•Dθ = D/θ where D is the real size of the object (e.g., standard ruler) and theta is the apparent angle on the sky (assuming no projection effects).
•Distance between ends of the ruler is given by D2 =
-ds2 = +R2(ts)r12 θ2 (see
figure) so D = R(ts)r1θ, so
•Dθ = D/θ = R(ts)r1 where r1 depends on the cosmology as before and is modified for spherical or hyperbolic cosmologies from the flat case (and keep in mind R(t)
varies)