Asteroid that broke up over Berlin was fastest-spinning one ever seen
newscientist.com
newscientist.com
That's a toy i had as a kid, essentially!
[1]: https://en.wikipedia.org/wiki/Crookes_radiometer#Explanation...
There is a moment in 2001: A Space Odyssey that I’ve always liked. It’s at about 1:13:15 or so, and is just a distant shot of the Discovery One. Suddenly two space rocks silently tumble past. I like the scene because it gives a sense of the scope and silence of outer space, but I suppose it would be incredibly rare to be so close to even one rock, let alone a pair. And they are tumbling at about the pace measured by the one in that article, so perhaps even rarer still.
Curious, what is that number for a space rock the size of Earth?
F_c = m_1 r ω^2 = F_g = G m_1 m_2 / r^2
cancel out the orbiting mass (m_1), rearrange it a bit
ω^2 = G (m_2 / r^3)
where you'll note that term in parenthesis is directly proportional to the density.
So the answer would probably be ~a 2.2 hour day.
I think this is correct, but then it can be simply calculated knowing the escape velocity on Earth is 11.2 km/sec and the circumference is 40e3 km:
40e3 / 11.2 = 3571 seconds
Therefore it's the Earth span at one revolution per hour, objects at the equator would escape gravity... I'm not sure where is your error in your formula that leads you to a different response.