Is it possible to make a small skale model of the moon orbiting the Earth using magnets?

After learning about cintripital force and the earth's gravity keeping the moon in orbit of the earth. I was wondering if it was possible to make a smaller skale thing that prove the concept using magets(magnetic force representing gravity)

Theoretically you could, but I don't think it would be stable.

For an object as large as the moon with a relatively high speed (just about 1 km/s), the "air resistance" from the residual atmosphere and interplanetary medium is negligible. Thus, the moon can travel around the Earth at essentially constant speed for several billion years (*). If you tried to set up something doing a "free orbit" it would very quickly slow down due to air resistance and friction with whatever surface you have it rolling on, messing up your demonstration.

The second problem with this idea is that magnets don't obey a inverse-square force law, which means they don't have stable elliptical orbits at all (it can be proven that the only Keplerian system is 1/r^{2}). Instead, dipole magnets have a force law which is 1/r^{3} in the plane perpendicular to the polar axis, and with a cos(theta) dependence on the angle from the pole.

I'm not saying it's impossible, just that you'll have some tricky engineering to get it to work right. In fact, using a combination of magnets and gravity itself (recall those conical "coin vortexes" you sometimes see) to produce an effective inverse-square central force for a rolling steel ball just might work.

(*) Yes, for you nit-pickers, tidal friction has been slowly reducing the rotation of the earth, and as a consequence increasing the orbital speed of the moon, pushing it to higher orbits over time. The point is that friction experienced by the moon is negligible.

What about the 'moon' rolling inside an upside down cone with the 'Earth' at the bottom of it.

Yes, there'll be friction, but I don't think anyone wants it to go on forever, and the advantages (a stable round 'orbit', from which the 'moon' doesn't wizz off with any slight tilt and so a constant distance and constant repulsive force for some time) should be large enough to think about how to cancel out friction for the time someone can see it.

Do you know a problem were a ball or something is put inside an upside down cone without friction and it goes down in spirals until it reaches

h=v*v/g (don't know how to put square on this computer) and then moves up and down periodically?

If you hold it with repulsive force from underneath, it should work for a bit, shouldn't it?

Sorry, I'm not used to writing Physics things in that very language...

Hi, Kiteman. Technically, you've just described the raw HTML markup (which is also only available to paid members. The Rich Editor has little button icons to do the work . Non-paid members only see the bold and italic buttons; paid members also see underline, strikethrough, sub- and superscripts, etc.

The HTML only works (at least, this was true the last time we discussed it with Staff) for paid members (i.e., the same folks who have access to the Source button in the Rich Editor). For non-paid members, HTML markup is (or is supposed to be) stripped out.

There's nothing wrong -- it's difficult to do. The ones that I have seen around are covered, and have a coin slot with a sloped track to get the coin going. Once it starts rolling, it'll act like a flywheel or gyroscope and maintain stability.

You're exactly right! That's what I mean by "coin vortex" in my comment. In the U.S., you sometimes see at shopping malls these large inverted cones with a coin slot at the top. The idea is you drop the coin in and it rolls in a slot into the cone, then slowly spirals down to the bottom into a bucket. They're used as fundraising devices.

To get the pseudo-gravity correct, it's not actually a cone, but rather a hyperboloid of revolution.

The case you describe where the ball moves between higher and lower levels on the cone is exactly the "elliptical orbit" I was talking about. If you look at it in projection from above, you'll see that the tip of the cone is exactly at one focus of the ellipse. In that projection the ball follows a nice Keplerian orbit.

But those elliptical orbits are stable if and only if the effective "central force" is 1/r^{2}.

It WOULD be interesting as a question in stability. I suspect that if you made a magnet spin around the outside of the cone, you would be stable - you'd have created a synchronous AC motor.

preciselay what i meant, i have before built a magnetic levitator before that is sealed, not 100% airtight, but enough, to allow the rotating magnet inside, to keep moving for months, of course using very strong rare earth metal magnets. you see, what i have made, has essentially created a small bowl, not bubble, magentic repelling field, in which the magent, so long as it does not roll over, which i fiixed by adding a bit of lead to the bottom, will stay airborn. the idea i meant was to try and extend that bowl into a more round shape, and that if in an airtight environment, it would move for quite a long time, not using centificul force, though i thought it may work.

Hi, Kiteman. Technically, you've just described the raw HTML markup (which is also only available to paid members. The Rich Editor has little button icons to do the work . Non-paid members only see the bold and italic buttons; paid members also see underline, strikethrough, sub- and superscripts, etc.

yes, it is infact, there is only one problem with that, you will need to have the moon spining around the earth at a very specific speed, not too fast that it is flung out of orbit (im talking about in the scale model), and not s slow that it doesnt smash into the earth. whats more!, the whole thing will need to be in an airtight container, or else wind resistance will stop it indefinately. keep in mind the moon is spining around the erath at extremely high speeds, which i would roughly guess to be 1 million kilometers on 24 hours . i would say though you could acheive this by placing magnets carefully below the moon, and using a magent to repell the moon form erath, so that the moon will be pushed away from earth, up from the ground, and if in an air tight container, if it spins, it will likely never stop.

It's only about 86,000 km/day. The orbital radius is 384,000 km, and the period is 28.3 days. The rest is arithmetic.

The problem with magnetic repulsion is that it's unstable (Earnshaw's theorem). If you tried to do it with attraction and centrifugal force, then you run into the fact that magnets are not 1/r^{2}, which complicates the orbital mechanics.

active| newest | oldestTheoretically you could, but I don't think it would be stable.

For an object as large as the moon with a relatively high speed (just about 1 km/s), the "air resistance" from the residual atmosphere and interplanetary medium is negligible. Thus, the moon can travel around the Earth at essentially constant speed for several billion years (*). If you tried to set up something doing a "free orbit" it would very quickly slow down due to air resistance and friction with whatever surface you have it rolling on, messing up your demonstration.

The second problem with this idea is that magnets don't obey a inverse-square force law, which means they don't have stable elliptical orbits at all (it can be proven that the only Keplerian system is 1/r

^{2}). Instead, dipole magnets have a force law which is 1/r^{3}in the plane perpendicular to the polar axis, and with a cos(theta) dependence on the angle from the pole.I'm not saying it's impossible, just that you'll have some tricky engineering to get it to work right. In fact, using a combination of magnets and gravity itself (recall those conical "coin vortexes" you sometimes see) to produce an effective inverse-square central force for a rolling steel ball just might work.

(*) Yes, for you nit-pickers, tidal friction has been slowly reducing the rotation of the earth, and as a consequence increasing the orbital speed of the moon, pushing it to higher orbits over time. The point is that friction experienced

bythe moon is negligible.Yes, there'll be friction, but I don't think anyone wants it to go on forever, and the advantages (a stable round 'orbit', from which the 'moon' doesn't wizz off with any slight tilt and so a constant distance and constant repulsive force for some time) should be large enough to think about how to cancel out friction for the time someone can see it.

Do you know a problem were a ball or something is put inside an upside down cone without friction and it goes down in spirals until it reaches

h=v*v/g (don't know how to put square on this computer) and then moves up and down periodically?

If you hold it with repulsive force from underneath, it should work for a bit, shouldn't it?

Sorry, I'm not used to writing Physics things in that very language...

Some, like this, are designed with ramps to launch coins down the "well", as a means of raising funds.

Oh, and it's

h=v^{2}/gI've seen 'gravity wells', but I never managed to launch a coin in it. There's something wrong with me...

It's the "rich editor" available to pro members.

You'd have to type in codes:

< sub > makes things

_{small and low}.< sup > makes things

^{small and high}.< em > makes

italics.< b > or < strong > makes

bold.< u > makes

underlining.Add a / to switch it off.

(remove spaces from the pointy brackets)

I does for me if I can't be bothered to click on the rich editor...

Sourcebutton in the Rich Editor). For non-paid members, HTML markup is (or is supposed to be) stripped out.To get the pseudo-gravity correct, it's not actually a cone, but rather a hyperboloid of revolution.

The case you describe where the ball moves between higher and lower levels on the cone is exactly the "elliptical orbit" I was talking about. If you look at it in projection from above, you'll see that the tip of the cone is exactly at one focus of the ellipse. In that projection the ball follows a nice Keplerian orbit.

But those elliptical orbits are stable if and only if the effective "central force" is 1/r

^{2}.you see, what i have made, has essentially created a small bowl, not bubble, magentic repelling field, in which the magent, so long as it does not roll over, which i fiixed by adding a bit of lead to the bottom, will stay airborn.

the idea i meant was to try and extend that bowl into a more round shape, and that if in an airtight environment, it would move for quite a long time, not using centificul force, though i thought it may work.

I resemble that remark.

whats more!, the whole thing will need to be in an airtight container, or else wind resistance will stop it indefinately.

keep in mind the moon is spining around the erath at extremely high speeds, which i would roughly guess to be 1 million kilometers on 24 hours .

i would say though you could acheive this by placing magnets carefully below the moon, and using a magent to repell the moon form erath, so that the moon will be pushed away from earth, up from the ground, and if in an air tight container, if it spins, it will likely never stop.

The problem with magnetic repulsion is that it's unstable (Earnshaw's theorem). If you tried to do it with attraction and centrifugal force, then you run into the fact that magnets are not 1/r

^{2}, which complicates the orbital mechanics.