At the solar wind has proton number density and speed

PHYSICS · Multi-part · Fermi University Physics · Astrophysics & Cosmology · Stellar structure, energy generation and evolution · Astrophysical fluid dynamics and plasmas

Stars from the Inside, Ch The Sun as a test: calibration, sound, neutrinos and a magnetised atmosphere

Problem

1\,\mathrm{AU}

the solar wind has proton number density

n = 6.0\times10^{6}\,\mathrm{m^{-3}}

and speed

v = 450\,\mathrm{km\,s^{-1}}

. Treating the wind as a steady, spherically symmetric, fully ionised hydrogen flow (so that the mass density is

\rho = nm_p

), use mass conservation

\dot M = 4\pi r^2\rho v

to estimate the Sun's mass-loss rate

\dot M

((a)) in

\mathrm{kg\,s^{-1}}

; ((b)) in

M_\odot\,\mathrm{yr^{-1}}

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