motion of both objects (ignoring all other celestial bodies for the moment) is to say that they both orbit around the center of mass, referred to in astronomy as the barycenter, of the combined system. Supported mass Any mass on earth is pulled down by the gravitational force of the earth; this force is also called its weight. The corresponding 'reaction' is the gravitational force that mass exerts on the planet. If the object is supported so that it remains at rest, for instance by a cable from which it is hanging, or by a surface underneath, or by a liquid on which it is floating, there is also a support force in upward direction (tension force, normal force, buoyant force, respectively). This support force is an 'equal and opposite' force; we know this not because of Newton's third law, but because the object remains at rest, so that the forces must be balanced. To this support force there is also a 'reaction': the object pulls down on the supporting cable, or pushes down on the supporting surface or liquid. In this case, there are therefore four forces of equal magnitude: F1. gravitational force by earth on object (downward) F2. gravitational force by object on earth (upward) F3. force by support on object (upward) F4. force by object on support (downward) Forces F1 and F2 are equal, due to Newton's third law; the same is true for forces F3 and F4. Forces F1 and F3 are equal if and only if the object is in equilibrium, and no other forces are applied. (This has nothing to do with Newton's third law.) Mass on a spring If a mass is hanging from a spring, the same considerations apply as before. However, if this system is then perturbed (e.g., the mass is given a slight kick upwards or downwards, say), the mass starts to oscillate up and down. Because of these accelerations (and subsequent decelerations), we conclude from Newton's second law that a net force is responsible for the observed change in velocity. The gravitational force pulling down on the mass is no longer equal to the upward elastic force of the spring. In the terminology of the previous section, F1 and F3 are no longer equal. However, it is still true that F1 = F2 and F3 = F4, as this is required by Newton's third law. Causal misinterpretation The terms