Effect of increased apparent mass at relativistic speed on gravity

[Pratyeka]

Since an object's apparent mass increases as it approaches the speed of light, does it's gravitational forces also increases? (From a stationary observer's point of view)

 

[Ibix]

No. Mass does not increase - relativistic mass does, but the concept has been dropped for decades except in popsci.

There can be no effect of velocity on gravity because velocity is relativee. Right now you are doing 99.99999% of light speed with respect to a passing cosmic ray. Do you notice any gravity from yourself?

The gravitational field of a moving object is a different "shape" from a stationary one due to relativistic effects, but it is no stronger.

 

[Pratyeka]

Thanks for the clarification. Relativistic mass is the proper term I was looking for, but I used "apparent mass" instead, which is really not proper.

Any simple way to show how the shape of the gravitational field of a moving object differs from a stationary one?

 

[Orodruin]

Any simple way to show how the shape of the gravitational field of a moving object differs from a stationary one?

Not really. Gravitation does not work like that in relativity. In relativity, gravity is the geometry of spacetime.

 

[Ibix]

Any simple way to show how the shape of the gravitational field of a moving object differs from a stationary one?

Not really because, as Orodruin says, you're trying to visualise a curved 4d structure that isn't even locally Euclidean.

That said, you can make some reasonable statements. The field must be symmetric perpendicular to the direction of motion, and it must be shortened parallel to the direction of motion, at least in the sense that one could build a large sphere enclosing the object at a large distance where spacetime is nearly flat and this sphere must length contract.

Your personal experience of traveling through the field would be a sudden and rather sharp direction change - more sudden and sharper at high speed.

 

[Pratyeka]

Your personal experience of traveling through the field would be a sudden and rather sharp direction change - more sudden and sharper at high speed.

Would it be possible to simulate the orbit of an object moving through this field using a computer, if the programmer understand the math? Has it ever been done?

 

[Mister T]

Since an object's apparent mass increases as it approaches the speed of light, does it's gravitational forces also increases? (From a stationary observer's point of view)

No. There is no apparent mass increase. 100 years ago researchers attributed the behavior of fast moving subatomic particles to an apparent increase in mass, called the relativistic mass. But researchers were already abandoning that notion, attributing the behavior instead to the geometry of spacetime. Unfortunately, textbook authors continued to speak of relativistic mass well into the 1990's. One good reason for removing it was that students thought of it as a genuine generalization of the Newtonian notion of mass, thinking for example as you have that it could be used as a substitute for mass in Newton's Law of Gravitation. Of course it's not that simple. Instead general relativity had to be developed to explain gravitation

 

[Ibix]

Would it be possible to simulate the orbit of an object moving through this field using a computer, if the programmer understand the math? Has it ever been done?

You just use a particle passing near a stationary star and transform the result to a coordinate system where the star is moving. The only difficult bit is arguing about what is a "natural" coordinate system for the second part. There isn't an obvious choice, so the problem is not that we don't have an answer but more that we have no clear winner for the way to present it. You could imagine a 2d array of small spaceships passing through the field and do a "what it looks like" video from inside one of them, but you cannot draw a map of everyone's trajectories.

I'm not aware of anyone making such a video. However, there's a 1985 paper by Olson and Guarino that skips the whole issue of messy coordinates by simply comparing trajectories of test masses long before and long after the interaction with the star. Unfortunately I'm not aware of a freely accessible version of it. What it says is that if you close your eyes during the interaction and only open them when the object is past, the final trajectories look like you passed near a Newtonian object of mass $(1+\frac vc)\gamma M$, where $\gamma=1/\sqrt{1-v^2/c^2}$ and $M$ is the mass and $v$ the velocity of the mass. Note that the "closing your eyes" bit is a fairly major caveat to this - if you keep them open then you will get a lot of clues that gravity isn't increased for moving objects, but rather the field is a different shape (as I said before).

 

[vanhees71]

This is utterly misleading, and it's misleading as almost any argument with "relativistic masses" necessarily are. It's already a confusing mess in SR. In GR it misses even qualitatively the point. The beauty of GR is, among other things, that it unifies the concepts of "inertia" and "gravity", which are different phenomena within Newtonian physics with the equality of "inertial mass" and "gravitational mass" an empirical (and thus astonishing) fact.

Already SR teaches us that the inertia of a body is related to its intrinsic energy (i.e., the energy as measured in the rest frame of its center of energy (sic!)), which is the content of the famous addendum Einstein wrote to his big 1905 paper, containing the equation $E=m c^2$. Einstein himself abandoned the notion of a relativistic mass (or even many relativistic masses) pretty soon and substituted it with the modern notion of invariant mass. See the very nice article by Okun in Physics Today on this:

https://www.docenti.unina.it/webdocenti-be/allegati/materiale-didattico/346435

In GR it turns out that since "inertia" and "gravitational interactions" are unified that the sources of the gravitational field are not the masses but the energy-momentum-stress tensor of matter and radiation.

 

[Ibix]

This is utterly misleading,

I think that's the German translation of "a fairly major caveat". 😁

 

[Pratyeka]

Thank you everyone, that was really informative and definitely corrected my concept of relativistic mass.