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

In summary, the experts discuss the potential destruction of the Earth by an object hitting it at 99% of light speed. They determine that the impact would have kinetic energy equal to 9 times the object's mass multiplied by the speed of light squared. This is equivalent to the energy released by using 810 pounds of antimatter or nine asteroids converted directly to energy. They also consider the Earth's gravitational potential energy and the amount of energy needed to cause destruction. They conclude that this is a significant amount of energy and would likely result in the need to find a new home.
  • #1
BosonJaw
40
0
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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  • #2
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.
 
  • #3
right when it hits the earth, it only has kinetic energy<--- in an ideal world
Ek = .5mv^2
m=mass
v=velocity
 
  • #4
> Ek = .5mv^2

For v=0.99 c, perhaps a different formula would be more apt.
 
  • #5
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:
  • #6
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.
 
  • #7
It would pretty much be "I have to find a new home."
 
  • #8
> 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?
 
  • #9
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.
 

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

1. What is energy transfer?

Energy transfer is the process of moving energy from one object or system to another. This can occur in various forms such as heat, light, electricity, or motion.

2. How does energy transfer happen?

Energy transfer can happen through different mechanisms, depending on the type of energy being transferred. For example, heat energy can be transferred through conduction, convection, or radiation, while electrical energy can be transferred through wires or circuits.

3. What are some examples of energy transfer?

Examples of energy transfer include the transfer of heat from a hot stove to a pot of water, the transfer of electrical energy from a power plant to homes through power lines, and the conversion of solar energy into electricity through solar panels.

4. What is the law of conservation of energy?

The law of conservation of energy states that energy cannot be created or destroyed, but can only be transferred or converted from one form to another. This means that the total amount of energy in a closed system remains constant.

5. How is energy transfer important in daily life?

Energy transfer is essential for many everyday activities, from cooking food to powering electronic devices. It is also crucial in industries such as transportation, manufacturing, and electricity production. Understanding energy transfer can help us make more efficient use of energy and reduce our impact on the environment.

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