Fantastic. Explain, in detail, how you arrived at your argument. Where did you get your initial figures from?

I did. You just aren’t connecting the dots.

Starting with two assumptions. The earth has been accelerating at 1g for at least a year or so and the meteor and the earth are moving towards one another.

The basic equation for relative velocity can be stated as:

The velocity of A relative to B is the velocity of A

**relative to something other than B** plus the velocity of B

**relative to something other than of A**.

I shouldn’t have to explain the bolded language, but given RET penchant for circular logic, I’m not so sure.

To find the relative velocity of two moving objects, you have to introduce a separate frame that is assumed to be inertial, like I did with the car example. Usually, the earth is assumed to be that frame, but we obviously can’t use it in this situation. So we have to use a hypothetical inertial observer, in the same way that is done here.

https://www.khanacademy.org/science/physics/special-relativity/einstein-velocity-addition/v/applying-einstein-velocity-additionHe finds the relative velocity of the two moving objects by adding their velocities relative to a third inertial observer. Notice he says that “both of these velocities are in my frame of reference”. The equation could be stated as:

The velocity of A relative to C is the velocity a A relative to B plus the velocity of C relative to B.

What would be the velocity of the earth as measured by the inertial observer? Since the observer is inertial and the earth has been accelerating for a year or more, its velocity will asymptotically approach c, but never reach it. So .9c is a good approximation of the velocity relative to the inertial observer.

What would the velocity of the meteor be as measured by the inertial observer? I chose to use 0 because the actual value doesn’t matter.

As long as the earth is accelerating, the earth’s velocity will continue to increase, but never reach c relative to an inertial observer. It doesn’t matter if relative to that observer, the earth is only accelerating at .00000000000000001 m/s^2, it’s velocity will continue to increase relative to the inertial observer, just very slowly. Acceleration is the rate of change in velocity, The only way it’s velocity would stop increasing is if it stopped accelerating icompletely.

In Newtonian mechanics, any velocity greater than .1c added to .9c will exceed c. That’s why we have to do a Lorentz Transformation to find the relative velocity, but all that does is keep the relative velocity from exceeding c, it doesn’t keep it from increasing.

Here’s a good illustration using the same set up as the Khan Academy Video. Note that the magnitude will be the same if viewed from either object.

http://hyperphysics.phy-astr.gsu.edu/hbase/Relativ/einvel2.html#c1If the velocity of A is .9c (the velocity of the earth relative to the inertial observer)

and the velocity of B is -.5c (because it is going in the opposite direction), then the relative velocity is -0.96.

if the velocity of B is -.9c, the relative velocity is -.99c

if the velocity of B is zero, the relative velocity is -.9c

The relative velocity will

*always* be “ludicrous”, no matter what the velocity of the meteor is relative to the 3rd inertial frame, as long as the velocity of the earth relative to the inertial frame is .9c or greater.

I hope that clears up your confusion.