No. It should be considered as angular motion, for the very reason you are pointing out. The distance moved is basically nothing. That is also the big problem with your zig-zag argument, the distance moved is nothing compared to how far away these objects is. The dominating factor is our turning.

Yes, for us, it is only that mere 0.68 mm, but what is the effect of that on the moon?

You are shrinking it by a factor of 100 000.

Well the moon is 400 000 km away.

That means the moon in your scaled down version is 4 km away.

Doing it the "common" way for those without great math skills, that puts its orbital circumference at 25 km.

That means 1 degree of that is roughly 7 m.

That is why the angular velocity is important, due to how little we are moving.

So, while 4km distant moon (in our scaled down model) moved 7m to the LEFT we moved (on our merry go round) 0,5 meter to the LEFT (also), and **expecting result of our 0,5 m long motion should be apparent translation of our moon to the RIGHT for 2,5 apparent moon's diameters**. While we are traveling these 0,5 m long trip we have to surmount 0,68mm bulge (which is less than 1 fucking mm which is 25th part of one fucking inch), and such lateral motion you are still ready to call "circular motion" (due to the fact that we have to overcome a whole 25th part of one fucking inch by moving along 0,5 meters (out of 157 m of total circumference) long path of our 50m (in diameter) big merry go round)?

No, that is not what I said at all.

However I did notice a mistake. That would have been 70 m.

The moon, in its 4km orbit, is moving at a rate of roughly 0.04 degrees per 5 minutes remember? The 70 m was for 1 degree, not even the 1.25 degrees.

Completely ignoring the rotation and instead just focusing on the translation, firstly, as you pointed out it can be approximated as a tangent and forget the in and out part.

Now then, we have our 50 m merry go round. I don't really care how accurate that is, I will leave it at that.

In 5 minutes we move 1.25 degrees around it. That means we would have moved ~ 1m. (closer to 1.09).

The moon, with its 4 km orbit, is moving 2.79 m.

That means the relative motion would be a maximum of 3.7 m and a minimum of 1.7 m (ignoring direction), and that is over 4 km.

If you were looking at buildings 4 km away, and just steps a few m to the left or right, do they appear to move? No.

That is because of just how small that is.

Using the maximum of 3.7 m, the angular displacement that causes is 0.05 degrees, for the 1.7 it is 0.02 degrees.

This linear motion is not causing the apparent motion of the moon.

Do you know what is? YOUR ROTATION. That is why it is important.

The motion, just due to translation would be a mere 0.05 degrees, at most.

But at the same time you have rotated 1.25 degrees.

You turning 1.25 degrees will make everything appear to move 1.25 degrees in the opposite direction.

Okay?

The translational motion of you and the moon combined will make it appear to move no more than 0.05 degrees. But your rotation will cause it to appear to move 1.25 degrees.

To put in another way:

You have moved 1.09 m (left or right, I don't give a shit).

The moon has moved 2.79 m, to the left.

But you are now looking at spot that is 70 m to the left of the moon.

What this means is that for your current view, the moon is roughly 70 m (if you like, again using simplified math to analyse it, you can say somewhere between 66.3 m and 68.3 m) to the right of where you are looking at.

That means the moon will appear to move to the right.

That is the primary thing which makes all celestial objects (i.e. everything except Earth) appear to move. The primary exceptions are close by meteors and artificial satellites if you wish to include them.

A better way to understand is to spin on the spot.

In this case your linear motion due to rotation is NOTHING.

So according to your reasoning, this means we should use that, treating it as linear motion.

And that should mean that everything appears to remain in the exact same position

But it doesn't. Instead, a slight turn can make far away objects appear to move a massive amount.

It isn't the linear motion or translation that makes it a big issue, it is that you are now looking in a different direction.

If you turn 1 degree, everything appears to turn 1 degree.

Try to verify this : move 0,5 m to the LEFT and see if 4 km distant object (with proportional dimensions to moon's alleged dimensions) would apparently translate 2,5 apparent moon's diameters to the RIGHT! You are perfectly aware that such experiment would prove that the moon is not so far away!!!

No, you are just helping to back me up.

This is exactly what I have said before, your little pathetic step to the left or right will have basically no impact on the apparent direction of this far away object.

But turning left or right will have a massive one.

So go and do it.

Go view a distant object (4km) and step even a few m to the left or right.

See if its position appears to change much.

Now, turn 1.25 degrees to the left or right and see what happens?

But even if we could achieve such result with our scaled down model, you would still have to verify THE CRUCIAL part of my argument : you should move to the RIGHT (Noon scenario) and see in which direction 2,5 apparent moon's diameters would move...

No, that is the most crucial flaw in your argument.

Moving to the left or right will have virtually no impact.

What will matter is the turning part.

Here is a simple experiment you can set up:

Get a turntable, where you can accurately control the angle.

Now if you like, for the moon, get either a much larger turn table, to mount the moon on (but make sure the small one can still turn independently or in a compensated way), or for the simplified version, just get a small linear track that you can move it along, or just move it yourself.

Now mount a camera on the turntable.

First, just as a control, mount in on the centre, then in a second run, mount it close to the moon (simulating the moon at closest point, so midnight for the full moon), then mount it far away

Now, set it in motion (or just take a before and after).

Notice what happens in all 3 cases?

The moon appears to move to the right.

Here is an actual scale drawing (using the equator to further emphasise the point):

https://cad.onshape.com/documents/896878716739e463043c15c5/w/738a02ab853e0a649e11fead/e/14f4cbf0e0fa6707e220bb0bThe one on the right is the initial condition, with the person close to the moon looking due south and the person far away looking due north, so both straight at the moon.

The one on the left is the final condition, after the 5 minutes. The moon is further along its orbit (to the left).

The person close to the moon is further along Earth (to the left), but the moon has moved an apparent 1.23 degrees to the right.

The person further away from the moon is further along Earth (to the right), but the moon has moved an apparent 1.19 degrees to the right.

Happy now?

This is one with the FE distances from before (with the moon turning 1.21 degrees to complete roughly 1 circle a day but go through a cycle once a month):

https://cad.onshape.com/documents/600d80bb7ae333fdbadf44fa/w/3bf7ef5d3de7e0031c3460d1/e/bce03ddfbf36eeab307c6195Again, the one in the middle is the initial.

The one of the left is after 5 minutes.

Now, it is just the moon moving along its path (to the right).

For the person close to it, the moon has appeared to move 1.87 degrees to the right.

For the person far from it, the moon has appeared to move 0.90 degrees to the right.

See how it is much worse for the close moon.

As a bonus comparison, there is another one on the right.

This has this much smaller system rotating just like the real one.

So, the moon is further along its path (0.04 degrees, to the left).

The person close to the moon has rotated with Earth, to the left, but the moon appears 1.87 degrees to the right.

The person further away from the moon has rotated with Earth, to the right, and the moon appears 0.90 degrees to the right.

Notice something quite significant?

These angles are exactly the same as the small stationary Earth, only moon moving case.

This is because IT DOESN'T MATTER WHICH IS MOVING! ALL THAT MATTERS IS THE RELATIVE MOTION!

And that relative motion is the same with a stationary Earth and moving moon, a stationary moon and rotating Earth, or a rotating Earth with a moving moon (as long as they are matched).

So this can NEVER be an argument against a moving Earth.

All this is an argument for is the distance to the moon.

If the moon was close, like in the FE situation with it circling above the tropics, then over the 5 minute observation, at mid night you would expect an angular displacement of 1.87 degrees and at mid day it would be 0.90 degrees. That is over double for mid night.

If the moon was distant (like in reality), with it circling in its orbit, then you would expect it to move 1.23 degrees to the right at mid night and 1.19 degrees at mid day. That is a difference of less than 2%.

All your argument does is show the moon isn't close.

It doesn't show Earth is stationary. It CANNOT show Earth is stationary.

At best, you could observe this double speed at mid night relative to mid day and conclude the moon is close, but that isn't observed.

So just like your previous zig-zag argument, this one is a complete failure.

I'm not going to bother with your pictures (especially as it seems to have nothing to do with the argument at hand and instead is just ignoring the third dimension.

I have put in more than enough effort refuting your crap 3 times, pointing out what is wrong with it and showing how to do it correctly, with you just ignoring it.

Now are you going to give me the same courtesy and actually read what I have said and process it and either refute it rationally or accept it?