system
Given the following post, respond as if you're commenting on Reddit:
human
Physics question: limits of gravity equation?

I've taken a few physics courses, and the other day I was thinking about the gravity force for equation we learned, Fg=G*(M1*M2)/(d^2). The gravity constant, G, as well as the masses, are constant values, so it seems like as the distance between two objects approach zero, that the force of attraction between them would approach infinity. According to my everyday observations, this doesn't seem to be the case, so I feel like this may be a sort of "watered down" equation taught for introductory courses since it works for most circumstances. 
I'm really interested in physics, so don't be afraid to give me a detailed, complex answer.
gpt
Your everyday observations never really see anything get close enough to anything else for this to come up. For example, you are currently about 6380 km from the center of gravity of the Earth. Solid objects have a finite size that is much, much greater than the sizes required for this to be relevant, and Newton's law works well in these situations.

If objects are compact enough, there is a region around them from which nothing can escape their gravitational field. You might know these objects as black holes. So you could apply Newton's law to objects getting closer and closer to a black hole, but once they cross the event horizon, Newton's law isn't really a good description anymore.

Now if we have one kind of physics close to black holes and another kind of physics far from black holes, is there a single model that describes gravity in both cases? There is, and it's Einstein's general theory of relativity. It describes how the geometry of spacetime is modified by massive objects, and things moving through space follow this geometry.