A satellite with mass $m = 100$ kg revolves around the Sun, on the orbit of the Earth. At some moment the satellite opens a solar sail, a thin mirror film and shaped as a circle of radius $r = 70$ m. During further flight the sail continuously changes its orientation so that its plane is always perpendicular to the direction of the Sun.

Ignoring the influence of the planets, find the period of rotation of the satellite with the open sail.

Consider the Earth's orbit circular. The luminosity of the Sun (light power) is equal to $L = 3.86 \cdot 10^{26}$ W, the mass of Sun is $M = 2 \cdot 10^{30}$ kg, gravitational constant $G=6.67 \times 10^{-11}~\mathrm{J} \cdot \mathrm{m}/\mathrm{kg}^{2}$.

Note: The momentum $p$ of a photon is related to its energy $E$ as $p c=E$, where $c$ is the speed of light.