# Gravity darkening

$F_{\text{centrifugal}} = m \Omega^2 \rho$
where $m$ is mass (in this case of a small volume element of the star), $\Omega$ is the angular velocity, and $\rho$ is the radial distance from the axis of rotation. In the case of a star, the value of $\rho$ is largest at the equator and smallest at the poles. This means that equatorial regions of a star will have a greater centrifugal force when compared to the pole. The centrifugal force pushes mass away from the axis of rotation, and results in less overall pressure on the gas in the equatorial regions of the star. This will cause the gas in this region to become less dense, and cooler.