If a massive object (A) is located at (a,b,c) and I am located at (d,e,f) I will experience a gravitational effect from (A). Now, If (A) is moving as it passes through (a,b,c) will I feel a different effect?
With most models of gravity all objects in the universe attract each other so the answer is yes but you will only feel an effect if the object is large enough for your senses to detect. There is a gravitational attraction between my pen on my desk and me but as the product of our masses is so low compared to me and the earth I can’t feel it. Mountains and other geologic formations can cause graviational anomalies but even that takes sensitive instruments to detect.
Classically, it doesn’t matter whether the object is stationary or moving at the instant it’s at point (a,b,c) because:[ul]
[li]Classically, the speed of gravity is infinite, and [/li][li]Classically, the gravitational interaction is not velocity dependent.[/li][/ul]I should note for completeness that what happens will be different, but the force at the instant in which the mass is at (a,b,c) is the same.
Relativistically, it’ll be subtly different, because in GR, it’s not mass which causes gravity per se, but rather energy and momentum; a moving object will have more of each and will warp space differently than a stationary object.
The whole idea of mass gain with motion always bothered me. Let’s take two spaceships and have them moving relative to one another at close to c. If I am on ship A I can regard myself at rest and ship B as moving close to c. Thus ship B has a large mass. Perhaps even so large that it would lie within it’s own Schwartschild radius and constitute a black hole. From the POV of ship B, though the situation is reversed and I am the one in danger of becoming a black hole. The usual solution to the twin paradox ( a related problem but with time dilation ) was to consider the accelerating body as the one that was “really” showing the effects of time dilation after the journey. Is the solution to this seeming paradox similar?
Gravitational fields do look different for an object moving relative to an observer, but it’s not in the simple way you might suppose from the notion of “relativistic mass”. Relativistic mass is somewhat of an outdated notion, and it’s much more useful to consider the “mass” to be the rest mass of the object (which is, for instance, what matters for determining if something is a black hole). So a thing won’t turn into a black hole just by moving relative to you.
There will be changes in the gravitational field observed, but you can’t discuss those changes without a full tensor model of GR, which would take at least a semester.
Thanks but I should have been clearer in my OP. I’m not asking about relativistic mass. I’m instead trying to get some idea of how the effects of gravity differ between Newton and GR.
Would the moving mass cause an increase in the gravitational force or just cause a directional change or would it be some kind of frame dragging effect? I know there’s no force per se in GR but I don’t know how else to ask the question.
I’ve actually studied some tensor algebra but that doesn’t seem to help me understand the stress energy tensor or how GR works. I also have Schutz, but I’d like to have some idea how gravity works before I start it.