The boundary of the Earth's magnetosphere, in the direction of the Earth-sun line, occurs at a distance
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The boundary of the Earth's magnetosphere, in the direction of the Earth-sun line, occurs at a distance where the kinetic pressure of the solar wind particles is equal to the (modified) Earth's magnetic field pressure. Show that the distance of the magnetopause from the center of the Earth, along the Earth-sun line, is given approximately by
where RE is the Earth's radius, ρm is the mass density of the solar wind, us is its undisturbed speed, and B0 is the surface value of the undisturbed Earth's magnetic field.
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