What Would Happen to Earth In This Scenario

thequestioner

What would happen if a coin sized object traveling at the speed of light were to collide with earth? What about a city sized object?

xAxis

I think more interesting question would be what would happen to a coin travelling at the speed of light. :)

phinds

Coins have mass and therefore cannot travel at c

Integral

Please rephrase your question so that it is physically meaningful. Objects with mass cannot travel at the speed of light.

mfb

A coin sized object slightly slower than light can release energy comparable to a thermonuclear bomb. See the relativistic xkcd-baseball for a description. With those numbers, the released energy is about 4 MT TNT-equivalent.

BruceW

agreed, objects with mass cannot travel at the speed of light. So I'm going to assume the OP'er meant to say travelling at almost the speed of light.

In this case, ummm, If the coin was travelling pretty fast, as mfb said, it could give off a massive explosion. If it was going even faster, it might potentially blow up the earth. If it was going really fast, then it might just become a black hole due to so much energy being in such a small space. I'm not sure on the exact physics of black holes though. I still need to learn general relativity.

Drakkith

At 0.9c a 5.6 gram quarter dollar coin from the US would have about 1.5 megatons of TNT worth of kinetic energy, or about 6.5x10¹⁵ joules.

At 0.99999c the same coin would have about 1.1x10¹⁸ joules of energy, or around 250 megatons of energy.

No object would ever collapse into a black hole, as in it's rest frame the object is not moving and has no additional mass or energy. As far as I understand very few people use relativistic mass anymore and use momentum instead.

Ryan_m_b

Wrt the city sized object; taking a spherical 5km radius asteroid with a density of 5g/ml travelling at .9c the kinetic energy is a mind boggling 9.54259E+30J. That's close to the total amount of solar energy output in a day. It's still only 1% of the gravitational binding energy of Earth though so presuming that all of the energy entered the system (i.e. part of the mass didn't simply shoot out of the other side of the planet) whilst the surface would be heated to incandescence and most likely the shape and orbit of the planet warped it wouldn't be totally destroyed by any means.

DrStupid

As we are talking about a coin hitting earth there is additional mass and energy. I don't know if the coin may form a black hole in this situation but if this happens it would cross earth within 32 ms and than escape into space. I even don't know what this would mean to Earth.

Ryan_m_b

I'm not sure how we'd work this out for sure but I'm betting the coin would fully disintegrate long before it made it through the Earth. Assuming the veracity of the baseball link above this would be a safe bet.

DrStupid

A black hole couldn't disintegrate. Therefore it seems to be an important question whether formation of a black hole is possible and if yes how it would happen in detail.

mfb

In theory, it can form a black hole in a collision with earth (but not as free object in space), as the center of mass energy density (which does not depend on the reference frame) can become large enough there. However, a black hole with a size of several millimeters would have a mass equivalent to the earth. The coin would probably need an energy which exceeds the mass of earth (times c^2), and I think it needs several orders of magnitude more as it collides just with a small fraction of earth.