# Would a sizeable object moving at relativistic speeds leave a wake?

I was reading about the chicxulub crater and decided for fun to calculate the approximate velocity of a million-Kg object that would approximate the energy expended by the impact. If I've done my math correctly, about 0.8c (obviously the actual impactor was much, much, much more massive). But this got me wondering.

While a million-Kg object isn't very large in the grand scheme of things, it's humongous compared to what we usually see traveling at reletivistic speeds (light, radiation, etc.). Would an object that massive leave a wake (whether classically in terms of particles of matter or more creatively in terms of warping space-time by its passage)? Something that, theoretically, we could use to detect the passage of a large object moving as such velocities?

Please note that I'm not worried about how my million-Kg rock became accelerated. For the purpose of the question, please assume that it's traveling from T=0 with a velocity of V=0.8c.

EDIT

Jim asked after my math. I used the following equation:

$$KE = \frac{\frac{mv^2}{2}}{\sqrt{1-\frac{v^2}{c^2}}}$$

• From the link above, KE = 1 x 1023J
• Though it doesn't affect the spirit of the question, could you show your math? The speed 0.8 c seems way too large. – jim Jan 8 '18 at 10:16
• All objects warp spacetime by their mere presence, as well as their passage. An electromagnetic and gravitational wake of sorts would be observed. But a thousand tons of anything is not very much in the scheme of things. – Steve Jan 8 '18 at 11:11
• @jim, I added the equation I used. – JBH Jan 8 '18 at 15:36

## 4 Answers

Massive objects moving very close to the speed of light will interact with the cosmic background radiation in a manner that should be detectable with current-generation observational equipment, according to an article in MIT Technology Review

https://www.technologyreview.com/s/536091/spacecraft-traveling-close-to-light-speed-should-be-visible-with-current-technology-say/

Traveling through vacuum, an object at any constant speed will not leave a wake. You can see this by Lorentz invariance- in the object's rest frame, it is not traveling at all, and so can't emit any radiation or warp space time or anything that would involve losing energy. Like any object with a mass, it has a gravitational field, but it's only a little larger than it would be for a ordinary million kilogram rock (which is to say immeasurably tiny, by astronomical standards).

• A real object travelling through space isn't in a true vacuum. Indeed, it's interactions with the CMB may be detectable technologyreview.com/s/536091/… – Eric J. Jul 9 '18 at 1:28
• @EricJ In my interpretation, the question wasn't about an object moving through interstellar space, it was about an object moving through an ideal vacuum. Clearly an object traveling through a space full of particles has some effect. – Chris Jul 10 '18 at 20:33
• That's a reasonable interpretation. My comment is in no way a criticism of your answer, just supplemental information. – Eric J. Jul 20 '18 at 5:21

Too long for a comment (given some of the assumptions I make, I'm not sure how accurate the final result for the speed $v$ is):

The density of rock may be taken as approximately $\rho \approx 3 g/cm^3 = 3 \times \frac{10^{-3} kg}{10^{-6} m^3} = 3 \times 10^3 kg/m^3$. According to your article, the crater was caused by an object of diameter $\approx 10 - 15 km$. Let us take the radius as $r = 10 km = 10^4 m$. This gives the mass as $\frac{4}{3} \pi r^3 \rho \approx 10^{16} kg$, which is a lot smaller than, say, the mass of the Earth, $\approx 5 \times 10^{24} kg$. However, the mass is much larger than the $10^6 kg$ you estimate, so that the speed will be a lot smaller than $c$ (as well, your formula for the KE isn't quite right, it should be $mc^2(\frac{1}{\sqrt{1 - v^2/c^2}}-1)$ and you should be able to use the non-relativistic version, $\frac{1}{2} m v^2$ to find $v \approx 10^4 m/s$. Still large, but non-relativistic.

However, I think the answer given by Chris is in the spirit of the question that was asked.

• I apologize that I was not clear. I was not attempting to ascertain the velocity of the chicxulub crater impactor, but an artificial object that was much smaller. My curiosity was spurred by the idea, "if the impact were intentional and not random chance, what would it take to create it?" Thus, my choice of a million Kg object. Realizing the speed such a small object would need to travel, I wondered if its passage would leave a wake or some indication of its passage, such as a bullet passing through air leaves. Thanks! – JBH Jan 9 '18 at 22:51

A particle can lose energy in a medium if its phase velocity is higher than the speed of light in that medium. For charged particles it is called Cerenkov radiation

is electromagnetic radiation emitted when a charged particle (such as an electron) passes through a dielectric medium at a speed greater than the phase velocity of light in that medium. The characteristic blue glow of an underwater nuclear reactor is due to Cherenkov radiation.

There have been proposals that charged particles would emit Cerenkov radiation in a gravitational field .

Also for gravitational Cerenkov type radiation in gravitational fields in a medium. These would be very hard to detect

So for particle physics there is radiation in a medium, the cosmic rays coming down the atmosphere for example, or particles in accelerators. Extended bodies do not reach relativistic velocities, but if they did have a velocity higher than the phase velocity of light in the medium, they might have some local charges (from friction of descent in the atmosphere for example) and radiate. It would be hard to detect for sure, a lot more would be happening to the extended body , as the burning meteors show, which have nothing to do with relativistic velocities.