Question

The red supergiant star Betelgeuse has an effective temperature of 3500 K and an angular diameter of 0.045 arcsec. Assuming the star is 200 pc away, determine the luminosity L of Betelgeuse. Express your final answer in solar luminosities, L⊙, to three significant figures.

Use the small‑angle approximation to determine the physical diameter of Betelgeuse. Convert arcseconds to radians before applying the small‑angle approximation.

Answer 1

Just like in stars far too many question depend on the equations of stellar structure, in cosmology too many questions
depend on the basic underpinnings of the FLRW universe. We will summarize the results below. This information
comes from Ch. 4 and 5 of Ryden (2003).
1.1.1. The FLRW Universe
In accordance with the cosmological principle (that there be a set of observers that see the universe as homogeneous
and isotropic), the spatial extent of the universe must have uniform curvature (unless we move to truly non-trivial
geometries). This restricts our metric to be of a form known as the Robertson-Walker metric
ds2 = cdt2 − a(t)
2

dx2
1 − κx2/R2
+ x
2
dΩ
2

(1)
where κ = −1, 0 1 and R scales κ. Another way of writing this metric (and making it perhaps more palatable) is
ds2 = cdt2 − a(t)
2