Abstract: The relative phase between the neighboring nodes in the adjacent planes of Walker- constellation was introduced as the connecting parameter K. The motion equations in the body-fixed coordinates system of reference satellite were established to obtain the azimuth angle, elevation angle and range (AER) of the inter-plane laser links. Then, the extremums of AER and the variation rates were calculated numerically. Among the AER, the azimuth angle rate, with the maximum value inversely ratio to the minimum range, impacts the stability of laser links significantly. In some extreme cases, it would be too fast to track the laser beam because of large azimuth angle velocities. K=0 is a good trade off between the linksstability and the complexity of the network topology, and is fit for low earth satellite optical networks.