eli5: What is an inverse square force and how is gravity an inverse square force?
In: Physics
The inverse square means that the force is proportional to 1/D^2 where D is the distance from the origin.
Let’s say you’re some distance away from a planet, and you get some amount of force acting on you.
If you get twice as far away, the force is a *quarter* as strong.
If you get three times as far away, the force is a *ninth* as strong.
If you get four times as far away, the force is a *sixteenth* as strong.
Now, why does it do this?
I used to read late into the night with just a lamp to read by – and my hands would get cold. This was in the bad old days of incandescent lightbulbs, which gave off a buttload of heat – so I’d warm up my hands by putting them close to the bulb.
Of course, the closer my hand got, the hotter it would get – within a few inches it would be painfully hot, but a foot away it would only be slightly warm, and from two feet I couldn’t feel it at all.
But here’s the thing: the closer my hand got, the darker the room would get, as well. Which makes sense – it was casting a bigger shadow… *because it was blocking a bigger share of the light.*
Oh my god.
The falloff in heat – the inverse square law – isn’t about *physics*, it’s about *geometry*.
If I didn’t mind burning my hand, I could have wrapped it right round the bulb, and covered the whole thing, using up absolutely all of the light.
The further away my hand got, the less area I could cover. At a foot away, I could only cover as much as a handprint on a basketball. At two feet away, I could only cover as much as a handprint on a gym ball.
The force doesn’t fall off with distance – the area it’s spread over just gets bigger.
The surface area of a sphere increases according to the *square* of the diameter.
The amount of that sphere covered by a given object, your share of the total force – is thus proportional to *one over the square* of the diameter.
Latest Answers