Two particle system - find their angular velocities

[Alexanddros81]

Hi! I want to start solving problems from the text
'Orbital Mechanics for Engineering students' by Curtis 2nd edition.
Is this the right place to post?

Homework Statement

2.1 Two particles of identical mass m are acted on only by the gravitational force
of one upon the other. If the distance d between the particles is constant, what is the
angular velocity of the line joining them?
Use Newton's second law with the center of mass of the system as the origin of
the inertial frame.
{Ans.: ##ω=sqrt{2Gm/d^3}

Homework Equations

The Attempt at a Solution

Is this the right way to solve this problem?

 

[haruspex]

Looks good.