Statics is the center of gravity around which any course in engineering is created. It was in my statics class that I was first introduced to the units of measure feet to the fourth power. This is the units for a moment of inertia. But what does it look like?
This was the question I asked my instructor. What does ft^4 look like? I mean in my life, which at the time was going on 50 years, I was able to see in my mind what ft.^2 (area) looks like. I also could “see” what ft.^3 (volume) looks like, but ft^4 was a mystery to me. So I asked my instructor.
He couldn’t help me. I told him that it must be similar to a sphere, and settled on a sphere at a radius as my mental image of ft^4. I don’t know how helpful it was to have this picture, but I ended up receiving an A- in the class, which I was real satisfied with.
But really, if you are able to hold a mental image of gravity, gravity has the units of measure ft^4. If you can’t hold that image, gravity is probably unitless.
Maybe if my statics class had been calculus based I would have come to this image as gravity sooner, as calculus, I was told, enables you to understand infinity better, which seems to me would have made the understanding of gravity better, but I am not sure.
I haven’t worked out the math for gravity yet, but then math was never my greatest advantage, in engineering class. I understood math, but I had the same ability in the maneuvering of numbers as I did in maneuvering letters for spelling, poor.
That said, gravity is basically acceleration at zero velocity, which, unlike acceleration where at zero velocity there is a change in time but not distance, in gravity there is a change in distance, but no change in time. The units of measure for acceleration is second^2 and the units for gravity is ft^4. I suppose ft^4 is a quantum.
Time is a position, as is space a distance (or a bunch of distances). That is why the speed of light is a constant. Once you reach the speed of light, you have positioned yourself in the same position as all time in all the moments in 3 dimensions. The only thing left in the fourth dimension is the change in distance, and that change is the same in all our solar system and beyond. So, upon reaching the speed of light, acceleration becomes constant, but velocity stops, and what you have left is ft^4 power.
As gravity is energy and not force, I guess I can start by writing: E=ft^4, which has zero meaning to me and probably everyone else. You got a moment? :)