And while I’m thinking about timescales, yesterday iTunes reminded me of the relevant Built To Spill song, “Randy Described Eternity”. The song starts out like this:
Every thousand years
this metal sphere
ten times the size of Jupiter
floats just a few yards past the earth
You climb on your roof
and take a swipe at it
with a single feather
Hit it once every thousand years
`til you’ve worn it down
to the size of a pea
Yeah I’d say that’s a long time
but it’s only half a blink
in the place you’re gonna be
It’s a cool metaphor, but the physicist in me has a few questions for this Randy guy if I ever run into him:
- Wouldn’t the gravity of the metal sphere crush the Earth into a thin paste? Or crush itself into a neutron star? Jupiter’s diameter is 142,984 km, so the volume of the sphere in the song is about 1.5×1027 m3. Assuming the metal is iron near room temperature, and without accounting for gravitational compression, the mass of the sphere is 1.2×1031 kg, or 6 solar masses. I believe this is actually a little bit above the threshold to become not a neutron star but a black hole. On the other hand, maybe “size” means volume rather than radius, so that the mass is only 6% of a solar mass. In this case I don’t think it turns into a neutron star, but gravity at the surface is still formidable. A quick calculation yields about 338 times Earth’s gravity (at the surface of each object), unless I made a mistake.
- Even ignoring the gravitational binding, would a swipe from a feather be enough to knock a non-zero number of atoms off the sphere? Maybe I could model this but it seems slightly difficult. Someone should do an experiment with a feather, some iron, and an atomic force microscope (or similar instrument).
- Suppose the feather does knock some atoms off the sphere. Where do they go? If the metal sphere has gravity, of course they’ll accrete right back onto the sphere. But if not, won’t they pile up on the Earth? Given the size of the sphere that could be a problem. On the other hand, if there’s magically no gravity from the sphere, maybe the individual atoms won’t be affected by Earth’s gravity either and they’ll fly off into space.
- Won’t the momentum imparted by the feather strikes affect the motion of the sphere over time, as well as the motion of the Earth? Will the thousand-year period change after enough swipes?
Clearly this song raises more questions than it answers. If I ever teach an elementary physics course, I should totally assign a problem based on these lyrics.