**P. 4829.** Two stars of different masses \(\displaystyle m_1\) and \(\displaystyle m_2\) are moving in the gravitational field of each other, while there are no other forces exerted on them. At a certain moment the distance between them is \(\displaystyle d_0\), and their velocities (magnitude and direction) are such, as if they revolve about their common centre of mass at an angular speed of \(\displaystyle \omega_0\).

\(\displaystyle a)\) What is the maximum value of \(\displaystyle \omega_0\) if \(\displaystyle d_0\) is the greatest distance between the two stars, and what is the minimum value of \(\displaystyle \omega_0\) if \(\displaystyle d_0\) is the least distance between the two stars?

\(\displaystyle b)\) What is the value of \(\displaystyle \omega\) if the gravitational field cannot keep the system together?

\(\displaystyle c)\) What is the period when gravitation keeps the system together?

(6 points)

**Deadline expired on 11 April 2016.**