 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2008/iii/paper-73/1/vi/b/solution

Motion toward incoming cosmic microwave background radiation produces a blueshift. The photon occupation function of a blackbody depends on

h ν / (k_{B} T)

, so the same Doppler factor multiplies both frequency and effective temperature. Looking forward along the Sun's peculiar velocity, one obtains

T_{forward} = T_{0} \frac{1 + β}{1 - β} ≃ T_{0} (1 + β), β ≃ 300/ (3 \times 1 0^{5}) = 1 0^{- 3} .

2.73 K

gives

Δ T_{forward} ≃ 2.7 mK, T_{forward} ≃ 2.733 K .

The numerical total inherits the rounded mean temperature; the robust estimate is the positive millikelvin dipole increment.

 New to topics? Read the docs here!