We study effects of gravitational waves which in the first order form a time-symmetric ingoing and then outgoing pulse of rotating waves. The influence of the angular momentum of these waves on the rotation of local inertial frames with respect to the frames at great distances is analyzed by solving the relevant Einstein equation to second order.
Also the apparent motions of the fixed stars on the celestial sphere as seen through rotating waves from the local inertial frame in the centre are calculated and displayed.