In truth, if both experiments are done independently, (so not to affect each other), and we measure how long it takes the two massive objects to hit, and both objects are allowed to move each other, then the pull from a feather moves the earth slightly less than the pull the bowling ball has on the earth, so technically they will be slightly different times.

But that difference is not really measurable and probably barely calculable - though I'm sure someone on here may do that.

Physicisty type here! It's actually easy to calculate because it's so small.

If you dropped them side-by-side the difference would require factoring in the curvature of the Earth and would really be way below anything you might measure... If you drop them in series then yes that does have another effect... the actual acceleration should be like g(1+m/M) instead of just g, so if a ball is 0.6 kg and Earth is 6e24 kg the fall time goes like √(2D/g) and so for a 10s (500 m) freefall in vacuum it changes the time by 0.5 yoctoseconds? Way smaller than any clock accuracy as far as I know...

No the real inaccuracy is that the drag force in air will scale like the square of the velocity,

    m dv/dt = m g – ½ ρ A v² c

Where c is a dimensionless geometric constant called the Drag Coefficient, you can handwave that for these rough sphere surfaces it's maybe 0.5 or so, ρ is the density of air which of course gets lower at high elevations, at sea level it’s 1.22 kg/m³, but decreases like 0.13 kg/m³/km or so. A is the cross-sectional area of the ball π r². If you pretend that these variables are fixed instead of changing then this is a soluble equation, defining U = √{2mg/(ρ A v² c)},

    dv/dt = g – g (v/U)²
    v(t) = U tanh(g t/U)

U is the terminal velocity. Note that for small times tanh( gt/U) ≈ gt/U and v(t) ≈ gt becomes independent of U and hence m...

So that's my pet peeve: The two things on Earth should fall side-by-side in tandem at first, then slowly the tennis ball should lag behind! That's not what we see in this simulation, unfortunately.

Bonus points, I tried to do these calcs and the basketball likely has a terminal velocity ≈ 19.7 ± 0.3 m/s whereas the tennis ball likely has a terminal velocity ≈ 22.7 ± 0.4 m/s... As air resistance kicks in the tennis ball should pull ahead, not lag behind!

GDoc: https://docs.google.com/spreadsheets/d/1AnUeQ0RR7a5GA6Nrtef7...

Extra credit if you consider object spinning or not to determine impact of Magnus effect

Yeah this is confusing me as well. Mass does not affect the velocity of a falling object. Unless the simulation is accounting for some air resistance too.

Not only does the page explain what you see, but it refers to the feather-bowling ball demonstration that was filmed on the Moon.

It does! However, when I scroll to the bottom of the page I only see the title of that section, not the explanation, nor the accompanying video.

I didn't realize the "Why balls fall at all" was a button.

If anyone wants to play around with this old-school, here's a text based Python script that drops various things simultaneously and prints a table of position and velocity over time relative to the starting point. https://pastebin.com/q1NGv71W

Predefined things you can drop are basketball, bowling_ball, massive_sphere, dense_sphere, lead_sphere, pine_sphere, pingpong_ball, ant, rat, cat, person, and phone. You can add other things if you know their mass, cross sectional area, and coefficient of drag.

Thanks for the comment. Disclaimer: I'm not a physicist:)

Yes, you're partially right...if we drop both balls on Moon, they'll fall at the same time. Because there's (almost) no air on the Moon. The ball with less mass has less force of gravity to fight with air resistance on the Earth. Therefore, it falls slower.

Maybe this video can help to visualize: https://www.youtube.com/watch?v=Esa0kKECZvM

> The ball with less mass has less force of gravity to fight with air resistance on the Earth. Therefore, it falls slower.

Even that is not correct. Air resistance is proportional to cross-section, and gravity is proportional to mass. A ball with less mass but much less cross section will fall faster. It has less "force of gravity", but it has much less air resistance. In other words, a marble will fall faster than a basketball when accounting for air resistance.

Note that the animation is inaccurate in any case because (assuming constant air density) the velocity of a falling ball will never decrease (until it hits the surface) if it started stationary.

I don't understand how you get to your drag equation, and I think that's why you see such an exaggerated difference between the falling speed of the two balls. Drag should depend on the velocity, but it seems your drag force doesn't?