Solar System in a Can May Reveal Hidden Dimensions

dylanduck writes "A model solar system, made of tungsten and placed in space, could reveal hidden spatial dimensions and test alternative theories of gravity. If the system's 'planets' moved slightly differently to the way predicted by standard gravity, it would signal the presence of new physical phenomena." From the article: "Once at the Lagrange point, the artificial solar system would be set in motion inside the spacecraft. An 8-centimetre-wide sphere of tungsten would act as an artificial sun, while a smaller test sphere would be launched 10 cm away into an oval-shaped orbit. The miniscule planet would orbit its tungsten sun 3,000 times per year."

Comments

Re:Gotchas, we got em

[d34thm0nk3y]

FTA:
And the spacecraft components themselves would exert gravitational forces on the spheres. These forces could be minimised by making the spacecraft as symmetrical as possible and putting its heaviest components as far from the artificial solar system as possible.

"Such an experiment would be quite challenging to set up, but I don't think it is technologically impossible," says MOND expert Stacy McGaugh of the University of Maryland, US.

Not impossible can be quite a stretch to feasible, though.

Re:Suspect this is rubbish - NS has been had?

[erice]

A tungsten sphere 10cm in diameter would have such a tiny gravitational field that I suspect even a hydrogen atom at the ambient temperature of local space would possess escape velocity.


No doubt. The only reason there is any hydrogen on *Earth* is because it binds readily with more massive elements. Helium does not and, as a consequence, any helium released into the atmosphere will ultimately escape. My understanding is that the only reason we have any helium at all is due to radioactive decay from heavier elements

Re:Gotchas, we got em

[Rob Carr]

In Freshman physics, it's common to demonstrate the net gravitational or electrical attraction inside a uniform sphere is zero. Any force with an inverse-square law will exhibit this peculiarity. If you want the details, there's a Wiki article on the Divergence theorem of vector fields.

The proof, involving triple integrals, is left for the reader.

Of course, designing a spacecraft that is as spherically symmetrical and uniform in density as possible will be difficult. TFA refers to this, and before much money is spent on this project, one would hope some number-crunching is done to see how extreme the effect is.

Another problem will be microgravity. Orbital velocity is dependent upon the distance from the center of the object being orbited. In Earth orbit, even a few inches difference can produce a velocity gradient that can result in minute accelerations. At L2, some of these effects might be minimized, although again, number crunching should be done.

The late Robert L. Forward proposed a system of massive spheres that could flatten spacetime in a local region. To further minimize extraneous effects due to microgravity, a system like this might need to be used. One advantage would be that this same system might eliminate some of the problems due to assymetry in the spacecraft. One of the problems with this situation would be mass lofted, which currently tends to be expensive, and additional calculations that might be required to analyze the data.

Re:Suspect this is rubbish - NS has been had?

[Cecil]

Actually, an 8cm tungsten sphere would exert the same gravitational pull on any object 10cm away, regardless of the other object's mass. It would have an escape velocity of 0.013 cm/s or 1.3 microns per second -- which, while very slow, is certainly within the realm of feasability. Your hard drive heads move accurately with tolerances significantly smaller than that.

I calculated the escape velocity using the formula sqrt(2Gm/r):

sqrt((2)(6.6742x10^-11)(5.16)/0.4) = 0.00013m/s or 0.013cm/s

Gauss's Law

[amightywind]

Gauss's Law says that the gravitational acceleration of a body anywhere in an enclosed sphere is 0. At L4, L5 Earth and Sun graviational forces are balanced. The only accelerations that don't cancel out are the two body accelerations of interest. It is surprising to me that the bodies orbit as fast as 10 times per day. I wonder why they don't use heavier Uranium as the mass. It is an interesting side note that a body can stably orbit one of these points. They orbit with no body (!) at the focus. The Genesis Probe and WMAP missions have already taken advantage of this.

Re:Gauss's Law

[bbaskin]

If I had a nickel for everytime I heard someone suggest replacing a tungsten weight with uranium, I'd have a buck or so. Uranium (238 anyway) isn't denser than tungsten. Tungsten is the densist material for semi-practical applications. It's more available than iridium or osmium, and far less expensive than platinum, three more dense elements. For a few reasonably obvious reasons, neptunium and plutonium aren't really good alternatives to tungsten if you just want a dense lump of metal.

Re:Gauss's Law

[Quantum Fizz]

Gauss's Law says that the gravitational acceleration of a body anywhere in an enclosed sphere is 0.

No it doesn't, re=read the law you linked to. It says the "surface integral of gravitational acceleration" will be zero over any arbitrarily-shaped closed surface, as long as that surface encloses zero mass. You cannot work backwards from this statement to assume that the local gravitational acceleration will be zero.

Simple example. Imagine a closed surface (say a small sphere) 20 feet above the ground (and also assume there's no air inside) such that the surface is closed. Since it encloses no mass, the net acceleration will be zero as summed over the whole sphere. However, any object placed within this hypothetical spherical surface (eg a brick) will fall to the ground.

High School Physics

[Soong]

Ok, some orbital mechanics.

Going with a circular orbit because they didn't specify the ellipse:
365.24*24*3600 = 31556736.00 seconds per year
./3000 = 10518.912 seconds per orbit
1/. = .00009506686623103225 orbits per second
.*.14*3.1415926*2 meters per orbit =
.0000836 meters per second
.*1000 = .0836 millimeters per second

Pretty slow orbit. About that tungsten, 19250 kg/m3
3.1415926*(4/3)*.04*.04*.04 = .000268 m^3
.*19250 = 5.16 kg
And let's say the planet is 8 mm in diameter, .004 m in radius
3.1415926*(4/3)*.004*.004*.004 = .000000268 m^3
.*19250 = .00516 kg

F = G m1 m2 / r^2 =
gravitational constant = 6.67300 × 10-11 m3 kg-1 s-2
.00000000006673000000 * 5.16 * .00516 / (.1*.1)
= .00000000017767262800 Newtons of force, resulting acceleration on the smaller body of
./.00516 = .00000003443267984496 m/s = .00003443267984496 mm/s

Sounds reasonable to me. Assuming they can get a clean launch at exactly .0836 millimeters per second everything should be fine!

Re:Gotchas, we got em

[Rob Carr]

We demonstrated that forces that follow an inverse square law follow this rule. We demonstrated that a charged sphere followed that rule in a lab by charging the sphere and then measuring the electrical force inside the sphere and out. We demonstrated that electrical forces follow the inverse square law in the lab. I'd argue that stable orbits demonstrate inverse square law for gravity, and we did visit the telescope and look at the moon in Freshman physics. We also calculated G using the old torsion technique.

Calculating the position of the moon throughout the month and deriving the orbit wasn't something I did until I got out of college. It's well within the capability of a Freshman physics student, so in theory we could have confirmed the inverse square law to a decent level of precision.

Tightening the exact value of that exponent (is it really -2?) further is the purpose of the proposed experiment.

If you know that gravity follows an inverse square law, then you know that inside a uniform sphere the gravitational acceleration will be zero.

You are correct. We never demonstrated experimentally for gravity that the net gravitational force inside a sphere was zero. Of course, I never said we did. The term "demonstrate" can, in fact, be used in a mathematical sense. When one of the kids on our dorm floor claimed the Ringworld was unstable, we had no trouble demonstrating that instability -- not that anyone had a Ringworld to work with.