Why Gravity-Powered Helicopters Aren't A Thing
Here's another little Streamlit app to ease the burden on my ageing calculator. This one calculates the dynamical mass of a galaxy given rotation speed at a known distance. Or indeed, it will calculate the unknown variable from any of the two supplied, e.g. radius if you already know the mass and speed. It converts between different units (you can even use mph if you're so inclined) but doesn't account for relativistic effects. For galaxies, which is what I actually need this for, this isn't a problem : rotation speeds tend to be <0.1% c. For compact objects like neutron stars and black holes this will give meaningless results, but the scales are about a dozen orders of magnitude different, so that doesn't matter.
The dynamical mass is basically how much mass you'd need to cause the observed speed from gravity alone. In some cases gravity is all you need : the orbits of the planets and the dynamics of star clusters are perfectly consistent with pure gravitational motions, with thermal effects in solar system bodies being important only as matters of detail. In some galaxies it also seems that their dynamics is dominated by the visible matter, but in most cases you need about ten times more mass than we see to explain their rotation speeds.
What's quite fun about this one is that you can input everyday numbers as well as astronomical ones. So for instance, if you spin your arms at a quite achievable 1 m/s with a length of 1 m, that's a dynamical mass of nearly fifteen million tonnes. A helicopter spinning its 5 m long blades at 125 m/s (from some quick Google searching) would have a dynamical mass of over one trillion tonnes ! To make a gravity-powered helicopter, you'd need it to have the mass of a mountain.
Which just goes to show how negligible gravitational fields from little objects like people and helicopters really are : they're completely dominated by non-gravitational effects (except, of course from the much larger external field of the Earth). If you were to plot the dynamics of helicopters in comparison with galaxies you'd find that helicopters would seems like far weirder, crazier outliers than any of the galaxies ever observed. The helicopter would have an apparent "missing mass" ratio of something like a trillion. For galaxies most have ratios of order a few, with some exceptional cases in the hundreds.
Of course, helicopters are easy to explain because we know their motion has bugger all to do with gravity. But nobody has proposed any plausible non-gravitational mechanism which would explain how to make stars and gas spin so much faster than expected. Either there's a fair bit of extra material there, or, much less likely, gravity itself does funky things at low accelerations.
There are no comments yet.