Could a 6ft Object Hitting Earth at 99% Light Speed Destroy It?

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Discussion Overview

The discussion revolves around the hypothetical scenario of a 6-foot object weighing 180 lbs colliding with Earth at 99% of the speed of light. Participants explore the potential consequences of such an impact, including whether it could destroy the Earth or what effects it might have, while considering energy transfer equations and kinetic energy calculations.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants suggest that the energy transferred during the collision could determine whether the Earth would be destroyed, comparing the object's kinetic energy to the energy required to overcome Earth's self-gravity.
  • One participant proposes using the kinetic energy formula Ek = 0.5mv^2, although another later suggests that a different formula may be more appropriate for relativistic speeds.
  • Another participant calculates the kinetic energy at impact as 9mc^2, arguing that this amount of energy is comparable to that of 810 lbs of antimatter.
  • There is a discussion about the implications of such energy, questioning what "destroying the Earth" would entail—whether it means cracking it in half, blowing it apart, or melting the crust.
  • Some participants clarify that the kinetic energy formula should account for relativistic effects, specifically using gamma factors for velocities approaching the speed of light.
  • One participant emphasizes that the impact itself is what would cause destruction, rather than a matter-antimatter reaction.

Areas of Agreement / Disagreement

Participants express varying opinions on the calculations and implications of the impact, with no consensus reached on whether the object would destroy the Earth or the exact energy calculations involved. Multiple competing views remain regarding the appropriate formulas and interpretations of the energy involved.

Contextual Notes

Participants reference different energy formulas and calculations without resolving the assumptions or dependencies involved in their arguments. The discussion includes unresolved mathematical steps and varying interpretations of what constitutes destruction.

BosonJaw
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Hello guys!

Would an object about 6 ft in length and about 180 lbs hitting the Earth at 99% of light speed destroy the Earth? If not, what would it do? Obviously assuming it did not disintegrate due to frictional forces first. Can this be solved by a simple energy transfer equation?

Thanks!
 
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The Earth has a certain amount of energy due to self-gravity, which is holding it together. If at least that amount of energy can be transferred by a collision, there's a chance that that the Earth would come apart (partly if not wholly, in reality). So, you just have to compare the two energies.

There are simple formulas to find both the energies.
 
right when it hits the earth, it only has kinetic energy<--- in an ideal world
Ek = .5mv^2
m=mass
v=velocity
 
> Ek = .5mv^2

For v=0.99 c, perhaps a different formula would be more apt.
 
The PE of a self-gravitating sphere of uniform density is -(3/5)Gm^2/r.

The KE would be m*c^2*(gamma(0.99) -1), provided there is no conversion of mass to energy.

You can plug in the values now and see.
 
Last edited:
BosonJaw said:
Hello guys!

Would an object about 6 ft in length and about 180 lbs hitting the Earth at 99% of light speed destroy the Earth? If not, what would it do? Obviously assuming it did not disintegrate due to frictional forces first. Can this be solved by a simple energy transfer equation?

Thanks!

Yes, this can be solved pretty simply. At impact, the object would have kinetic energy equal to 9mc^2. Where m is the mass of the object. That's about as much energy as the use of 810 *pounds* of antimatter. You'd have to work out the exact numbers (plug in for c and convert 180lbs to grams or kilograms), but my sense is that that is a ridiculuously large amount of energy. You also have to decide what you mean be "destroy the Earth" (crack it in half? blow it to bits? or just melt the crust so that nothing survives?). You can then intergrate the gravity potential to find the total amount of energy you'd need. Again, I could be wrong.. but that is a whole lot of energy.
 
It would pretty much be "I have to find a new home."
 
> At impact, the object would have kinetic energy equal to 9mc^2.
Why?

> That's about as much energy as the use of 810 *pounds* of antimatter.
Why?
 
Shooting star said:
> At impact, the object would have kinetic energy equal to 9mc^2.
Why?

> That's about as much energy as the use of 810 *pounds* of antimatter.
Why?

Well.. as you said, the kinetic energy is (gamma-1)mc^2. For v=.99c, this works out to 9mc^2. That is also equal to the energy that would be liberated if 9 such asteriods were converted directly to energy. This could be accomplished if half that amount was antimatter. Since the asteriod weighs 180lbs, we'd need 810 lbs of antimatter.
 
  • #10
I'd given the formula for KE, that is, total energy minus rest energy. I considered it to be made of matter, and had mentioned it. It's the impact which is "breaking" up the earth, not matter-antimatter reaction.

Read post #2.
 

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