For anyone wondering it’s because the bowling ball slightly pulls the earth faster toward itself. This amount is too small to possibly measure. But imagine if the bowling ball were the size of another Earth and it’s easier to see why it happens.
Thanks for the non-jargon version
This amount is too small to possibly measure
What the fuck did you say to me you little bitch? I’m going to go get $300 million in funding to create a device so complex and so sensitive that a butterfly sneezing 30 miles away will fuck it up and then I’m going to directly measure the the acceleration of the earth as a result of the mass of that bowling ball. You fucked up, kiddo.
- Average metrologist, probably
But being more massive means that due to inertia the ball will take just a tiny little wee bit longer to start moving no? So they end up falling at the same time.
Also, are these Newtonian mechanics? How do they compare to relativity at the “bowling ball and feather” scale?
Someone please correct me if I’m wrong. It’s been a while since I read anything physics-related.
The acceleration from gravity would be the same no matter the object mass (~9.8m/s²).
Oh yes! I omitted that part, but what I meant to say is that mass and inertia balance each other, so that in the end the acceleration from gravity ends up the same for any object.
The bowling ball will still pull the Earth more. For us, everything accelerates at 9.8m/s² (because we all fall to the same Earth), but the Earth accelerates differently per attracting object.
When you drop them at the same time, it doesn’t matter though.
because of two bodies can not occupy the same space, the feather and the ball will be in different position when you drop them. And therefor gravitation will pull the earth slightly more toward the ball and slightly less toward the feather.
It’s not even because it’s heavier, it’s because it’s way more dense.
The guy on the right, if he be so wise in the ways of science, should be using the word “massive” instead of “heavier”.
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It’s not density, it’s mass. A mass of 1kg compressed to the density of the Sun’s core would pull the Earth with just as much force as a 1kg ball of styrofoam.
Just to add some formality to this, the original commenter might want to look up the shell theorem for classical mechanics and Birkhoff’s theorem for general relativity.
And is the Sun was replaced with a black hole of the same mass, the Earth would just keep on rotating around it without issues, if slightly frozen
Xkcd did a what if on a black hole moon (getting it to collapse into one may be impossible, but a black hole the mass of the moon is theoretically stable), and it has the same conclusion, except just slightly colder instead of slightly frozen. And by slightly, I mean almost imperceptible.
Can you explain please
Heavy is a subjective term based on the force of gravity. You are heavier if we weigh you on the earth compared to if you are weighed on the moon.
Your mass in those two examples is unchanged. The amount of mass you have is finite and not subjective like weight.
Does the bowling ball ever so slightly increase the gravitational constant because of it’s greater mass? Is that what the right guy is getting at?
The gravitational constant G, no, the mutual gravitational force between the earth and the ball approximated as g, yes.
Edit: Since this is a little pedantic, G is used to calculate g.
But how would that make the bowling ball fall faster? F = G × m₁ × m₂ / r² and F = m₁ × a ⇒ a = F / m = G × m₂ / r², where m₁ is the mass of the ball and m₂ the mass of the planet. So the gravitational acceleration of a bowling ball is independent of its mass (assuming the planet has way more mass than a bowling ball).
I guess the bowling ball attracts the Earth towards it, shortening the distance so it hits the ground faster
No. F=GMm/d2. The mass of the earth doesn’t change so g=GM/d2 will not change
So why does the bowling ball fall faster in a vacuum? Does it appear faster locally because the heavier object makes local time slower than the lighter object compared to a distant observer? I’m trying to understand what the meme is getting at.
That’s the neat thing: it doesn’t
The bowling ball also pulls the earth towards itself. This amount is imperceptibly small but still there
I’m trying to understand as well.
because of its* greater mass
Since we are in avaccum
That’s where you’re wrong kiddo
More like failing
This is fascinating! Both of them accelerate toward the earth at the same rate, but because of the bowling ball’s greater mass, the EARTH accelerates faster toward the bowling ball than it does toward the feather, so it’s imperceptibly faster XD
But they are being dropped at the same time for dramatic effect, so the earth will also be accelerating towards the feather at bowling ball speeds because the feather is next to the bowling ball, therefore they still land at the same time.
That’s only be true if the feather was in the same position as the ball. Otherwise, the earth is moving ever so slightly more towards the ball.
Can someone explain how the Earth accelerates towards an object? Is this just because objects with mass attract things?
The gravitational force equation actually takes into account the mass of both objects and their distance. The only reason we can throw out a gravitational constant of 9.81m/s^2 for most objects on Earth is because the mass of the Earth is so large that the mass and/or distance of the other object would have to be equally large in order to make any significant change in that value. Technically though, a bowling ball at sea level falls slightly faster than a bowling ball at the top of Everest, as does a bowling ball and feather from the same height. The reason is more accurately that they are experiencing slightly higher or lower gravitational forces, which cause them to accelerate (in conjunction with all the other forces acting on them).
Yes. And that force is proportional to acceleration so it accelerates earth
You got it.
In the same way that earth has gravity that attracts objects, the objects have gravity that attracts earth. See also Newton’s third law, also known as “For every action, there is an equal and opposite reaction.” - for the earth to attract something, the earth also has to be attracted with the same force. It’s just that the earth has a lot more mass, so the force barely accelerates it.
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They are being moved, it is just imperceptible to the human eye.
It is all a matter on how precise you want to be
I haven’t seen anyone mention this yet, so here’s how I understand it. The feather falls slower in non-vacuum conditions because it reaches its terminal velocity much more quickly than the bowling ball.
How would it reach terminal velocity in a vacuum?
I imagine terminal velocity with no air resistance would be 9.8m/s/s. I was saying that the feather reaches terminal velocity more quickly than a bowling ball in non-vacuum conditions
9.8 m/s/s is acceleration due to gravity, not a velocity, or its units would be m/s
