I'm curious, if based on what we know with Newton's law, can we determine if a random planet, knowing it's mass and gravitational pull, can hold a moon in it's orbit.
Or to phrase it another way, is there a gravitational force "range" in universe where if a planet has a force less than that range, a moon won't stay in orbit and just escapes and if the planet has a force more than that range, the moon is pulled into the planet.
No, celestial mechanics doesn't work like that. Newton's law of universal gravitation says that the gravitational force $F$ between two bodies is $$F = G\frac{m_1m_2}{r^2}$$
where $G$ is the gravitational constant, $m_1$ and $m_2$ are the masses of the two bodies, and $r$ is the distance between their centres. So the "gravitational pull" between the two bodies is fully determined by their masses and the distance.
It's also useful to consider the energy of a gravitational system. The kinetic energy $E_k$ of a body of mass $m$ with a speed of $v$ is $$E_k = \frac12mv^2$$
The gravitational potential energy $U$ of a two body system is given by $$U = -G\frac{m_1m_2}{r}$$
The two bodies are gravitationally bound to each other if the sum of their potential energy and their kinetic energies is negative.
In principle, any two bodies can be in orbit around each other, no matter how big or small they are. In our Solar System, all of the planets except for Mercury and Venus have moons, and according to Wikipedia
As of January 2022, there are 457 minor planets known or suspected to have moons.
For example, the asteroid 243 Ida and its moon Dactyl:
In the Solar System, everything is orbiting the Sun. For a body to retain a moon, the moon's orbit must be within that body's sphere of influence, known as the Hill Sphere. Otherwise, the moon's orbit will be perturbed too much by the Sun, and it will end up in an orbit around the Sun that's independent of the other body.
Any planet can hold a moon in orbit. It just has to have the right distance and velocity, the moon and the planet circle around there center of mass.
