Csdrhrt

If I have two asteroids. One dead still in space and one whizzing by at 10,000mph. What is the difference between the two, physically?

If I freeze time and look at the two of them - what differences would they have? How could one tell that one was moving really quickly, and the other not?

Is there some sort of Quantum difference with the particles in front or behind the asteroid?

Does it have a different gravitational force on spacetime surrounding it?

No images online seem to suggest this as Earth moves quickly through space but has a simple, aligned bump beneath.

I'm just a programmer who is interested in Physics & has been watching too many Leonard Susskind lectures recently.

I'll choose to interpret the question as specifying that one of the objects is stationary with respect to an observer, and the other object is moving with respect to the observer. Then the question goes on to ask if the observer can discern any difference between the two in an instantaneous "snapshot" of the two objects.

It's really a good question, and the answer is yes, there is a discernable difference.

Suppose that the objects are charged particles with no intrinsic magnetic moments. The observer will see no magnetic field around the "stationary" particle, but will see a magnetic field around the "moving" particle.

Even in the case of uncharged particles, there is a difference. An observer who sees a mass moving relative to himself sees an additional field besides the gravitational field of the mass. The additional field is a consequence of general relativity and is analogous to the magnetic field that's observed around a moving charged particle.

I will only cover the case of special relativistic effects

In the following discussion I take the frame of either one of the asteroids. It doesn't matter which one we take.

In order to be able to tell anything from a snapshot due to relativistic effects we need to have a relativistic $gamma$ factor.

However, since $v = 10,000$ mph this corresponds to a

$$ beta = frac{v}{c} = 1.5 times 10^{-5}. $$

This will correspond to a lorentz factor of

$$gamma = 1.00000000011 $$

which means that the prospect of distinguishing the moving (in our chosen frame) asteroid due to any of our relativistic machinery (i.e. length contraction, doppler shift, time dilation etc.) is a lost cause.

Other possibilities: I don't immediately see any other realistic possibilities for two bodies that have every property in common except for their speed (in your frame of reference). Indeed if you took the CM frame (which is inertial) they would be moving precisely at the same speed! Perhaps this is a more elegant argument that the one I just gave above, but it at least reinforces the conclusion.

Adding to the previous paragraph: Of course if you knew that the proper radius $R_0$ of the planets beforehand you could in principle be able to tell that they were both moving in the $CM$ frame. However, again, the $gamma$ factor would be too small to make this a reasonable measurement.