IPhO_2025_Q1-07
Circular velocity in a galaxy (B.1)
IPhO · 2025 · Mekanika
Hydrogen and galaxies (Part B — Rotation curves of galaxies; official 2025 IPhO question). Model the galaxy as spherical and centered at a fixed point . At a point , let , let be the volumetric mass density, and let be gravitational potential energy per unit mass. A mass moves in a plane through . Determine the velocity of an object on a circular orbit passing through in terms of and .
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