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
The issue isn't so much the sensitivity (although that is a significant issue), it's all the other crap going on. You'll probably be able to filter out the Mains Hum, but every anything moving in the same axis as the test will confount the data.
I'm thinking we might set up the instuments near counterweight energy storage or pumped hydro, and some on the exact opposite side of the planet, and try to measure the movement of the earth that way.
We can already see a change in the length of a day after big earthquakes and dam construction/destruction, but I don't think the acceleration has ever been measured directly.
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.
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 above is just referring to the fact that the standard "feather vs. bowling ball" question assumes the earth/moon/ground is immovable. In that case, Newton says they fall the same.
The fact that the ground is not immovable is what's being referenced --- in this picture, things don't "fall," they are each accelerated towards each other.
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.
Can someone explain how the Earth accelerates towards an object? Is this just because objects with mass attract things?
You got it.
Yes. And that force is proportional to acceleration so it accelerates earth
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).
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.
Thank you.
That's a good one. Did not know that xkcd yet.
It's not even because it's heavier, it's because it's way more dense.
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.
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).
No. F=GMm/d2. The mass of the earth doesn’t change so g=GM/d2 will not change
because of its* greater mass
There's a video of astronauts doing the heavy thing vs feather in vacuum experiment. I think it was a hammer rather than a bowling ball tho.
they did it on the moon
Yeah
I get that the heavier bowling ball affects the acceleration of the earth more than the lighter feather, but I don't see how that means it's falling faster as the meme is stating. The bowling ball would meet the earth first when dropped separately and from the same height because the earth is (imperceivably) accelerating toward it faster than it does the falling feather, but both the bowling ball and feather are falling at the same rate due to Earth's gravitational force.
Or am I missing something?
One definition for a "rate of falling" would comfortably be "the time it takes the surfaces of two free gravitational separated by some distance to meet." With this in mind, the imperceptible but very real difference in the acceleration of the earth towards the bowling ball would become part of that equation, as it shortens the distance between the two from the other side.
Think of it like a head on collision of two vehicles. You can do the math as two bodies colliding with opposite velocity vectors, or you can arrive at the same mathematical result (at least for some calculations) by considering one of them to be stationary and the other to have the sum of the two speeds in the direction of its original velocity. "Two cars colliding head on at 60mph is the same as one car hitting a brick wall at 120mph." It is rough and doesn't work for all calculations, but the idea is the same.
Since we are in avaccum
That's where you're wrong kiddo
I think the answer to this question changes based on your interpretation of 'falling faster'. I.e. whether that refers to the total time between the start and end of the fall or to the speed of the feather/ball to an outside observer.
This only true when you drop it like it's hot.
Right off the chain.
More like failing
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.
Edit: terminal velocity: https://en.m.wikipedia.org/wiki/Terminal_velocity
