right , some meters a years, because there is some cosmic dust along its orbit
However it may exist in some remote part of the universe a planet moving along a 100 % clean path
This would be e perpetuum mobile
Instead of a planet I mentioned the atoms
Nobody has ever seen an electron falling on the nucleus

I did not go through Finsrud's Perpetuum Mobile

However if you need to create a magnetic field only at the beginning then it would be a perpetuum mobile ,regardless of the initial cost of energy
It is also possible both in theory and in practice to create a permanent magnetic field using super conductors

If you use the magnetic field to generate a current then the current itself shall induce in the super conductor a counter electromagnetic force which quench the magnetic field

The magnetic field is permanent as long as it does not supply energy

i always wondered about orbits of planets and moons. even with a perfect vacuum with no dust, wouldn't the velocity have to be perfectly adjusted too if there never should be a collision?

I guess this is the quirk then in such a device? The field weakens at the friction of the passing ball?

The centrifugal force Fc = m * V^2 / r

must match

The gravitational force Fg = g m * M / r^2

From the equation you get V

The exact calculus is much more complicated because the center of mass of the system is not the center of mass of the sun
The orbit is not a perfect circle
You should consider also a tangent inertial force

However the final result wiil be very close to the one you get from the simplified equation, the mass of the sun being much bigger than the one of the earth

two-body problems can still be solved analytically, you can reduce it to a one-body problem with fixed center. just replace the orbiting body's mass by its reduced mass (µ = (m*M)/(m+M)).
besides, circles are not the only stable orbits; in fact, any orbit is stable since the effective potential includes a repulsive centrifugal term which goes ~ 1/r^2, while gravity is ~ 1/r, so in principle you can't ever reach the center.
there are two orbit types (in theory there are three but the third one is not interesting):
1. passing by (high velocity): you get nearer to the center, pass by it and then fly away and never come back
2. oribt: everything else, you're captured in the potential. always stable

with stable i mean, of course, that the planet never falls into the sun. this is not correct, obviously, since the sun has a specific diameter and like that even not reaching its gravitational center could destroy the orbiting planet.

as for the moon: it is not a perfect perpetuum mobile, mostly because it pulls on earth's water and the friction on earth then drags energy out of the moon.

Interesting, I searched for that, and I ended on Tidal Acceleration
But it appears that your description is only the case for moons that orbit faster than their host planet rotates. Like Phobos moving much faster than its host, it slowly spirals down towards Mars. In turn the planet rotation speeds up (tides also exist on planets without liquid, the effect is just smaller).

The moon is slower, causes the tides on earth to move ahead of the moon which accelerates the moon and decelerates earth's rotation.

You did not get the point
I know that the atom of Bohr is just a rough rappresentation of the reality
But if it were also in conflict with the law of thermodynamics, it would have been refuted from the very beginning
Just a matter of common sense

I wonder how much you are into this stuff

In fact it has always been known that this model is wrong when you describe it classicaly, this is because moving charge emits an electromagnetic wave which drags energy out of the system. You can calculate how much time it has before the electron falls into the nucleus and its, as far as I can remember, less than a second. So yes, it contradicts classical electrodynamics. Bohr knew about that problem.
The thing is that the Bohr model was successfully describing the discrete energy lines of quicksilver with high accuracy, something which other models were not able to do, so there has to be some truth to it (and there is, namely the quantization of angular momentum and the probabilistic interpretation of quantum mechanics which give discrete energy levels).

There are many more problems with this model:
1. emission of electromagnetic energy
2. atoms are not "flat": conservation of angular momentom suggests flat orbits, though
3. angular momentum of the ground state is in fact zero, so there is no orbital movement
4. it contradicts Heisenberg's uncertainty principle: you cannot know momentum and position to an arbitrary high precision; alternatively you cannot know the complete angular momentum vector.


I've once read a physics book when I was... dunno... fourteen or so.

What does classic electromagnetism have to do with thermodynamics laws ?

Bohr claimed : let's assume that the moving charges do not emit energy in some conditions
He did not say : Lets assume that the termodynamica laws are not valid at atomic scale

Once you accept , by hyphotesis, that the electron does not emit energy then you accept also that certain orbits are stable even though the thermodynamics laws remain valid