Arcane Gazebo

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.

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.

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.

The latest movie on Ask a Ninja is very informative about ninjas and their relationship with physics.

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..."

That would be because the Sun is a mass of incandescent gas, a gigantic nuclear furnace...

...that's one of the songs too...

"Inside the Sun" is one of my favorite cards in Apples to Apples.

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.

One of my "favorite" (well, it kind of has to be now) Apples to Apples cards is "Angry Hornets."

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.

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?

Cosmic Variance is way ahead of us, Clifford had a musical final exam question last year. Link