Finn Boire

[1 Hour of Thought] Gravity being a force

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To start this off, I'm asking myself the question: What if instead of a constant acceleration, gravity was a constant force regardless of mass?

Of the fundamental forces of the universe, the gravitational force that is applied to objects is arguably one of the most important, and much like any other force, it follows the idea of Issac Newton’s second law, namely $$F=ma$$, where $$m$$ is the mass of the object that the force is getting applied to and $$a$$ is the acceleration. This applies to all forces. The force of gravity, much like any other force, is governed by this law, and can also be determined by the law of universal gravitation (thanks again, Newton!), which is $$F=G\frac{M1 M2}{d^2}$$. Now, with the knowledge that a force is composed of a mass times an acceleration, we can remove one of the masses to get the acceleration that is occurring due to one object’s gravity, based off of the distance. Phew, that took a lot of words.

I guess this is just a long-winded way of saying that things accelerate equally due to an object’s gravity, as the other object’s mass cancels out, like the old experiment done by Galileo where he dropped two objects of unequal masses only to find they land at the same time. The acceleration due to gravity by an object, like the earth, is constant, a 9.81 meters per second per second down towards the center of the earth, and that’s simply how the universe is. This got me thinking, what if gravity wasn’t a constant acceleration (provided equal distances from the center of mass of the earth), and was instead, a constant force? Wouldn’t that be strange? All objects would be the exact same weight, exerting the exact same force downwards.

The physical world would be drastically different. On a large scale, solar systems would still appear to be similar, as the larger an orbiting body gets, the less angular acceleration it would have, and therefore for it to stay in orbit, it would need to either slow down or go further out. That means that we would still have smaller, faster planets orbiting stars closer in, and the longer, larger-massed planets orbiting further out, just like lots of solar systems. However, this is with the assumption that planets of reasonable size would even form at all. In solar nebulae, when typically dust begins to group together and begin forming planets, their masses get larger and larger and therefore the acceleration on other objects gets larger and larger, clumping larger and larger bodies together till they eventually form planet-sized objects. With $$F = G\frac{M}{d^2}$$ in action instead of $$a = G \frac{M}{d^2}$$, regardless of the other body’s mass, there would always be constant forces pulling them together, not acceleration, and depending on the other object’s mass, it could accelerate towards the other object slowly or quickly. With small objects (dust particles and the like), they would be accelerated towards each other very quickly, so a large amount of small asteroid-sized objects would form, and not end up getting much larger than that, because as soon as the mass increases to a large amount, for the force acting on the object to stay the same, the acceleration has to decrease, and all these small asteroids composed of several hundred tons(ish) would take a very long time to clump together to form the normal-sized planets we know and love. Although it’s not impossible for large planets to form, I’m pretty sure that they’d take a lot longer than they would in our current universe.

Jumping around some more (cut me some slack, I’m doing this with a time limit so I don’t have much time to edit things or make them make sense), let’s pretend that the solar system somehow still did form into the way it did. On the Earth itself, creatures would have evolved completely differently. If there was no increase in weight based off of mass, then there would not be any reasonable limit on how large creatures could become. In fact, avian creatures might have evolved to become really big, as they would then be accelerated less by gravity and it would be easier to fly (that’s ignoring the fact that it would require a lot more force to accelerate a large-massed object, whoops). Geographically, the landscape would be different, as a large mountain (point mass!) would weigh the same as a small tree, and so there would be lots of things that would appear unstable in our universe and world (A few trees holding up giant rocks, or a large boulder floating on water).

It occurs to me as I’m writing this that I’m assuming everything to be point masses (a large mountain, etc). If they weren’t point masses, not only would it make it a lot harder to think about, but it would make it almost impossible for any productive speculation to happen, as any particle would experience the same force as the largest thing imaginable when subjected to the same gravitational field, so I don’t think anything would be able to form out of the particles when under such forces. Problematically, there’s also the question of “What would happen if you put a rock on top of another rock?” Would the upper rock be exerting the same force down on the lower rock as the lower rock would be exerting upon the ground? And if so, what happened to the lower rock’s force that was getting exerted onto the ground? If you remove the upper rock, it’s still exerting the same force? Oof that’s actually quite a problem to think about.

I’ve run out of the time I allocated to thinking about this, but hopefully this was interesting for you to read, or at least it raised some interesting questions that you might think about for a while!