Month: August 2025

Gravitational Force and “Relativistic” Mass 

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 objects).

Actually, the quantity normally identified as the “mass” of an object is a property of the object itself (that used to be called “rest mass”) which does not depend on the observer, though it is true that the apparent resistance to acceleration (which used to be called “inertial mass” or “relativistic mass”) does depend on the object’s 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.

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).

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 Schwarzschild metric provides 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 “kick” 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.

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.

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).

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

Does mass increase with velocity? 

The claim of “mass increase with velocity” is based on using the word “mass” for something that is not a property of the object itself but rather depends also on the relative velocity of the observer.

Although this usage is not “wrong” and was fairly common in the early days, most physicists soon chose to use the word “mass” just for the invariant “rest mass” and followed the title of Einstein’s initial paper on the effect by just using the word “inertia” for the velocity-dependent quantity that used to be called the “inertial (or relativistic) mass”.

In order to prove that the observed “inertia” depends on the relative speed (and direction) of motion of the observer it is necessary first to define it.

One way is to define it as the ratio of applied force to observed acceleration, but this in turn requires a clear definition of force. For example you could perhaps look at the dynamics of a collision with an object of known mass at rest in the observer’s frame.

Or perhaps you could just read Einstein’s original paper on the subject.

Source: (915) Alan Cooper’s answer to Why does mass increase with velocity as an object approaches the speed of light? How can I prove it mathematically? – Quora

How do CO2 molecules heat their neighbours? 

By hitting them!

A CO2 molecule in the atmosphere, after having absorbed an infrared photon, is vibrating or rotating more vigorously than it was before. When such a molecule collides with a neighbouring molecule (most likely an N2 or an O2) some of that vibrational energy contributes to the speed or vibration or rotation of the one it hits.

The atmosphere doesn’t continue heating up though, because in the equilibrium situation the molecules in the atmosphere collectively emit radiation at the same rate as they absorb it. But they do this equally in all directions, so what they are absorbing from below gets re-directed and only half of it ends up going outwards (with the other half going back down to warm the Earth’s surface).

Source: (901) Alan Cooper’s answer to How does a CO2 molecule in the atmosphere, after having absorbed an infrared photon, transmit that energy to neighbour air molecules to heat up the atmosphere? What’s the mechanism? – Quora