There are of plenty of pop science books about cosmology of the type extra good because formula-free.

That however is a BS approach. Talking around physics instead of writing it down – at least when it can be taken down from the realm of differential equations and monster integrals to simple formulae – only leads to misunderstandings, a false feeling of grasp and to wrong conclusions.

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Prof. Edward – Ned – Wright, PhD from UCLA uses a completely different approach. He makes the readers get their hands dirty with the required math right from the beginning in

Ned Wright's Cosmology Tutorial.

One can also use a kinda side-track and start at his

Cosmology Calculator

and use the links to get right into the mess.

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It's good to recall some high school stuff beforehand.

I) The power [in watts W] per unit area [in square meters m²] goes with the fourth power of black body temperature T [in kelvins K]:

P/A = σ T⁴.

That's the so-called Stefan-Boltzman law for a black body, that "σ" (small Greek sigma) is the Stefan-Boltzmann constant

σ ~= 5.67E-8 W/(m² K).

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II) The area A_S of a sphere of radius R goes with the radius squared.

A_S = 4πR².

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III) From I and II we get it that the total power P [in watts W] of an (idealized) star of radius R [in meters m] and Temperature T [in kelvins T] goes

P = 4πR² σT⁴.

When at a distance d from a star, that power once radiated gets distributed over a sphere of radius d and area A_d.

A_d = 4πd².

So the power P_d per unit area we measure at distance d goes like

P_d/A = (P/A) · R²/d².

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IV) Photon energy goes with frequency ν [in Hertz Hz = 1/s].

E = hν

with h ~= 6.626E-34 Js denoting Planck constant.

or with ν = c/λ like

E = hc/λ.

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V) Redshift z is the ratio of wavelength change Δλ and original wave length at emission λ_e :

z = Δλ/λ_e = (λ_o - λ_e)/λ_e = (λ_o/λ_e) - 1

or 1 + z = λ_o/λ_e

with λ_o being the observed wavelength.

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About Edward Ned Wright:

After graduating from Harvard in 1976 he worked on COBE, WISE and WMAP – milestones of contemporary astronomy no serious hobby astronomer would not have heard of, let alone professionals.

After teaching in the MIT Physics Department, he went to UCLA in 1981. He was science editor of The Astrophysical Journal, likely the second most influential periodical about physics after Physical Review.

Have fun!

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