Figure 7: (a) Here is a space-time diagram of motions relative to the inertial frame in which \(O_1\), \(O_2\), and \(P_1\) are at rest. This can be seen as arising from the projection of each of their inertial trajectories onto a single point of space. \(O_3\) is in uniform motion. \(O_4\) is accelerating any old way. \(O_5\) and \(O_6\) are revolving around their common center of gravity \(P_1\), which (as noted above) is at rest. \(O_7\) and \(O_8\) are revolving around their center of gravity \(P_2\), which is in uniform motion.  (b) Here is the same situation viewed from an inertial frame in which \(O_3\) and \(P_2\) are at rest. Now \(O_1,\) \(O_2,\) and \(P_1\) are in uniform motion. \(O_4\) is accelerating any old way. \(O_5\) and \(O_6\) are revolving around their common center of gravity \(P_1\), which is in uniform motion. \(O_7\) and \(O_8\) are revolving around their center of gravity \(P_2\), which (as noted above) is at rest.