Well that’s lovely, thank you 😊
So Newton’s law of universal gravitation is:
F= G×M×m/r^2
which is simple enough to be able to say it in a sentence: "the force of gravity F on two masses M and m is proportional to their masses and square of the distance between them, r " so the heavier and closer planets/suns/black holes are, the greater the gravitationnel pull.
Coulomb’s law is:
F= k×Q×q/r^2
which is pretty much exactly the same as you have probably noticed: "the force of electrical attraction F on two charged particles Q and q is proportional to their charges and the square of the distance between them, r "
So the exact same rule applies to planets and atoms. Their behaviour can be explained in the same way. It’s called an “inverse square law”, it’s got a name because they happen everywhere. And it’s just, like… Why? Why does the universe work that way? You’re not really encouraged to ask that sort of question as a science student, because it “goes nowhere” and doesn’t lead to actionable results. But I think it quite spooky. There are loads of weird results like that in science and maths (see quantum theory for abundant examples!) but it’s unusual to be able to sit and think about it. There is, for the inverse square law, a pretty elegant mathematical explanation for why they’re so common, but it doesn’t quite scratch the itch for me, it just raises more questions
Edit sorry for text wall. This is probably why I shouldn’t do this!
You mentioned a mathematical explanation for why it’s so common. Got any further reading on that? It’s mind blowing that the math for calculating planetary movement and atomic behavior is exactly the same formula, with different variables. Do you have any theories on why inverse square law is so common?
I think inverse square laws are so common because they apply to situations where the distance of one object from another (a one dimensional line) is used to calculate the force potentially felt at any point across the surface of a sphere (a TWO dimensional surface) at that distance.
But then you also have the strength of magnetic fields that follows an inverse CUBE relationship. The simple way I model this in my head is that magnetic dipole fields kind of fill a three dimensional volume with curved field lines, as opposed to gravity or electric charge where the “lines” go straight out, and at any specific distance the total strength of the omnidirectional field is spread throughout that two dimensional surface of a sphere of the same radius.
The Wikipedia page is a good start. In a nutshell:
Since the surface area of a sphere (which is 4πr2) is proportional to the square of the radius, as the emitted radiation gets farther from the source, it is spread out over an area that is increasing in proportion to the square of the distance from the source. Hence, the intensity of radiation passing through any unit area (directly facing the point source) is inversely proportional to the square of the distance from the point source.
There’s a good visualisation of that explanation which is the banner picture on the Wikipedia page.
I don’t have any better theories than the existing ones, for sure! But there is an underlying pattern that goes deeper even than that law - the principle that physical objects follow the path of least resistance links these laws and many many others.
This is actually really cool. I have no idea about any of it, but I remember watching a documentary a long time ago that said certain mathematical patterns repeat all over nature. What you said seems similar to that.
Well that’s lovely, thank you 😊 So Newton’s law of universal gravitation is:
F= G×M×m/r^2
which is simple enough to be able to say it in a sentence: "the force of gravity F on two masses M and m is proportional to their masses and square of the distance between them, r " so the heavier and closer planets/suns/black holes are, the greater the gravitationnel pull.
Coulomb’s law is:
F= k×Q×q/r^2
which is pretty much exactly the same as you have probably noticed: "the force of electrical attraction F on two charged particles Q and q is proportional to their charges and the square of the distance between them, r "
So the exact same rule applies to planets and atoms. Their behaviour can be explained in the same way. It’s called an “inverse square law”, it’s got a name because they happen everywhere. And it’s just, like… Why? Why does the universe work that way? You’re not really encouraged to ask that sort of question as a science student, because it “goes nowhere” and doesn’t lead to actionable results. But I think it quite spooky. There are loads of weird results like that in science and maths (see quantum theory for abundant examples!) but it’s unusual to be able to sit and think about it. There is, for the inverse square law, a pretty elegant mathematical explanation for why they’re so common, but it doesn’t quite scratch the itch for me, it just raises more questions
Edit sorry for text wall. This is probably why I shouldn’t do this!
You mentioned a mathematical explanation for why it’s so common. Got any further reading on that? It’s mind blowing that the math for calculating planetary movement and atomic behavior is exactly the same formula, with different variables. Do you have any theories on why inverse square law is so common?
I think inverse square laws are so common because they apply to situations where the distance of one object from another (a one dimensional line) is used to calculate the force potentially felt at any point across the surface of a sphere (a TWO dimensional surface) at that distance.
But then you also have the strength of magnetic fields that follows an inverse CUBE relationship. The simple way I model this in my head is that magnetic dipole fields kind of fill a three dimensional volume with curved field lines, as opposed to gravity or electric charge where the “lines” go straight out, and at any specific distance the total strength of the omnidirectional field is spread throughout that two dimensional surface of a sphere of the same radius.
4D thinking. That’s where my brain says “no more”
The Wikipedia page is a good start. In a nutshell:
There’s a good visualisation of that explanation which is the banner picture on the Wikipedia page.
I don’t have any better theories than the existing ones, for sure! But there is an underlying pattern that goes deeper even than that law - the principle that physical objects follow the path of least resistance links these laws and many many others.
This is actually really cool. I have no idea about any of it, but I remember watching a documentary a long time ago that said certain mathematical patterns repeat all over nature. What you said seems similar to that.