Earth in the picture is scaled to roughly 300,000 feet per pixel; Earth's surface and both flying altitudes would be the same pixel if drawn to scale.
(~42M feet diameter shown in ~134 pixels).
Very Wrong Math
91–100 of 109 posts
Re: Very Wrong Math
#92Holy crap is one drop of stupid consuming a lot of mental energy. This is after the drop of stupid that was Terence Howard's "1 x 1 = 2" physics rant fell on everyone's head. Individual drops quickening into rain would drown us all, apparently. Do serious people like Charles Petzold (here) and in other venues address this stupid out of fear that the stupid spreads, or because they just can't stand someone being wrong somewhere like a cognitive itch that must be scratched?
If one troll flooded the zone with 30 of these over a month, mayhem would ensue. Absent knowing the true origin for this diagram, we don't even know if was stupid or malicious.
Re: Very Wrong Math
#93Earlier quoted context omitted.
For convenience, we set τ=2pi. :-) x = τ(r+1) - τr = τ(r+1-r) = τ(1) = τ
How do you pronounce that symbol?
Re: Very Wrong Math
#94Earlier quoted context omitted.
The theological argument I recently heard is, the creator just made up and down. And things move down. But it is not gravity.
> And things move down. It's not a bad way to look at it for a start. Things move down because it is their nature to move downwards. And this kind of empirical law is what we rely upon for most thought. It takes a lot of work to get to a theory that makes more general predictions. And even after having that, 98% of the time my thought is effectively just "things move down." Another 1.5% it's "things move down at 9.8…
"with a force proportional to their masses and inversely proportional to the square of their distances" ... if you ask me why, it's because "uh, they just do that?""
To be fair, that is somewhat the current scientific consensus on gravity. It just is. We can meassure it and determine a general constant and calculate with it (and even though some people claim to have understood way more, it is highly debated terrain as far as I know)
And in general, I was actually arguing with flat earthers recently a lot, I even met a flat earther in real life. It is an interesting intellectual challenge debating them. Basically rebasing all the physical theory I have. (Main summary is, they have a high ego, but lack understanding of everything and make up for it with make believe.)
If I found a school one day, one of the lessons will be the teacher telling the students: "The earth is flat! Proof me otherwise." Or more advanced, model a flat earth on a computer. Flat earthers try that for real - it gets weird very quickly, so much that I could not believe anyone taking it serious and it all is just satire. But they are for real (but with a very different concept of reality).
Re: Very Wrong Math
#95Earlier quoted context omitted.
> And things move down. It's not a bad way to look at it for a start. Things move down because it is their nature to move downwards. And this kind of empirical law is what we rely upon for most thought. It takes a lot of work to get to a theory that makes more general predictions. And even after having that, 98% of the time my thought is effectively just "things move down." Another 1.5% it's "things move down at 9.8…
"with a force proportional to their masses and inversely proportional to the square of their distances" ... if you ask me why, it's because "uh, they just do that?"" To be fair, that is somewhat the current scientific consensus on gravity. It just is. We can meassure it and determine a general constant and calculate with it (and even though some people claim to have understood way more, it is highly debated terrain a…
> To be fair, that is somewhat the current scientific consensus on gravity. It just is. We can meassure it and determine a general constant and calculate with it (and even though some people claim to have understood way more, it is highly debated terrain as far as I know)
Sure, and if we come up with some fancy unified theory, and ask "why" once more, the answer will still be "uh, because they do?."
> But they are for real (but with a very different concept of reality).
We think ourselves so advanced. I wonder what big counterfactual scientists believed in the 1900s and 2000s will be laughed at a few hundred years from now.
And, of course, some of that will be libel; e.g. that we thought the world was flat "just like Christopher Columbus's compatriots" [who didn't].
Re: Very Wrong Math
#96Earlier quoted context omitted.
That way you should be able design a disc-shaped earth with constant strength of the gravitational force on the whole surface. But it would still have a center of mass (likely lying outside the shape you're describing, in the void beneath the center point), and the direction of the force should still be pointing towards that center, no? So the problem the GP has described, that you're starting to tilt as you move tow…
I believe the strength of gravitational force would not be constant either, as your center of mass would still have a fixed location, so every point on the disc have different distances to that center of mass (in addition to not being orthogonal to the surface). But maybe it might be approximated with an infinitely long cylinder, so the center of mass is infinitely far away below the surface ?
The thinking in the other post, that the mass increases as you move away from the center, in a manner that the two effects cancel out, intuitively seems like it should be feasible. Remember that the center of mass is just an abstraction, you need to take the full integral over all mass to get the force vector at each point. And if you're closer to more mass further away from the center, which a shape like the one described above should give you, it might work. But one would have to do the math to be sure.
Edit: come to think of it, maybe that effect would let you adjust the direction of the force, too. Thinking about center of mass can be treacherous with more complex shapes...
Re: Very Wrong Math
#97Earlier quoted context omitted.
I'm considering what flat-surfaced shape you could construct with equal gravitational pull at all points. Maybe something where the center is thin as a point, the edges have a lot of depth, and they curve towards the center either convex or concave. Might run some calculus to figure it out.
yes, we call it a sphere. I am just joking with you, I know what you mean, however the fruit was hanging too low not to pick.
A sphere is only locally approximable by flat surfaces, but it's nowhere actually flat, which was a requirement in the previous post.
Re: Very Wrong Math
#98Earlier quoted context omitted.
yes, we call it a sphere. I am just joking with you, I know what you mean, however the fruit was hanging too low not to pick.
A sphere is only locally approximable by flat surfaces, but it's nowhere actually flat, which was a requirement in the previous post.
Eh, the original post wanted a convex disk that would have a uniform gravitational pull, flatness was already thrown out as a design requirement. Once convex disks are allowed, a specific category of convex disk that provides a uniform perpendicular gravitational field comes to mind. The sphere. The very object we were trying to avoid. It is one of those it's funny because of the irony things.
Re: Very Wrong Math
#99Earlier quoted context omitted.
It does not really, at least not directly. What matters is relative velocity compared to the starting and final locations, and relative to the air around the aircraft. It just happens that there are very powerful atmospheric currents that go west to east (those are due to the earth’s rotation, among others phenomena). So, when flying towards the east, catching these currents can significantly reduce flying time. When…
Thanks for this explanation; quite interesting. But it still seems to me that there might be a gravitational/inertial effects at play as well. At a (hypothetical) infinite altitude, it can no longer be said the the plane is moving perfectly in lock-step with the gravity/rotational acceleration of the earth. This implies the inertia of the plane relative to the rotation of the earth still has an effect at lower altitu…
What gravity/rotational acceleration ?
Something like this does exist under general relativity :
https://en.m.wikipedia.org/wiki/Frame-dragging
However,
> This does not happen in Newtonian mechanics for which the gravitational field of a body depends only on its mass, not on its rotation.
Re: Very Wrong Math
#100Earlier quoted context omitted.
He is talking about orbital mechanics, rather than free space. When you are in an orbit, the shape of the orbit is determined by your speed. At every distance from the center of the object you are orbiting (such as the Earth), there is a speed that makes your orbit a circle. If you are going at any other speed then your orbit will be an ellipse instead. Too fast and your orbit rises higher above the Earth. Too slow a…
Just to point out here what's different between "space" and "not space": "Space" assumes no "height control",i.e. ways to exert force "down or up" along the earth-object direction. That's obviously not true for a plane. If you can exert force in that direction, you can change speed and keep the shape of the trajectory around earth constant.
Wait, why wouldn't an orbiting satellite not be able to apply its thrusters "down"?