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Unformatted text preview: 9mm for the CMB and 8.8 × 103 ˚ for the Sun.
For (c) (d) using E = /n ≈ 2.70kT , the result is 6.3 × 10−4 eV for the CMB and 1.4
eV for the Sun. Problem 2 (Ryden 2.3)
We assume that we are a sphere (as Ryden suggests) taking a radius of R = 1m.
(a) As we ﬂoat in space, we are absorbing CMB photons isotropically at a rate given by
the number density of the CMB photons x the surface area of our bodies x the speed
with which the photons travel (c):
Lnum = nγ 4π R2 c = 4.11 × 108 m−3 · 2.998 × 108 m/s · 4π · 1m2 = 1.55 × 1018 photons · s−1
(b) The rate at which we absorb radiative energy from the CMB is given by the energy
density of the CMB photons x the surface area of our bodies x the speed with which the
photons travel (c):
L = γ 4π R2 c = 4.17 × 10−14 J m−3 · 2.998 × 108 m/s · 4π · 1m2 = 1.57 × 10−4 J s−1 (c) The energy luminosity of the CMB is equivalent to the rate of energy input which is
the rate of increase in heat, L = Q/∆t s...
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