Frame-dragging does very, very slightly slow down the Earth's orbit around the sun. We can see this more notably in the case of very very massive objects orbiting very very close to each other, e.g. two black holes. The reason they get closer together (and eventually merge), and in the process give off a bunch of gravitational waves that we can now detect, is that they gravitationally sap each other's orbital energy (via frame dragging), which energy goes into powering the gravitational waves. The same thing happens to the Earth and sun, just on a much, much smaller scale, because they're so tiny compared to black holes, and relatively far apart.

Even if it weren't for that, though, two objects in perpetual orbit around each other still wouldn't be a perpetual motion machine in the ordinary sense, because you couldn't get any useful work out of the system without then slowing it down. If frame dragging wasn't a thing, and two bodies were in a perfect orbit together, they would continue like that forever so long as you didn't try to take any energy away from either of them. If you did take some energy away, then they would get closer, and eventually stop orbiting each other when they merged.

Frame-dragging does very, very slightly slow down the Earth's orbit around the sun. We can see this more notably in the case of very very massive objects orbiting very very close to each other, e.g. two black holes. — Pfhorrest

The laws of General Relativity tell us that whenever a mass moves through curved space, it will emit gravitational radiation, causing it to lose energy and become more tightly bound to the mass causing the spatial curvature. Any two masses gravitationally bound together — whether they're stars, white dwarfs, neutron stars, brown dwarfs, black holes, or even planets — will radiate their kinetic energy away until they eventually merge. — Ethan Siegal

Source: No, Black Holes Will Never Consume the Universe

Is Siegal explaining the same thing you are in different terms or is frame-dragging unrelated to gravitational radiation? They both contribute to orbital decay given enough time?

Frame-dragging is what causes gravitational radiation. Basically, a moving mass moves what "stationary" is relative to it as it moves (this is frame dragging in general; the moving mass "drags spacetime", or at least inertial frames of reference, with it), so an oscillating mass (moving back and forth, like in an orbit) produces waves in spacetime as it drags spacetime back and forth with it, and those waves in spacetime are gravitational radiation.

Thanks. It appears that there actually is no force being applied to the Earth - it's just travelling at a constant speed through space curved by the Sun. No acceleration, no force. No force, no work done.

One thing that bothers me is that in circular motion, an approximation of planetary orbits, the direction of motion is continuously changing i.e. a planet's velocity is also changing continuously and change in velocity implies planet's are experiencing acceleration and that means the planet is being subject to some non-zero amount of force and that indicates actual work being done in keeping planets in orbit.

The "explanation" I offered in the first paragraph - mass curving space - doesn't seem to do the job then, no?

Also, take another known type of force-at-a-distance, magnetism. I don't recall any scientific claim that magnets bend space and yet it seems possible to put a magnetic object in orbit around another magnet. :chin:

Regarding perpetual motion machines, my understanding is that the biggest obstacle in constructing such machines is friction - the engineer's arch adversary. However, with force that acts at a distance, friction is not of any concern, no?

The "explanation" I offered in the first paragraph - mass curving space - doesn't seem to do the job then, no? — TheMadFool

In the orbiting object's frame of reference, it's not changing velocity. It's going in a straight line. "Straight" just looks curved to us who expect space to be flat. ("Straight" actually does look much much straighter for objects moving at a proper speed, c -- actually, what looks straight is defined by that -- but all the stuff that gets slowed down by the Higgs field etc curves a lot faster per its minuscule distance traveled; hence why such interaction gives rise to rest mass). So it's experiencing no acceleration. "Straight" in a curved spacetime is actually defined by whatever motion happens in the absence of acceleration: whatever path something in free fall takes. An orbit is just a free fall ("ballistic") trajectory that arcs "high" enough to loop back to where it started before hitting the thing it's falling toward.

Also, take another known type of force-at-a-distance, magnetism. I don't recall any scientific claim that magnets bend space and yet it seems possible to put a magnetic object in orbit around another magnet. — TheMadFool

Magnetic field lines spiral toward poles, not in ballistic arcs, so it's not really so easy (if it's even possible) to put magnetic objects in "magneto-orbit" or something around each other. In free fall, they'll move however makes their opposite poles touch, not in nice ellipses around each other.

Regarding perpetual motion machines, my understanding is that the biggest obstacle in constructing such machines is friction - the engineer's arch adversary. However, with force that acts at a distance, friction is not of any concern, no? — TheMadFool

Friction is the first line of concern, and frame dragging is basically a kind of gravity friction, which radiates gravity waves the same way regular friction radiates heat. But even if you did have a completely frictionless system, it would only continue in perpetual motion so long as you didn't extract any energy from it, which would make it at best useful for a battery: put energy in, later take the same amount out, with no loss. Which would still be really useful, but not a source of unlimited free energy like the usual perpetual motion people want them to be.

In the orbiting object's frame of reference, it's not changing velocity. It's going in a straight line. — Pfhorrest

This is the curved-space explanation I was referring to - has to do with non-Euclidean geometry. So the force observed from another frame of reference is just an illusion caused by space curved by the sun's mass.

Magnetic field lines spiral toward poles, not in ballistic arcs, so it's not really so easy (if it's even possible) to put magnetic objects in "magneto-orbit" or something around each other. In free fall, they'll move however makes their opposite poles touch, not in nice ellipses around each other. — Pfhorrest

How about electricity? Electrons in orbit around an atomic nucleus? I haven't come across claims that electric charge causes space to curve and so the explanation that electrons are actually traveling along a "straight line" in curved space doesn't work. A non-zero amount of work is being done by electrons in orbit then, no?

Friction is the first line of concern, and frame dragging is basically a kind of gravity friction, which radiates gravity waves the same way regular friction radiates heat. But even if you did have a completely frictionless system, it would only continue in perpetual motion so long as you didn't extract any energy from it, which would make it at best useful for a battery: put energy in, later take the same amount out, with no loss. Which would still be really useful, but not a source of unlimited free energy like the usual perpetual motion people want them to be. — Pfhorrest

It seems that to do work, we need to subtract from the total amount of energy in a system and if that system depends on the total amount of energy in that system, any extraneous work done with it will bring it to a halt.

How about electricity? Electrons in orbit around an atomic nucleus? I haven't come across claims that electric charge causes space to curve and so the explanation that electrons are actually traveling along a "straight line" in curved space doesn't work. A non-zero amount of work is being done by electrons in orbit then, no? — TheMadFool

Electrons don’t actually orbit, there’s some fuzzy quantum mechanical stuff that goes on there instead. Before QM existed, it was a problem in physics as to why electrons stayed in orbit and didn’t either crash into the nucleus or fly away instead.

It seems that to do work, we need to subtract from the total amount of energy in a system and if that system depends on the total amount of energy in that system, any extraneous work done with it will bring it to a halt. — TheMadFool

Correct.

:up:

Electrons don’t actually orbit, there’s some fuzzy quantum mechanical stuff that goes on there instead. Before QM existed, it was a problem in physics as to why electrons stayed in orbit and didn’t either crash into the nucleus or fly away instead. — Pfhorrest

But we can construct a planetary model of an electron orbiting a positively charged center, no?

That's basically a toy model; it's not actually true, but it's a useful false visualization for learning purposes.

Wikipedia on Atomic orbitals explains why in full, but the short answer is "a classical charged object cannot sustain orbital motion because it is accelerating and therefore loses energy due to electromagnetic radiation".

:up: So an electron is just there? That sounds even less plausible than it orbitting?

The electron is kind of smeared out along its orbital path, which is not a nice neat ellipse like you would expect of an orbit, but one of several weird flowery shapes. It doesn’t have a definitive position or momentum along that path, but its observed position or momentum at any moment will always be somewhere along that path. And it can only be on one of those specific weirdly shaped paths or another, jumping suddenly between them when it absorbs or emits a photon.