Memes

The relation between them is that they're both forces that scale with the inverse square of the distance between the objects. Any force that scales with the inverse square of distance has pretty much the same general form.

Another similarity is that both are incomplete, first approximations that describe their respective forces. The more complete versions are Maxwell's laws for electromagnetism and General Relativity for gravity.

There is one thing particularly interesting, and that is that the inverse square laws appears again. It appears in the electrical laws for instance.

That is electricity also exerts forces inverse to the square of distance with charges. One thinks perhaps inverse square distance has some deep significance, maybe gravity and electricity are different aspects of the same thing

...

Today our theory of physics, laws of physics are a multitude of different parts and pieces that don't fit together very well. We don't understand the one in terms of the other. We don't have one structure that it's all deduced we have several pieces that don't quite fit yet.

And that's the reason in these lectures instead of telling you what the law of physics is I talk about the things that's common in the various laws because we don't understand the connection between them.

But what's very strange is that there is certain things that's the same in both

Richard Feynman and 45:48 https://youtu.be/-kFOXP026eE?si=hAIvDhWVGxMOvEi1

Electromagnetism and gravity are both mediated by massless bosons; photons and gravitons respectively. This is why both forces follow the inverse square law.