The physics of Built To Spill

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:

  1. 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.

  2. 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).
  3. 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.
  4. 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.

13 thoughts on “The physics of Built To Spill

  1. Justin

    A 6 M_sun chunk of iron should indeed turn into a black hole – by way of a type II supernova. Far too close to Earth, unfortunately. Actually, it would technically be a completely new kind of supernova, as I recall the types were originally defined by relative strength of hydrogen and/or helium lines, and this would lack the stellar envelope providing the various lighter elements in the spectrum.
    Personally, I’d read the song as referring to a seriously wacky and unphysical planet ten times the mass of Jupiter (radius depends heavily on temperature – ignoring gravitational compression is a bad idea). Composition doesn’t have to be iron – carbon, oxygen, and every other element not named “hydrogen” or “helium” counts as a metal in astronomy. If this thing’s orbit intersects the Earth’s atmosphere, the Earth won’t survive – it’ll either be accreted or disrupted. Most of the solar system should be pretty messed up by this object, in fact.

  2. Arcane Gazebo

    I had a feeling I should be consulting an astronomer on this issue. :) As a condensed matter guy I naturally think of materials with certain conductive and band structure properties when I hear “metal”, all of which have about the same density in order-of-magnitude terms. So I picked iron from this set more or less arbitrarily.
    I don’t know whether Doug Martsch is more of an astronomy guy or a condensed matter guy, but at least one other song on that album (“Kicked It In The Sun”) suggests he may have astronomical objects on his mind.

  3. Lemming

    How about a hollow shell?
    Intuition also makes me side with your momentum consideration, as I can see the effect of the feather on the momentum of the earth and MetalSphere(tm) being far more signifigant than any lost particles.
    Also, at any speed where the bodies wouldn’t collide into one another, I expect the net effect of the atmosphere would be orders of magnitude greater than the feather, both in terms of particles and momentum.

  4. Jolene

    Tangentially: I’ve been coaching a team of 7th graders for a couple science competitions on the solar system. This definitely goes on a list of songs I should play to them so hypothetical discussions can ensue.
    One time when I was driving away from the middle school, I heard the Weezer song “Island in the Sun” on the radio, and my first thought was, “Wow, it would be pretty hot to live in an island in the sun…”

  5. Justin

    Speaking of educational astronomy songs, the best by far is the Dark Matter Rap by David Weinberg, first performed at the IAS in 1992. Looks like he has an mp3 available here.

  6. Arcane Gazebo

    Now you’ve got me going through iTunes looking for sciencey songs. The Pixies have a song called “Space (I believe in)” which contains the lyric d equals r times t; two tracks later on that album is a song called “Distance Equals Rate Times Time”, but neither of these songs are particularly kinematics-themed otherwise.
    The Flaming Lips is another one to look at: there’s “A Spoonful Weighs A Ton” (And though they were sad / they rescued everyone / they lifted up the sun / a spoonful weighs a ton), and of course “Race for the Prize” (Two scientists were racing / for the good of all mankind and so forth).
    Now that I think about it FrinkTank did a thread on science-related songs recently, with the resulting playlist here.

  7. Mason

    I can definitely add a lot to their playlist–such as Thomas Dolby’s “Quantum Mechanic,” Tears for Fears’ “Schrodinger’s Cat,” Counting Crows’ “Einstein on the Beach,” numerous songs by MC Hawking, and many others.
    Who’s down with entropy?

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