Also note that the 3 body problem applies to ALL forces of nature, not just gravity.
For example, while we can perfectly solve the Schrodinger equation for a simple hydrogen atom with a single proton and a single electron, we can't get a simple solution for anything else.
We can get a very good approximation if we only have 1 electron, regardless of what is in the nucleolus, but throw in a single second electron and all that goes out the window.
So do you discard all forces, or is it just gravity you hate so much due to its connection to the shape of Earth.
One of the troubles here is the infinitesimal effect.
It isn't infinitesimal.
We are talking about a variation in g of ~0.05 m/s^2. This is quite large compared to what we can measure. It is also quite significant.
After a day (86400 seconds) this variation would cause a variation in distance of ~187 Mm.
So this is a massive variation which would tear Earth apart in less than a day.
Buoyancy is insignificant, especially when you use a vacuum.
Remember, the buoyant force on an object is given by F=-g*rho(f)*v.
Meanwhile, the force due to gravity is given by F=g*rho(o)*v
So the total force is F=g*rho(f)*v-g*rho(o)*v = g*v*(rho(o)-rho(f)).
And the acceleration (what is actually measured) given by a=F/(rho(o)*v)
This means a=g*v*(rho(o)-rho(f))/F/(rho(o)*v)
=g*(rho(o)-rho(f))/rho(o).
And without the buoyant force we instead have a=g = g*rho(o)/rho(o)
This means the difference is:
Deltaa = g*rho(o)/rho(o) - g*(rho(o)-rho(f))/rho(o). = g*rho(f)/rho(o)
So even if you were using air, instead of a vacuum, with a density of roughly 1.2 kg/m^3, with a steel ball with a density of roughly 8000 kg/m^3, you are looking at a difference of 0.00147 m/s^2. Quite a lot smaller than the observed variation of 0.05 m/s^2.
But more importantly, that would be a difference between a perfect vacuum and air.
In order for this to explain the observed variations across Earth, you are looking for variations in that difference.
So what you actually need is a difference in density to give a difference.
And with that variation of 0.05 m/s^2, that would be a variation in density of roughly 40 kg/m^3, for steel. This would also vary with the material used.
If instead you used water, you only need a variation in density of 5 kg/m^3.
Meanwhile, if you use a vacuum at a very low pressure, say 1 mbar, then you cut that difference by a factor of 1 thousand, and there is no hope of having that explain it.
The error due to difference in the buoyant force is miniscule and has no chance of explaining the variation in g across Earth.
Seismic activity has a completely different reason.
This activity is not continuously up nor down. If it was, it would tear Earth apart.
Instead it varies. If this was the cause, then at times you would get larger values of g and at times you would get smaller.
So no, it doesn't explain it either.
Also note that unless you have a reason for these causes to vary systematically across Earth, you would expect it to fluctuate, such that some times the poles would appear to have stronger gravity and sometimes weaker gravity.
So how about instead of just asserting it can be explained, you actually try to.
Because we know that the air pressure isn't going to be an issue due to units sealed in a vacuum. We know it isn't seismic activity as that would tear Earth apart. There are also non-magnetic versions and versions which are shielded from magnetism. There is even temperature compensation or control. They also have tilt sensors and that can be corrected for by levelling the instrument, or just by taking multiple measurements to correct for tilt.
Experimentally, this has never been established as gravitation is unscientific fiction with no reality. It cannot be measured or manipulated, so it cannot be shown to be real in any way. It is not even defined rigorously enough to begin to do so, if one were so inclined.
Youi discarding it and all the evidence in no way impacts reality.
It has been established quite conclusively, with plenty of evidence to support it.
It has been shown to be real beyond any sane doubt.
Just like mass, which you also dismiss.
Again, the fact that weight varies, while mass doesn't, shows weight is not the intrinsic property, mass is.
"If Earth was flat, we would have a vastly different time setup."
If the earth is flat
Notice the difference between what I said and what you said?
I said if Earth WAS flat, because we know it isn't.
You said if Earth IS flat.
You start with the baseless assumption that Earth is flat, and use it to conclude that whatever is seen is what you would expect on a flat Earth, to dismiss the things which show Earth isn't flat.
We grasp this circular reasoning quite easily, we just discard it as illogical garbage.
Instead, we accept that what is observed in reality is inconsistent with a flat Earth and use that to discard the idea of a flat Earth as not matching reality.
The fact that Earth is not flat makes your tautology unsound.
One such example is how time works, especially with sunrise and sun set.
The observation of sunrise and sunset shows that the sun would go below a flat Earth, just like in the ancient FE models which have more in common with todays RE model than todays horribly flawed FE models.
What this means is that the sun would rise for pretty much the entire Earth at once and set at once.
And the fact that it's apparent size does not vary throughout the day nor with location on Earth shows it must be quite far away from Earth, many times the size of Earth.
This means it would appear in roughly the same location for everyone on Earth.
This means there would be a single time zone for all of Earth.
Meanwhile, with a RE, only roughly half would be illuminated by the sun at any time, giving rise to time zones.
And the inclination of Earth w.r.t. its orbit means that the half which is illuminated will appear to rock back and forth, causing the time of sunrise and sunset to vary throughout the year, causing people to invent DST.
Now, some FEers try to get out of that by appealing to a spotlight sun, but that doesn't explain the observed patterns of illumination and darkness. For example, with the common NP centred map, and a simple spotlight sun, you cannot illuminate half the equator, without having also illuminating the north pole. That would mean the north pole would be perpetually in daylight never having any night.
It also fails to explain sunrise and sunset.
And during the equinox, you need a semi-circle for the spotlight pattern.
It also has no chance of explaining why the further south you go during the southern summer you have more hours of daylight, and the sun appears to rise from south of east.
You need so much extra convoluted BS to make it work (and this convoluted BS goes directly against other claimed evidence for a FE), when a RE explains it so simply.
So because Earth IS round, we have the time setup that we do.
If earth WAS flat, the time setup would be vastly different and much easier.
For such an example, consider the Minecraft overworld. The entire world has day at the same time, and night at the same time. The sun and moon have identical positions regardless of where in the world you are. That is the kind of time setup we could enjoy if Earth WAS flat.
And I see that there are still lots of points you haven't addressed, but I will give you time to do so.