# vacuum free fall

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so, galileo said, everything falls at the same speed in vacuum.

correct me if i'm wrong but isn't it true that the more mass object has, the more it attracts other objects around it (basically, the gravity), so if you drop a feather that has a mass of roughly few grams and a huge rock with a mass of few tons on the moon, logic tells me rock will hit the ground first

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so, galileo said, everything falls at the same speed in vacuum.

correct me if i'm wrong but isn't it true that the more mass object has, the more it attracts other objects around it (basically, the gravity), so if you drop a feather that has a mass of roughly few grams and a huge rock with a mass of few tons on the moon, logic tells me rock will hit the ground first

More massive objects attract other objects with a larger force, true. But more massive objects have... well... more mass. Thus, it requires more force to cause the same acceleration, so the acceleration is still constant. Hope that helped

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To show it in math:

Let m1 be the mass of your object (rock, feather, etc), and m2 be the mass of the other body (the moon in your example).

F=m1*a

F=G*(m1*m2/r^2)

m1*a=G*(m1*m2)/r^2)

a=G*m2/r^2

Thus the acceleration is independent of the mass of the falling object.

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Only if the rock has enough mass to have a substantial gravitational field itself.

Even then it would be negligible, only slightly faster than the feather.

There should be videos of actual vacuum chamber tests that show that objects fall at the same speed.

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Yep.

The only reason the feather falls slower is due to air resistance. If the feather was replaced with a pebble of the same mass, it would fall at the identical speed to a bowling ball.

The rock and the feather will always travel at the same speed without the air. You'd have to have an object the size of Ceres falling with a feather to have any noticeable difference in time, and then you'd have the problem where you don't even get to publish your findings because the world has ended. Edited by GregroxMun

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Thanks for the responses

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You'd have to have an object the size of Ceres falling with a feather to have any noticeable difference in time, and then you'd have the problem where you don't even get to publish your findings because the world has ended.

Why would a "sufficiently more massive" object accelerate faster than the feather? As far as I understand it still falls just as fast because attractive force is increased proportional to mass exactly as much as is inertia.

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Why would a "sufficiently more massive" object accelerate faster than the feather? As far as I understand it still falls just as fast because attractive force is increased proportional to mass exactly as much as is inertia.

The reason is that both objects fall towards their common centre of mass. If the test mass is much smaller than the mass of the body we are standing on, this centre of mass is very much identical to the centre of mass of the bigger body. If both objects have similar mass that changes drastically.

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Yep, if both objects are of significant mass they both start moving appreciably.

There's this awesome little simulator.

Try the following settings:

[TABLE=class: grid, width: 500]

[TR]

[TD][/TD]

[TD]Mass[/TD]

[TD]Position x[/TD]

[TD]Position y[/TD]

[TD]Velocity x[/TD]

[TD]Velocity y[/TD]

[/TR]

[TR]

[TD]Body 1[/TD]

[TD]200[/TD]

[TD]-150[/TD]

[TD]0[/TD]

[TD]0[/TD]

[TD]0[/TD]

[/TR]

[TR]

[TD]Body 2[/TD]

[TD]1[/TD]

[TD]150[/TD]

[TD]0[/TD]

[TD]0[/TD]

[TD]0[/TD]

[/TR]

[/TABLE]

Set the accuracy slider all the way to accurate.

When you run the simulation, it will take about 4.1 time units for the collision to occur.

Reset and change the mass of the Body 2 to 100.

The collision will now take place after about 3.4 time units.

When you're done with that, try out some presets. They're awesome!

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Ah you meant that it would fall faster in the sense that the collision will happen sooner, not that the heavier of the two falling objects would accelerate faster as I first thought you were implying. OK.

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Yep, if both objects are of significant mass they both start moving appreciably.

There's this awesome little simulator.

Try the following settings:

[TABLE=class: grid, width: 500]

[TR]

[TD][/TD]

[TD]Mass[/TD]

[TD]Position x[/TD]

[TD]Position y[/TD]

[TD]Velocity x[/TD]

[TD]Velocity y[/TD]

[/TR]

[TR]

[TD]Body 1[/TD]

[TD]200[/TD]

[TD]-150[/TD]

[TD]0[/TD]

[TD]0[/TD]

[TD]0[/TD]

[/TR]

[TR]

[TD]Body 2[/TD]

[TD]1[/TD]

[TD]150[/TD]

[TD]0[/TD]

[TD]0[/TD]

[TD]0[/TD]

[/TR]

[/TABLE]

Set the accuracy slider all the way to accurate.

When you run the simulation, it will take about 4.1 time units for the collision to occur.

Reset and change the mass of the Body 2 to 100.

The collision will now take place after about 3.4 time units.

When you're done with that, try out some presets. They're awesome!

Thats cool! Try:

200, 0, 0, 0 -1

50 142 0 0 140

1 -50 0 0 280

I think i know why that happens...

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Why would a "sufficiently more massive" object accelerate faster than the feather? As far as I understand it still falls just as fast because attractive force is increased proportional to mass exactly as much as is inertia.

Because if its as big as Ceres, then Earth will start falling closer to Ceres as well.

- - - Updated - - -

Ah you meant that it would fall faster in the sense that the collision will happen sooner, not that the heavier of the two falling objects would accelerate faster as I first thought you were implying. OK.

Sort of. The basic thing is that if Earth and Ceres are colliding rather than Earth and the Feather, Earth and Ceres accelerate towards each other, whereas the feather only accellerates towards the Earth.

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If objects of different masses accelerated differently in the gravitational field, this would not be possible.

Any attempt in orbiting would end up badly. Also the universe would look a lot different because stellar and planetary accretion would not be possible. It would be a dull universe, dark and dull.

- - - Updated - - -

Too bad the moronic producers never showed us the real time free fall. How frustrating and idiotic...

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Sort of. The basic thing is that if Earth and Ceres are colliding rather than Earth and the Feather, Earth and Ceres accelerate towards each other, whereas the feather only accellerates towards the Earth.

Aha, but if the feather is falling side by side with Ceres then they'll still impact at the same time

Unless the feather decides to land on Ceres before that ofc...

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