{"id":1795,"date":"2025-08-29T04:27:57","date_gmt":"2025-08-29T04:27:57","guid":{"rendered":"https:\/\/qpr.ca\/blogs\/physics\/?p=1795"},"modified":"2025-08-29T04:53:09","modified_gmt":"2025-08-29T04:53:09","slug":"gravitational-force-and-relativistic-mass","status":"publish","type":"post","link":"https:\/\/qpr.ca\/blogs\/physics\/2025\/08\/29\/gravitational-force-and-relativistic-mass\/","title":{"rendered":"Gravitational Force and “Relativistic” Mass\u00a0"},"content":{"rendered":"

A Quoran asks: “I see questions about how mass increases with speed relative to an observer. Does the gravitational force between objects depend on the relative speed between them?<\/a><\/em>”<\/p>\n

I think the answer to this question is basically yes (although the way General Relativity predicts trajectories is not usually expressed in terms of forces between objects).<\/p>\n

Actually, the quantity normally identified as the \u201cmass\u201d of an object is a property of the object itself (that used to be called \u201crest mass\u201d) which does\u00a0not\u00a0depend on the observer, though it is true that the apparent resistance to acceleration (which used to be called \u201cinertial mass\u201d or \u201crelativistic mass\u201d) does depend on the object\u2019s speed of motion relative to the observer (and to the direction of the applied force relative to that motion). So if gravity were due to (rest) mass alone we might expect the answer to be no.<\/p>\n

But in General Relativity the trajectory of a freely falling object is governed by an equation in which all kinds of energy (and momentum) contribute. So it it reasonable to expect that a relatively moving object has a stronger effect than one which is stationary relative to the observer. However this is not completely obvious as we need to rule out the possibility that the momentum contributions cancel out those of kinetic energy (like they do in the equation E^2-p^2=m^2 for example).<\/p>\n

In order to really answer the question we need to restrict our attention to a situation in which the idea of an inter-particle force does arise as a good approximation. One such is the case of a relatively tiny mass in free fall around a larger one, in which case the\u00a0Schwarzschild metric<\/a>\u00a0provides a good approximation. And in that situation there is an extra non-Newtonian term in the effective potential so that the centripetal acceleration is slightly stronger when the distance is smaller (which gives an extra \u201ckick\u201d at perigee and contributes to the precession of orbits). This stronger attraction could perhaps be interpreted as Newtonian attraction with an increased gravitational mass, and since the orbiting body is moving faster when closer to the central mass it may well look as if the central mass increases with the speed of the orbiting observer.<\/p>\n

Perhaps it would also be possible to calculate the second derivative of the distance to the central mass in the coordinates of the observer and I would not be surprised to find that this is proportional to the combined total of mass and kinetic energy of that mass in those observer coordinates.<\/p>\n

On the other hand, we should NOT expect the gravitational force between two objects to appear stronger from the point of view of a third observer passing by at high speed (since that would shorten the orbital period while time dilation should make it seem longer).<\/p>\n

Source: (899) Alan Cooper’s answer to I see questions about how mass increases with speed relative to an observer. Does the gravitational force between objects depend on the relative speed between them? – Quora<\/a><\/em><\/p>\n","protected":false},"excerpt":{"rendered":"

A Quoran asks: “I see questions about how mass increases with speed relative to an observer. Does the gravitational force between objects depend on the relative speed between them?” I think the answer to this question is basically yes (although the way General Relativity predicts trajectories is not usually expressed in terms of forces between … Continue reading Gravitational Force and “Relativistic” Mass\u00a0<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[],"topics":[],"class_list":["post-1795","post","type-post","status-publish","format-standard","hentry","category-quora-answers"],"_links":{"self":[{"href":"https:\/\/qpr.ca\/blogs\/physics\/wp-json\/wp\/v2\/posts\/1795","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/qpr.ca\/blogs\/physics\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/qpr.ca\/blogs\/physics\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/qpr.ca\/blogs\/physics\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/qpr.ca\/blogs\/physics\/wp-json\/wp\/v2\/comments?post=1795"}],"version-history":[{"count":2,"href":"https:\/\/qpr.ca\/blogs\/physics\/wp-json\/wp\/v2\/posts\/1795\/revisions"}],"predecessor-version":[{"id":1800,"href":"https:\/\/qpr.ca\/blogs\/physics\/wp-json\/wp\/v2\/posts\/1795\/revisions\/1800"}],"wp:attachment":[{"href":"https:\/\/qpr.ca\/blogs\/physics\/wp-json\/wp\/v2\/media?parent=1795"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/qpr.ca\/blogs\/physics\/wp-json\/wp\/v2\/categories?post=1795"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/qpr.ca\/blogs\/physics\/wp-json\/wp\/v2\/tags?post=1795"},{"taxonomy":"topics","embeddable":true,"href":"https:\/\/qpr.ca\/blogs\/physics\/wp-json\/wp\/v2\/topics?post=1795"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}