Tap for spoiler
The bowling ball isn’t falling to the earth faster. The higher perceived acceleration is due to the earth falling toward the bowling ball.
The bowling ball isn’t falling to the earth faster. The higher perceived acceleration is due to the earth falling toward the bowling ball.
Why your spoiler is wrong:
The gravitational force between two objects is G(m1 m2)/r²
G = ~6.67 • 10^-11 Nm²/kg²
m1 = Mass of the earth = ~5.972 • 10^24 kg
m2 = Mass of the second object, I’ll use M to refer to this from now on
r = ~6378 • 10^3 m
Fg = 6.67 • 10-11 Nm²/kg² • 5.972 • 1024 kg • M / (6378 • 10^3 m)² = ~9.81 • M N/kg = 9.81 • M m kg / s² / kg = 9.81 • M m/s² = g • M
Since this is the acceleration that works between both masses, it already includes the mass of an iron ball having a stronger gravitational field than that of a feather.
So yes, they are, in fact, taking the same time to fall.
Uh… That’s not how that works. The distance between two objects changes with acceleration a1-a2 where object 1 moves with acceleration a1 and object 2 a2 (numbers interchangeable). In the bowling ball’s case a2 is the same but a1 is bigger in the negative direction so the result is that the bowling ball falls faster.
Calculate the force between the earth and the bowling ball. It’ll be G • (m(earth) • m(bowling ball)) / (r = distance between both mass centers)²
Simplify. You’re getting g • m(bowling ball).
Now do the same for the feather. Again, the result is g • m(feather).
Both times you end up with an acceleration of g. If you want to put it that way: The force between the earth and the bowling ball is m(bowling ball)/m(feather) times as high as the force between the earth and the feather, but the second mass also is m(bowling ball)/m(feather) times as high, resulting in the same acceleration g.
Higher force on same mass results in stronger acceleration. Same force on higher mass results in lower acceleration. Higher force on equally higher mass results on equally high acceleration.
I just asked my professor this exact thing (if the ball would get to the earth sooner because it accelerates the earth towards it) like two weeks ago and my previous message + this message was his explanation.
PS: If you’re looking at this from outside, the ball travels less distance before touching the ground (since the ground is slightly nearer due to pulling the earth more towards it), but also accelerates slower while accelerating the earth faster towards it. The feather gets accelerated faster towards the earth and travels a longer distance before touching the ground but doesn’t accelerate the earth as fast towards it.
But because we’re not outside, we only care about the total acceleration (of the earth towards the object and the object towards the earth), and that’s g. We don’t notice if (fictional numbers) the earth travels 1m and the object travels 1m or if the earth stays in place and the object travels 2m, what matters for us is how long it takes an object 2m away from the earth to be 0m away from the earth.
So let’s just look at that again. The bowling ball’s (mass m1) acceleration is GM/R². The feather’s is also GM/R². They have the exact same acceleration, which is g. I’m not sure where you’re getting that the bowling bowl accelerates slower. Meanwhile in the bowling ball’s case the Earth’s acceleration is higher, as you already said. This results in less free fall time overall.
The acceleration relative to the earth is the same, relative to some point from another system the bowling ball accelerates very slightly slower but accelerates the earth very slightly more towards it. The total acceleration of these two bodies towards each other is g.
Yeah you’re making that statement but it’s not true. Their acceleration relative to an inertial reference frame is g. That’s what the law of universal gravitation says, I have no idea where you’re getting that stuff from.
You said the two objects accelerate at the same rate, but then in the PS you said the feather gets accelerated faster. What do you mean?
Are you saying the feather gets pulled on more because the mass of earth minus feather is greater than the mass of earth minus ball? You would be right. If you lift the feather, measure how long it takes to fall, then lift the ball and measure, you should get the same number. This meme was assuming you either let them fall side by side, or measure them separately but each time conjure the object out of thin air.
Both accelerate at the same rate relative to the earth (the bowling ball accelerates slightly slower relative to some outside point, but it accelerates the earth slightly more towards it, resulting in the same relative acceleration to the earth as the feather)
Newton’s second law works in inertial frames. The acceleration of both objects would be the same in the inertial frame. But in the inertial frame, the earth would accelerate faster toward the object if the object was a bowling ball than if it was a feather.
the fact that you got upvoted, you clearly said force on both objects is gM and the feather or ball will move with g BUT earth will move with gM/m1 which is more in case of ball, and no its not acceleration between mases, its the force experiencec by both mases so, fg=m1.a
No. Multiplication is associative, you can switch the masses around as you please, nowhere in the formula does it say “the greater mass” or “the smaller mass” you could just as well re-arrange the formula and come up with “earth moves with gm1/M”. Last but not least there’s only one force acting on both objects… and gM/m1 is neither a speed nor a force. G * 100kg / 20kg is 5G. Measured in Nm²/kg² which is the same we started with because the two kg cancel each other out.
They both fall towards their shared centre of gravity. It’s this “the earth revolves around the sun” thing again, no it doesn’t, they both revolve around their shared centre of gravity (which, yes, is within the sun but still makes it wobble). That centre is very far away from the ball and very close to the earth and both are moving at the same speed towards it (because acceleration doesn’t depend on mass), blip to the next frame of the simulation now the centre of gravity moved towards the ball, next frame still closer to the ball, that is the reason both reach it at the same time, not because one is faster than the other.
…or so it would be, if the shared centre of gravity of ball and earth wouldn’t lie within the earth so they don’t actually both reach it, the earth is in the way, the rest of the acceleration is turned into static friction: Because they both are still falling even when in contact. But really that complication only exists because they have volumes which is why I factored it out from the rest of the reasoning.
all that is only brain-rot statements with no technical meaning. lemme make this completly clear
mf= mass of feather mb= mass of ball me= mass of earth ae=accelaration of earth fg=force experienced by both
now in case of feather
force on earth is what? yes thats fg =G.mf.me/r^2
now thats the net force on earth, now what is newtons law? me.ae=G.mf.me/r^2
we get ae=G.mf/r^2
similarly in case of ball ae=G.mb/r^2
and accelaration of earth is clearly more in case of ball, and yes this is accelaration in non inertial frame study newtons laws of motion again if you didnt know, so your second paragraph is utter nonsense
instead of nonsense brainrot statements like 'Multiplication is associative, you can switch the masses around as you please, nowhere in the formula does it say “the greater mass” or “the smaller mass” you could just as well re-arrange the formula and come up with “earth moves with gm1/M” tell me where in equations you think i am wrong
It’s not nonsense when it makes people understand, buddy. And don’t get all “oh be technical” on me when you say things like “earth will move with <something with the same units as G>”. Something that’s definitely something, but not m/s.
I was talking about time-steps when I said frame. Hence “simulation”, and “one frame, then another, then another”, referencing successive moments in time.
yet another brain rot reply, man i am done,
““earth will move with <something with the same units as G>”. Something that’s definitely something, but not m/s” you idiot i was talking about accelwration, if you need units just put in dementions of all the variables, thats trivial stuff you dont understand nlm at all.
second para is another non technical nonesense
Then why did you say “move” instead of “accelerate”. And the units don’t match acceleration, either. Best I can tell it’s some fraction of a term. If you want it to be an acceleration then you’re missing a squared distance, and if you want it to be acceleration, why are both mass terms in there.
For someone who throws around things like “that’s non-technical brainrot” damn is your prose fuzzy.
tell me how Gm/r^2 dosent match acceleration, the fact that i wasted my time on low iq person like you
That’s not what you wrote, or at least not what I complained about. You wrote:
where it was previously established that m1 and M are masses, and I interpreted g to be G (Newton’s gravitational constant) instead of g as in “gravitational acceleration caused by earth” because… well, I’m not actually sure. The whole thing is already a mess of capitalisation but more importantly then it’d be acceleration, not movement, worse, the specific properties of the earth are included twice (once in g, then in one of the mass terms).
Maybe you should spend less time on insulting people and more on communicating your thoughts clearly.
This is not correct, the force on the objects is the same sure, but the accelerations aren’t so you can’t calculate them both in one go like this.