We find that the cosmic microwave background temperature and polarization power spectra measurements from Planck constrain the parameter Ωbh2 mostly through (i) the amplitude of Thomson scattering and (ii) a factor that ensures Thomson scattering does not violate momentum conservation of the baryon-photon fluid. This allows us to obtain two distinct but comparably strong constraints on Ωbh2 from the Planck data alone. They are consistent, showing robustness of the Planck Ωbh2 constraint. We can alternatively rephrase these constraints as (i) the change of the Thomson scattering cross section since recombination is less than ∼2 % and (ii) momentum during recombination is conserved to better than ∼2 % by Thomson scattering. Decoupling the eight various ways in which Ωbh2 affects the Planck data leads to H0 only slightly higher than in the standard analysis, (68.3 ±1.6 ) km /s /Mpc . The overall consistency of all Ωbh2 constraints does not suggest any problem with the standard cosmological model.