I asked exactly this question a while back - it does seem weird to be using an analogy that relies on gravity, to explain gravity.
One way you could picture it instead is that, rather than causing a dent in spacetime, gravity causes a ‘pinch’ distortion - like this - so that objects in motion keep going in straight lines, it’s just that the straight lines have been bent.
>Mass is Force divided by acceleration.
No. Force is not mass times acceleration. Force is the time derivative of momentum. Only in the special case that mass is constant does force equal mass times acceleration. Newton himself was careful to point this out. He was also careful to point out that the property giving rise to inertia and the property giving rise to gravitational force appear to be the same thing, but that he did not know the significance of that.
>Now that I’m thinking about, is gravity a force or a pseudo-force? Since it’s just an effect of the coordinate system, I’m thinking it’s actually more of a pseudo-force (like the Coriolis force, for example).
Yes, this is fair. It was Einstein’s general theory that explained this. Mass makes the space around it accelerate radially outward, so that two masses require the addition of a repulsive force to maintain their distance. Although Newton did not know it, the two agencies he speculated about are identically the same - at least, according to Einstein.
I don’t understand this. Is it supposed to mimic 3D movement?
I agree and this same thought occurred to me a few years ago. The “warping” explanation actually explains nothing. It’s like saying that the universe rests on the back of a giant turtle which in turn rests on another turtle. After that, it’s turtles all the way down.
We have no direct way to measure the propagation speed of gravity, but as far as anyone can tell, gravity does move at c also.
No, it’s just a different analogy that doesn’t rely on gravity to demonstrate it - if you imagine spacetime as a flat sheet that, instead of being pulled down into a dip, is puckered or gathered by the gravity source - objects moving along that sheet in what they percieve to be a straight line actually end up curving towards the mass, because the geometry of the sheet has been warped by it.
I plead guilty to not pointing out that mass equals force divided by acceleration is an approximation which is valid only at velocities that are small compared to c.
True, but not what Napier was talking about. Momentum is mass times velocity, and as Napier said, force is the derivative of that with respect to time. If mass is constant over time, then force is simply mass times acceleration. However, if it is not, force is mass times acceleration plus velocity times the change in mass over time. Or, in symbols:
P=mv
F=ma+v(dm/dt) If mass is constant, dm/dt=0, and the second term is 0.
To be even more pedantic about it, dm/dt is not zero but merely so small that the term vdm/dt is so small compared to mdv/dt that it can be ignored. That’s why F = ma is an approximation.
But after they pass the planet, they curve away again?
No, paths always curve towards other masses. It’s just that when you’re far away, they don’t curve very much.
Correct; gravity is the same sort of force as the Coriolis force, or centrifugal force. It’s a matter of semantics whether you consider such forces “real”, but you should assign the same status to gravity and Coriolis.
On the question of relativistic mass, in the terminology used by modern physicists, “mass” refers strictly to what might be called “rest mass”, the energy an object or system has in a reference frame where it has no momentum. This is actually strictly conserved for a closed system, and a collection of photons, for instance, can and usually does have mass, even though an individual photon by itself does not. What’s sometimes referred to as “relativistic mass” is usually just referred to as “energy” by physicists. And energy which includes kinetic energy is not gravitationally equivalent to mass: If you travelled past the Earth at sufficient speed, for instance, you might find that it had sufficient total energy confined in a small enough space that, were all that energy mass, it would collapse into a black hole. But something is either a black hole or it isn’t; two observers travelling at different speeds can’t disagree on whether something is a black hole, and the Earth isn’t one.
Don’t we? The solar system is hurtling through space. Can we measure the change in direction of Jupiter’s velocity to get the direction of the gravitational pull on it from the Sun and then measure the time it took for the propagation of that pull?
Yes, but at a very nearly constant speed, which is the same as not moving at all. There are methods to measure the propagation speed based on interactions between the planets, but they’re not very reliable. We should very soon have direct measurements, though, once we detect gravitational waves (probably within the next half-decade or decade).
Something that I don’t believe was mentioned is that it is a stars gravity that can cause it to explode. A star has several forces acting on it that are in equilibrium - forces caused by the fusion reactions pushing outward balanced against gravity pulling inward.
When a star’s core ceases to generate enough energy to push it outward, it collapses in on itself very rapidly. The collapse causes a shock wave that expels the outer shell. This is a supernova.
Also, as a star burns energy, it loses mass so it’s gravity does become weaker.
Yes. My comment was not about reality, but about the picture Mangetout provided. If objects follow the paths of the lines in this picture, they would curve away from the object after they pass it.
In a sense, all forces can be considered abstractions. Certainly the nuclear (residual strong) force is a result of particles interaction, and similarly gravity is, from the quantum gravity point of view, a result of exchange of gravitons, and even a general relativist will point to distortions of spacetime as being the causative mechanism that results in the appearance of a force.
Gravity can be considered a characteristic of mass as charge is to charged particles like the electron or photon. Of course, there is not, to our knowledge, anything like negative gravity which pushes things away, and charge definitely comes in discrete quanta. (Whether gravity does or not is a question still unanswered, lying uncomfortably at the boundary between general relativity and quantum mechanics.)
In considering the effect of gravity upon a body, the use of conic sections–ellipses, parabolas, and hyperbolas–are useful both in graphical comprehension and mathematical plotting of orbits. And object which passes within the influence of a much larger, relatively slower moving mass will, in at least first approximation demonstrate a path of motion which, to the objective observer, resemble one of these curves; one that stays in orbit indefinitely will be an ellipse, while one that barely escapes orbit will make a parabolic path, and one that merely makes a fast approach will be in a hyperbola. None will ever “curve away” from the massy body on their own accord though an additional influence may create a path that is extemelly complex and convoluted.
Stranger
Has someone demonstrated gravity by measuring it between two masses, one not being our panet? If I put two masses on a level table would they attract? Is there direct experimental evidence of this? On a human body scale? Can they do this in orbit?
Ah, gotcha. I hadn’t checked out that image before. While the specifics don’t really match, Mangetout does have the right idea that “curvature” represents a distortion in the distances between points. He just didn’t illustrate the right sort of distortion.
Maybe it’s the case that, unless you look at the math involved, no analogy makes sense.
Because, for the above analogy to make sense,
“space-where-objects-exist-and-move” would have to be some sort of grid that existed in some “greater, grid-less space”, into which the grid points of “space-where-objects-exist-and-move” could be warped (like in the ‘pinched space’ example above)
Objects in our universe are compelled, for some reason, to follow the gridlines in the “space-where-objects-exist-and-move”. Why don’t they just go “straight” in this “greater, grid-less space”?
I assume that this “greater, grid-less space” does not exist, and the image in the link showing the ‘pinch’ in space is yet another failed attempt to show the lay people what the equations are telling us.
As a side note, can any of our resident physicists show us the equations for mass warping space? Maybe a two-dimensional space example to keep it simple? Or are they too complex?
