# Kinetic Energy of an object at the speed of light

If you could fire a piece of lead at the earth that was 1cm3, at close to the speed of light, what would be the amount of enery released? What would be the effect on the planet with and without an atmosphere?

thanks guys

GRB

http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/releng.html

You can input your own values into the topic titled "Relativistic Kinetic Energy" to find out.

As for your 2nd bit, no idea. Probably would either melt or oxidise.

Can you pretend that you're talking to an idiot? :)

I was hoping someone could do the calculations for me, and then translate that into something that I could grasp with my limited intellect... I really have no idea what a joule even is.

I'm not a student, and the only reason for this question is personal curiosity.

If the earth had no atmosphere, and the object hit the surface, what do you educated guys think would happen? Any guesses?

...at close to the speed of light, what would be the amount of enery released?

As much as you want, depending how close you mean by "close". The question doesn't really make sense.

DrGreg
Gold Member
Kinetic energy is$$E = mc^2 \left( \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} - 1 \right)$$ where m is the mass of the lead, and v is its speed, and c is the speed of light. So it depends how fast you go: the closer to the speed of light, the larger the energy gets. If it were possible to reach the speed of light (it isn't), the energy would be infinite.

Drakkith
Staff Emeritus
Well, for a 1 kg mass travelling at 0.9 c, 90% the speed of light, it would have kinetic energy equal to 1.163 x 10^17 joules. 2.1 x 10^17 joules is roughly what was released by the 50 megaton Tsar Bomba nuclear weapon. So 1kg of mass travelling at 0.9 c would have about 25 megatons worth of energy.

0.9 c is about equal to 269,000,000 meters per second, or 269,000 km per second...so its REALLY fast.

Well, for a 1 kg mass travelling at 0.9 c, 90% the speed of light, it would have kinetic energy equal to 1.163 x 10^17 joules. 2.1 x 10^17 joules is roughly what was released by the 50 megaton Tsar Bomba nuclear weapon. So 1kg of mass travelling at 0.9 c would have about 25 megatons worth of energy.

0.9 c is about equal to 269,000,000 meters per second, or 269,000 km per second...so its REALLY fast.

Thanks Drakkith. The Tsar bomb reference was something that I could visualize. Ive watched the Tsar bomb video and am amazed every time I see it. I enjoy reading your posts, even though lots of things you talk about are way over my head.

I guess another one of the things i was curious about was if a very tiny object could destroy the planet, if it was moving fast enough. Someone said earlier that at the speed of light, the object's KE would be infinite. So that means that any amount of mass could destroy the earth, if it were travelling at 1c? I realize this is impossible, but theoretically?

Ryan_m_b
Staff Emeritus
Thanks Drakkith. The Tsar bomb reference was something that I could visualize. Ive watched the Tsar bomb video and am amazed every time I see it. I enjoy reading your posts, even though lots of things you talk about are way over my head.

I guess another one of the things i was curious about was if a very tiny object could destroy the planet, if it was moving fast enough. Someone said earlier that at the speed of light, the object's KE would be infinite. So that means that any amount of mass could destroy the earth, if it were travelling at 1c? I realize this is impossible, but theoretically?

I think you need to look up the word theoretically. It is an impossibility, you cannot get infinite energy. The statement barely makes any sense!

Drakkith
Staff Emeritus
Thanks Drakkith. The Tsar bomb reference was something that I could visualize. Ive watched the Tsar bomb video and am amazed every time I see it. I enjoy reading your posts, even though lots of things you talk about are way over my head.

I guess another one of the things i was curious about was if a very tiny object could destroy the planet, if it was moving fast enough. Someone said earlier that at the speed of light, the object's KE would be infinite. So that means that any amount of mass could destroy the earth, if it were travelling at 1c? I realize this is impossible, but theoretically?

It not even theoretically possible. It is 100% impossible for anything with mass to reach c. But, theoretically, almost any amount of mass could be given a high enough velocity to destroy Earth. But that is only theoretically, and far from feasible.

There is also the issue of energy transfer. While a 1 cc object may have enough kinetic energy to destroy the earth that doesn't mean that an impact will destroy the earth. It may just punch a hole straight through and keep going on the other side.

I think determining what would actually happen would require either massive amounts of programing and computer simulation or building a gun that can fire a round a .99 c (pick your own velocity).

I think you need to look up the word theoretically. It is an impossibility, you cannot get infinite energy. The statement barely makes any sense!
You sure know how to make a guy feel stupid! Maybe the word I should have used was "hypothetically"? I barely graduated high school, and you guys humble me.

It not even theoretically possible. It is 100% impossible for anything with mass to reach c. But, theoretically, almost any amount of mass could be given a high enough velocity to destroy Earth. But that is only theoretically, and far from feasible.
Thanks, that was what I was getting at.

There is also the issue of energy transfer. While a 1 cc object may have enough kinetic energy to destroy the earth that doesn't mean that an impact will destroy the earth. It may just punch a hole straight through and keep going on the other side.

I think determining what would actually happen would require either massive amounts of programing and computer simulation or building a gun that can fire a round a .99 c (pick your own velocity).
Thanks mrspeedybob, you answered on of my questions from my OP.

-Thanks for all of your replies, Ill do my best to ask questions that make sense. I'm just a normal guy that has an appreciation for science, even if I don't understand most of it.

GRB

Its never late in life

Ryan_m_b
Staff Emeritus
You sure know how to make a guy feel stupid! Maybe the word I should have used was "hypothetically"? I barely graduated high school, and you guys humble me.

It wasn't my intention to make you feel bad. Even hypothetically doesn't make too much sense because if you break it down what you are asking is;

"What do the laws of physics say about X (where X is something the breaks the laws of physics)".

Don't worry, everyone learns this at some point.

Last edited:
It wasn't my intention to make feel bad. Even hypothetically doesn't make too much sense because if you break it down what you are asking is;

"What do the laws of physics say about X (where X is something the breaks the laws of physics".

Don't worry, everyone learns this at some point.

Thanks ryan, my questions were answered. Its just intimidating posting on this site, where questions have to be very specific for things to make sense. I have no desire to become a scientist of any sort, just some childish curiosities that I would like to hear experts opinions on. Again, thank you all for taking time to help me out!

GRB

Drakkith
Staff Emeritus
Thanks ryan, my questions were answered. Its just intimidating posting on this site, where questions have to be very specific for things to make sense. I have no desire to become a scientist of any sort, just some childish curiosities that I would like to hear experts opinions on. Again, thank you all for taking time to help me out!

GRB

Don't be afraid to ask a question, even if you think it is stupid!

Someone said earlier that at the speed of light, the object's KE would be infinite. So that means that any amount of mass could destroy the earth, if it were travelling at 1c? I realize this is impossible, but theoretically?

As noted, this can't happen...but if you get enough high energy radiation (no mass) that could also destroy just about everything on earth.....life goes first and rather easily, but enough radiation (energy) to rip atoms apart is quite unlikely. Such fracturing of atoms is what happens in fission (nuclear) bombs.

And with enough radiation energy earth could be pushed out of it's orbit if that energy exceeded gravitational attraction between earth and moon or earth and sun.

Don't worry about feeling dopey here: we all learn from others and feel "dopey" from time to time...feeling dopey is also called "growth" if taken constuctively....and growth is usually uncomfortable.

Isn't there an outside chance that a big glob of material ejected from a black hole could be going 99.999999% relative to earth, and impact hard enough to break the planet up?

Ryan_m_b
Staff Emeritus
Isn't there an outside chance that a big glob of material ejected from a black hole could be going 99.999999% relative to earth, and impact hard enough to break the planet up?

Nothing can be ejected from a black hole. However the more mass there is the more energy, same as increasing speed.

Drakkith
Staff Emeritus
Isn't there an outside chance that a big glob of material ejected from a black hole could be going 99.999999% relative to earth, and impact hard enough to break the planet up?

I don't think so. Anything with enough mass to be ejected from the accretion disc and pose a threat to a planet would probably be torn apart in the process.

Hey gamma, check out the "boom table." Its a random list of things/events and their associated energy and TNT equivalent.
http://www.projectrho.com/rocket/spacegunconvent.php#id--Nukes_In_Space--Boom_Table

For the smarter people, at the bottom it has the energy of all observable stars and the energy of the big bang. What do yall think of these values? They almost seem a little small considering how many stars are out there....Im guessing these are estimates lol.

Drakkith
Staff Emeritus
Hey gamma, check out the "boom table." Its a random list of things/events and their associated energy and TNT equivalent.
http://www.projectrho.com/rocket/spacegunconvent.php#id--Nukes_In_Space--Boom_Table

For the smarter people, at the bottom it has the energy of all observable stars and the energy of the big bang. What do yall think of these values? They almost seem a little small considering how many stars are out there....Im guessing these are estimates lol.

Small? Looks pretty big to me. 3x10^69 joules for the Big Bang isn't twice as big as the one before it, it is about a trillion trillion times as much.

Yes I know it is definitely a big number. I was talking about the energy for the observable stars. I didnt notice that it said "output each second." I was thinking it was stating that was the mass-energy equivalence of all the stars in the universe lol. But oh yeah thats alot of energy.

Isn't there an outside chance that a big glob of material ejected from a black hole could be going 99.999999% relative to earth, and impact hard enough to break the planet up?

There is a definite, perhaps 100% chance, that the reverse happens.....that the earth, or what remains of it after our sun goes red dwarf, will be gobbled up by black hole(s)...that seems to be the ultimate fate of the entire mass and energy of the universe...cold,dark,empty..black hole

Ryan_m_b
Staff Emeritus
There is a definite, perhaps 100% chance, that the reverse happens.....that the earth, or what remains of it after our sun goes red dwarf, will be gobbled up by black hole(s)...that seems to be the ultimate fate of the entire mass and energy of the universe...cold,dark,empty..black hole

Don't forget that after that the black holes will decay via hawking radiation! Fun times.

Hey gamma, check out the "boom table." Its a random list of things/events and their associated energy and TNT equivalent.
http://www.projectrho.com/rocket/spacegunconvent.php#id--Nukes_In_Space--Boom_Table

For the smarter people, at the bottom it has the energy of all observable stars and the energy of the big bang. What do yall think of these values? They almost seem a little small considering how many stars are out there....Im guessing these are estimates lol.

thanks easyrider, that is a really cool page!