Gravity from the Ground up -- Schutz

Saw a show on tv last night about Dark Matter and computer simulations and all that and one competing theory is apparently about 'variable gravity' where gravity is not a constant but can change in some circumstances. Has anyone else ever heard of this? This is contrary to Newton's theories but the proponents say Newton knew what he knew but didn't know everything, and as new stuff comes in theories must be changed.

None of us know everything, Newton included .... :-)

This the area of MOND : MOdification to Newtonian Dynamics ( many variants ). Essentially the idea is a fair one, but to date it hasn't yielded much fruit. The missing mass is the difference ( or placeholder for the label ) between what matter we see and what matter ought be there to explain the rotation curves of galaxies. As you recede from a galactic centre the assumption is Keplerian orbits, or at least approximately so, by allowing the galaxy's mass ( within a given radius ) to act in effect from it's centre point. That means periods should diminish with distance from the centre according to Kepler's Third Law ( radius cubed goes like period squared ) after allowing for known mass distributions. They don't. They have rather higher rotation rates ( shorter periods ) in outlying galactic areas.

So I'd assume that 'variable gravity' is a phrase denoting a modified inverse square force law at rather larger distances than it was originally hypothecated from. Strictly speaking Newton himself could only verify his famous inverse square gravity law within the confines of the solar system ( apple -> Moon -> planets ). Interestingly globular star clusters are well understood without varying his laws one whit, so 'some circumstances' might refer to the contemporary theorist's preference towards his objects of especial interest! :-)

One can always introduce a variant force profile to answer the given case of a certain galaxy, but you have to change that in detail when you look at another galaxy. You see we seek universal laws, so the question is begged as to why 'law' on a per galaxy basis ..... either you make the rules uniform and/or explain why 'local' factors produce variation. The current 'status quo' is to accept Newton's Laws en face but suspect extra local mass. Either way the onus still resides upon the theorist to resolve toward the observations ..... if it was described as a 'competing theory' that's probably rather cheeky, and overstates the merit or generality I'd say. Bit like saying that I could 'compete' with an Olympic sprinter simply by arriving at the starting blocks. Probably kinder to say that investigations are continuing to find alternate fits to data. No one has yet found the Dark Matter either .....

Cheers, Mike.

Whoops, yes my bad. Radius and periods trend together. I was thinking of the speed curves, as they measure that across the face of the galaxy's disk and that tells them that the speed doesn't go down as expected. It's supposed to increased to a certain radius and then dip and die away, but it stays well up toward the visible edge of the galaxy.

I should have also mentioned that while GR is a modification to Newton's Laws ( but isn't called MOND ), it isn't thought to apply to the detail here as neither accelerations/velocities/mass-densities are high enough to bring sufficient correction to align to observations.

There's a group that have been laser range finding to the Moon on the corner-cube arrays left by Apollo. Bit of a hit-or-miss affair apparently but they kept at it! In their modelling they've been allowing free variation of all sorts of parameters - including ones which would say, breach the big conservation laws - to at least locate in parameter space where any MONDs should go or apply. But that's only over Earth_to_Moon scale so wouldn't necessarily apply galactically ie. if it shows no variations ( or places upper bounds too small upon variations ) from Newton then what of it?

Also the further away into the universe that we look is also older light from earlier times, but that's more an issue for ( or a trigger indeed to invent ) that other Darkness - Dark Energy. Interestingly that is yet another placeholder for our ignorance of scales well above our local neighborhood. As we could well require another data collection point somewhere well far away ( not in my lifetime at least! ) to sort this out, then we may always have that level of ignorance. Meanwhile we use all manner of proxies.

Cheers, Mike.

A small step beyond the moon might be Pioneer. The Planetary Society rescued the Pioneer anomaly data. Has anything further become of that?

Keep searchin',
Martin