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?
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)
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.
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 • 10^24^ 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.
You can write down an infinite amount of numbers without ever leaving [0, 1]
Oh you're saying opposite site and adjacent site in English
Anyway how is the r=1 circle harmful for that?
Please elaborate.
New parties have to get big at local levels first before shooting for the stars
Why?
Gorilla gorilla gorilla
To save you some time
But the timeline is:
Prevent worse
After that protest and show the democrats how much you disagree with their stance on that
Saving others some time:
Palestinians’ preference for Harris over Trump stems from the former US president’s policy towards Palestinian issues, such as recognizing Jerusalem as the capital of Israel in 2017 and moving the US embassy from Tel Aviv to Jerusalem the following year. These actions were seen by Palestinians as undermining their aspirations for East Jerusalem as the capital of a future Palestinian state and as a firm endorsement of Israeli sovereignty over the contested city.
In 2019, Trump recognized Israeli settlements in the West Bank as legal, in blatant defiance of international law, and halted US support for the United Nations Relief and Works Agency for Palestine Refugees in the Near East (UNRWA). This action was seen as tacit approval of Israel’s expansion into occupied Palestinian territories.
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.