The short answer is, No. The gravitational potential can be, also, deduced from what is known as Gauss' theorem, which implies that the size, or shape, of the mass distribution doesn't matter at distances beyond it.

The relations presented are just the result of dimensional analysis, they don't describe the dynamics, unless additional assumptions are made.

Stam Nicolis : "Gauss' theorem"

To my understanding the Gauss as well as the Shell Theorem applies to field gradients.

"they don't describe the dynamics"

The dynamics will come in with the acceleration of e.g. rotating bodies.

https://www.researchgate.net/post/How_to_probe_the_local_gravitational_potential_originating_from_remote_masses_of_the_universe

That dynamics is (a) non-relativistic and (b) doesn’t place any restriction on the size of objects, either.

The statement referring to field gradients is incorrect.

There's no bound on the size of objects in the non-relativistic approximation to gravity.

The only restriction on the size of objects comes from general relativity, that implies the existence of spacetime singularities. So an object of mass greater than a specific, finite, value, whose size is less than a specific, finite, value, can’t exist-in spacetime, since it will suffer collapse and produce a singularity for certain observers.

Stam Nicolis

Thanks for your kind instruction. I'm sorry to say that I presently cannot respond in adequate manner.

Dear Johan K. Fremerey , dear Stam Nicolis ,

following my basic idea to a ToE, the answer is yes, but it not so easy to see the relationship:

Imagine a 3D-grid of scalar voltage values. Between neighbors a simple balancing mechanism works per time-step: take-over the mean value of all 6 neighbors' values. This is a non-linear, dispersive medium, allowing voltage waves to propagate.

One obvious consequence is the smallest wave period time, which can establish. This is the "specific, finite, value" Stam talked of above. No wave can have higher frequency than this. This is the PLANCK time.

The second consequence is the constant propagation speed of the voltage wave periods within the medium. Certainly, this is c.

The third consequence is that superposing voltage waves can interact, they can transport momentum mutually, because the medium is non-linear, dispersive.

The forth consequence is a very tiny redshift of forwarding wave periods. There is a factor K = 2G∙mᵥₑᵥ²/(ħc) = 8.13434(6)∙10⁻³⁴ by which each wave period gets longer and longer.

Yet, one can already see the dependency on gravitation: G.

I.e., since K is a structural constant, VEV is dependent on G.

VEV is the basis of all particles, also, determines the base of their sizes.

VEV is the Vacuum Expectation Value, the Higgs-field's energy, which is the base of all particles' masses, thus, of their sizes, also. -> See more below, related to gravitational mechanism...

K is a structural constant: The redshifted voltage waves, focused at a PLANCK oscillator (with the smallest wave period, as explained above), at a certain number of periods, build a spherical shell due to resonance: the energy of the shell's standing wave (opposite points of sphere) is exactly the "beat"-frequency-related energy of the redshifted arriving wave's energy, arriving from the opposite point, and the local PLANCK-energy, thus, resonancing.

With this info, your question is answered, within my ToE model.

But, how does gravitation act, based on waves and momentum?

There is a fifth consequence: an energy-backflow, exactly backwards, due to energy conservation: forward energy decreases per wave period by K∙E, thus, K∙E is flowing backward per wave period. E is wave period's energy.

Assuming a PLANCK-oscillator, all its radiated voltage waves send back K∙E per wave period, contemporaneously. The complete energy-backflow will focus at the PLANCK-oscillator again, but delayed.

To accelerate such oscillator, its focus has to be displaced!

Since the waves of the energy-backflow of one oscillator interact with other waves of other energy-backflows of other oscillators, their backward paths can be slightly different, they can be "bent" by the other energy-backflow-momentae. The consequence is a slightly shifted focus of returned energy: the oscillator accelerates, delayed.

Thus, we "feel" inertia when accelerating masses...

Hence, VEV-oscillators, the "vacuum", the Higgs-field, are resonances of the PLANCK-oscillators, QM-fluctuations at PLANCK-level.

Particles are resonances of the VEV-oscillator.

Gravitation is the result of the energy-backflow of each particle.

"Does the universal gravitational potential determine the dimension of elementary particles?"

The leading question becomes even more evident by introducing Iω=ℏ/2, with I=mr2/2 denoting the polar moment of inertia of a solid cylinder as already applied in our mechanical proton analogue, see reference below. This will takes us to

ℏω/m = (rω)2 = c2 = 2GMu/Ru

for the peripheral speed of an elementary particle* as related to the universal gravitational potential. In analogy to the de-Broglie electron model in atoms we may assume a threefold standing wave in order to explain the proton radius in its triple-quark configuration.

*(added October 10, 2024) Please note that according to our triple-gyro proton model the above relation applies to a single gyro with mass mg = mp/3 and radius rg = 3ℏ/mpc ≈ rp/2.

Research Proposal Triple-gyro model for deduction of proton radius and magnetic moment

I just have posted a new comment to my proton model:

Research Proposal Triple-gyro model for deduction of proton radius and magnetic moment

Yes, Hans Reissner and Erwin Schrödinger first hypothesized this relationship. It was popularized by Dennis Sciama and Hans Jürgen Treder. Please refer to this work from Bonn also: Preprint A unified theory of gravity and inertia