Stefan Ram

2024-01-15 21:10:10 UTC

What would happen if a penny with a mass of 0.003 kg and a speed of

0.99999999999999999999999999999999999999 c

from outer space would hit the earth (being directed at its center)?

[[Mod. note --

There are 38 9's in that speed, i.e., the speed is (1 - 1e-38)*c.

That implies a Lorentz gamma factor of (1 - v^2/c^2)^(-1/2) = 7e18,

so the penny's total relativistic energy is gamma*m*c^2 = 2e33 Joules.

That's rather a lot of energy. :) In fact, it's about 8 times the

Earth's gravitational binding energy (2.5e32 Joules according to the

all-knowing Wikipedia).

So, the tricky question is, how much of the penny's energy would go

into disrupting the Earth, versus how much would go into kinetic energy

of whatever came out the other side?

And finally, I'll note that (IMHO not superb, but still an enjoyable read)

the 1993 science-fiction novel "Flying to Valhalla", by Charles Pellegrino,

is based on a similar question.

-- jt]]

0.99999999999999999999999999999999999999 c

from outer space would hit the earth (being directed at its center)?

[[Mod. note --

There are 38 9's in that speed, i.e., the speed is (1 - 1e-38)*c.

That implies a Lorentz gamma factor of (1 - v^2/c^2)^(-1/2) = 7e18,

so the penny's total relativistic energy is gamma*m*c^2 = 2e33 Joules.

That's rather a lot of energy. :) In fact, it's about 8 times the

Earth's gravitational binding energy (2.5e32 Joules according to the

all-knowing Wikipedia).

So, the tricky question is, how much of the penny's energy would go

into disrupting the Earth, versus how much would go into kinetic energy

of whatever came out the other side?

And finally, I'll note that (IMHO not superb, but still an enjoyable read)

the 1993 science-fiction novel "Flying to Valhalla", by Charles Pellegrino,

is based on a similar question.

-- jt]]