupied a larger fraction of the size of the Universe.
In other words, objects appear larger because the entire Universe acts
as a → gravitational lense.