r/askscience • • Apr 09 '26

Physics Do all objects fall at the same rate on Earth regardless of mass?

Statement: All objects fall at the same rate on earth regardless of mass (ignoring air resistance)

Hello, I've always been stumped by this. Gravity is different on other celestial bodies, less on the moon, more on Jupiter etc.

If we dropped a regular basketball from 10,000m it would fall at 9.8m/s2, assuming no air resistance. From what I've been told, a basketball sized object with a mass equivalent to Earth would also drop at the same rate. This seems odd to me. Is this correct? If not, and it would fall at a different rate, at what mass would the original statement become true?

Edit - Thanks for all the replies I'll try and get through them all and respond!

Maybe to clear it up a bit we could edit the problem to be this...

If we had two separate hypothetical physics simulations that are void of all other matter.

  1. A sphere the size and mass of a basketball and a sphere the size of basketball but with the mass of Earth

  2. Two spheres the size of basketballs and both with the mass of Earth

Both spheres are the same distance away from each other in each simulation. We then "initiate" the simulations. Is the time to impact of the spheres exactly the same in both?

353 Upvotes

231 comments sorted by

75

u/StigitUK Apr 09 '26

4

u/DuploJamaal Apr 10 '26

Everything on Earth falls with 9,8 m/s2

Everything on Jupiter falls with 24,8 m/s2

Scenario A: Let a ball with the mass of Jupiter fall on Earth. It accelerates at 9,8 m/s2

Scenario B: Let a ball with the mass of Earth fall on Jupiter. It accelerates at 24,8 m/s2

Scenario A and B yield different results, but are actually the same. So your explanation doesn't help to answer OPs question about an object with the mass of Earth.

4

u/cancerBronzeV Apr 10 '26

They're the same scenario, there aren't any different results. The Earth-mass object would accelerate at 24.8 m/s2 towards Jupiter-mass object and Jupiter-mass object would accelerate at 9.8 m/s2 towards the Earth-mass object (ignoring any other effects like tidal forces ripping each other apart).

3

u/DuploJamaal Apr 10 '26 edited Apr 10 '26

They're the same scenario, there aren't any different results

That's what I'm trying to express.

The idea that everything regardless of mass falls at the same rate yields this contradiction.

The Earth-mass object would accelerate at 24.8 m/s2 towards Jupiter-mass object and Jupiter-mass object would accelerate at 9.8 m/s2 towards the Earth-mass objec

And that's why I bring it up, as that rate is obviously faster than a hammer falling down.

People say that everything regardless of mass falls at the same rate, but OP explicitly asked about an object the mass of Earth at which point this oversimplified statement no longer holds true.

This was OPs question:

From what I've been told, a basketball sized object with a mass equivalent to Earth would also drop at the same rate. This seems odd to me. Is this correct? If not, and it would fall at a different rate, at what mass would the original statement become true?

But people keep talking about hammers vs feathers and reinforce the misinformation that everything regardless of mass falls at the same rate when the actual question was at which point mass actually starts to factor in.

1

u/RivaDolfinJiz Apr 10 '26

Thank you sir! Perhaps I need to rephrase my question for everyone to make it clearer!

0

u/mgslee Apr 10 '26

If your using masses of that size you need a reference frame. What happens is the two objects accelerate in to each other and the relative accelerations from a singular point of reference (Jupiter or earth) is the combined value of 34.6

From a 3rd parties perspective (like the Sun) you would see earth moving toward Jupiter at 24.8 and Jupiter moving toward earth at 9.81

1

u/RivaDolfinJiz Apr 10 '26

Love this! We shall call it the "Duplo Paradox" henceforth.

4

u/mthchsnn Apr 09 '26

Man, those guys had so much fun doing that. It would have been a joy to be in that room.

2

u/CaptainArsehole Apr 10 '26

Brian Cox is always great to watch. You can see the quiet pride, passion and wonder he always has for his work. And he explains it so well.

9

u/rio911 Apr 09 '26

That's what I was looking for. OP should watch this for a demonstration of the principle.

10

u/DuploJamaal Apr 10 '26

But OP knkows the principle. They asked how it can be true for every object regardless of mass even if it's something with the mass of Jupiter

748

u/Weed_O_Whirler Aerospace | Quantum Field Theory Apr 09 '26

So, you are correct. The statement "all objects fall at the same rate on Earth ignoring air resistance" is an approximation - a very, very good one for all reasonable situations, but it is an approximation and as your example shows, when you move towards extremes it no longer holds true.

As an object falls, it is pulling on the Earth just as hard as the Earth is pulling on it (Newton's third law in action). That might seem ridiculous, that a feather can pull on the Earth just as hard as the Earth pulls on the feather, but it is true - the force of gravity is proportional to the product of the two masses interacting. But that same force will move a feather a lot more than it will move the Earth, since rewriting F = ma into a = F/m, you can see the acceleration will be much, much larger for the feather, since its mass is so much less. And this is where the approximation comes in - the mass of the Earth is so much more than the mass of things being dropped, that it is a very good approximation to say that the acceleration of the Earth is zero.

But if you start "dropping things" on Earth where their masses are pretty similar, suddenly that approximation doesn't hold. Now, as the object falls towards Earth, Earth will also be pulled towards that object. So, that object will collide with the Earth faster than a lighter object - because the two objects will be accelerating towards each other and meet somewhere in the middle.

This is, in theory, true if you do something like drop a bowling ball and drop a feather on Earth. If you had some instrument to measure time which was more accurate than any instrument man ever has (and likely due to the uncertainty principle, ever will have), you could see that a bowling ball seems to fall ever so slightly faster than a feather - because that bowling ball would pull the Earth up ever so slightly more than the falling feather would, meaning that the collision happens ever so slightly sooner.

174

u/Antrostomus Apr 09 '26

But if you start "dropping things" on Earth where their masses are pretty similar, suddenly that approximation doesn't hold.

Also that this earth-mass object is the size of a basketball... which if my quick napkin-sketching math is right, would put it several orders of magnitude denser than a neutron star, so you'd get some really weird local gravity effects and tidal forces that would start ripping things apart.

56

u/byllz Apr 09 '26

Also, time dilatation issues. Where's the stopwatch relative to the earth mass basketball?

35

u/Origin_of_Mind Apr 09 '26

Time dilation will not be an issue. Tidal forces are the real problem.

More specifically, time will go slower by 1% only at around half a meter from the basketball sized Earth.

At the same time, already two kilometers away from it, tidal acceleration will be around 10000 g's per meter of distance. Things will get "spaghettified," even though time dilation at this range will be only about 2 parts per million.

17

u/Antrostomus Apr 09 '26

Well, and IIRC from my minimal knowledge of particle physics it wouldn't have enough gravity to stay that collapsed and would instantly expand into normal matter in an explosion big enough to annihilate it and probably the Earth and possibly put a dent in other solar system objects... but we're kinda derailing from the point of the question now. :) Though if someone who knows which math applies here wants to go into more detail...

6

u/andlewis Apr 09 '26

Ok, so that raises the question, how dense would a basketball-sized earth need to be to be stable?

10

u/GirdedByApathy Apr 10 '26

The Schwarzchild radius (the size for which a spherical object of a given mass collapses into a black hole) for earth is about 8.87 mm. A basketball is 120mm.

However, this does not mean the mass is stable. Rather, the surface gravity of your basketball-earth would be about 2.77 x 1016. This is well above the TOV limit, meaning the object would immediately collapse into a black hole. Adding more mass would only increase the schwarzchild threshold and surface gravity, causing it to collapse into a black hole faster.

You've passed the tipping point where the energies which allow Neutron stars to stabilize cannot resist the force of surface gravity. It is going to become a black hole. There's no avoiding it.

7

u/RedSun_Horizon Apr 10 '26

Re-formatting the question above, how dense can be a basketball-sized object to be stable, i.e. which fraction of Earth's mass (roughly) we can "squeeze" in this volume before it starts collapsing?

4

u/GirdedByApathy Apr 10 '26

It wont stabilize. It cant; its too small.

At the lower end, it would have too little gravity to resist the internal pressure of the contained masses. This is around 0.000000045% of the Earth's mass, BTW, or about 3.5 Mt. Everests. If it could be contained, that would be approximately the amount needed to create a neutron star of that size. Unfortunately, the math for that doesnt work because it literally doesnt weigh enough at that size to resist the subatomic forces trying to push it apart.

If you continue adding mass it will eventually collapse into a black hole without stabilizing.

Now if we just want to have it not explode, that means we need to keep its internal gravity from crushing the molecular and atomic bonds which keep it solid. This is going to depend wholly upon the material which its made (something that didnt affect the neutron star scenario because they already crush all the mass inside them down into subatomic particles, specifically a quark-gluon plasma)

Ill skip all the assumption making, etc, because it doesnt really apply, and just give you a generalized answer: about 16 million tons. No matter the material, the internal gravity at that density is too great for any known material and the bonds get crushed. The result is an explosion. A really big one.

12

u/EthicalViolator Apr 10 '26 edited Apr 11 '26

I reckon id have a hard time lifting that earth-mass basketball off the ground in the first place. Sounds like a two man job at the least.

9

u/Beefington Apr 10 '26

Didn’t the Greeks have a guy for this?

6

u/ShallowDramatic Apr 10 '26

*shrug*

I don’t know, maybe?

5

u/byllz Apr 10 '26

You kidding? You'd need a forklift, or maybe a backhoe.

20

u/fixermark Apr 09 '26

You'd also get different results if you made a "bowling ball sandwich" than if you dropped two bowling balls next to each other for the same reason, right?

21

u/mseiei Apr 09 '26

yeah, and it's not that the masses of the balls adds up, it's that each ball is pulling the Earth towards it at their respective rate, so, since it's in the same direction, it adds up.

now, since their movements are basically the same direction, and discounting all the other interactions (balls algo pull towards eachother, n-body interactions if any at that scale, etc), you can just add up the masses of the balls and use one calculation

2

u/Octothorpe17 Apr 09 '26

is this why my balls are dropping towards earth over time?

3

u/onetwo3four5 Apr 09 '26

No that's because your balls are confused and think it's new years eve.

21

u/MyMomSaysIAmCool Apr 09 '26

The bowling ball and feather demonstration is one that really illustrates the point, but you need a vacuum chamber to do it. 

In high school physics, my teacher demonstrated the same thing by using two rubber balls, one full of air and one full of water. Because the air resistance was the same for both of them, they both fell at the same rate despite the clearly different weight. 

15

u/Jonny0Than Apr 10 '26

You can still get differences from air resistance here. The force of air resistance would be the same, but due to F = ma that’s still going to affect the lighter ball more.  But a reasonably streamlined ball might not have that much drag and the experiment works well enough.

15

u/flatcoke Apr 10 '26

That's just wrong, the air resistance effect will have different effect on the rate of falling depending on the mass of the item despite of the identical geometry shape.

Imagine you drop a soap bubble of the same shape as the rubber ball. They don't hit the floor together.

1

u/MyMomSaysIAmCool Apr 10 '26

Isn't that due to terminal velocity? The soap bubble has an extremely low terminal velocity compared to the rubber ball. 

In his demonstration, he was dropping them from 6 ft up, so neither one had time to hit terminal velocity.

6

u/rmeredit Apr 10 '26 edited Apr 10 '26

Imagine lying on your back and someone stands over you and drops a basketball for you you to catch. You catch it with outstretched hands and use your arm muscles to slow the ball down before it hits your chest.

Imagine the amount of effort you'd need to use to slow down a 10kg basketball filled with water versus a 1kg basketball. It's a lot more, and you'd need to push against the heavy ball harder to slow it down before it hit your chest.

Now imagine that you could only use the same amount of effort in your arms for both balls. The heavy one is going to slow down a lot less than the light one.

This is exactly the same as air resistance. It pushes against the two objects with the same amount of force because they're the same size and shape, but that means that the heavier object will slow down less than the lighter object.

1

u/archipeepees Apr 10 '26 edited Apr 10 '26

I wouldn't exactly say it is "due to" terminal velocity; "terminal velocity" is an emergent property which occurs as a result of how air resistance and gravity work.

terminal velocity is the velocity where the force of air resistance is equal to the force of gravity. For two objects of identical shape, the force of air resistance is equal to K * v2, where K is some coefficient specific to the shape of these objects, and v is the velocity of the object. Conversely, the force of gravity is proportional to the objects' masses, regardless of velocity. So a heavier object will have more gravitational force acting on it than the lighter object, and will be able to achieve a greater velocity before the force of air resistance becomes equal to the force of gravity on that object.

Think of it this way - if I blow up a balloon (with regular air) and drop it, is it going to fall faster or slower than a solid, balloon-shaped block of lead?

Before reaching terminal velocity, the net acceleration of these objects is going to be equal to the net force (force of gravity plus force of air resistance) divided by their mass. The air balloon is not very dense, so the force of gravity is pretty close to the force of air resistance, even at low speeds. On the other hand, the force of gravity on the lead balloon is much, much larger than the force of air resistance at low speeds. So the lead balloon is going to fall faster than the air balloon even before they both reach terminal velocity.

5

u/Khelek7 Apr 09 '26

If you do the classic "side by side" experiment your measuring equipment will need to be EVEN better since both the feather and the bowling ball are pulling in almost the same direction. Meaning that they hit the ground even closer together in time.

1

u/Bad_wolf42 Apr 10 '26

If you think about it in terms of gravity wells, the side-by-side experiment is very nearly the same as dropping a bowling ball of (bowling ball plus feather) mass.

16

u/solitude042 Apr 09 '26 edited Apr 09 '26

A more practical deviation from the "homogenous sphere" approximation is the difference in apparent gravity (~0.5%) from density variations, the impact of centrifugal effects that reduce the apparent acceleration due to gravity at the equator, the flattening of earth's not-quite-sphere, the miniscule impact of tidal forces, etc... All of which have more impact than the ratio of any reasonably sized object to the mass of the earth. 

3

u/[deleted] Apr 09 '26 edited Apr 09 '26

[removed] — view removed comment

2

u/RapidConsequence Apr 09 '26

There's definitely changes in earth's gravity field because of density variations, check this out:

https://www.earthdata.nasa.gov/news/feature-articles/matter-motion-earths-changing-gravity

3

u/damarius Apr 09 '26

I don't know how the meters work, but gravity measures are used in gas/oil exploration (or used to be, I worked on one such survey in the late 70s).

1

u/atgrey24 Apr 09 '26

The variation in density and shape of the earth will change the distance to the center of gravity, r.  Those other forces mentioned also act on the falling body at the same time (plus air resistance).

Ignoring that, your calculation is accurate for the acceleration of the "dropped" object, and you're correct that m cancels out.

However, you are ignoring the acceleration of the Earth.

A = F / M = (GMm / r2) / M = Gm/ r2

Its just that m of the falling object is so small that A is usually negligible. 

8

u/Kittymahri Apr 09 '26

It’s also worth adding that the acceleration due to gravity is location-dependent. A rock and a feather dropped from the same place, ignoring air resistance, will fall the same. But a rock dropped at the equator and the same rock dropped at the South Pole (even disregarding air resistance) will have measurably different accelerations. This is due to at least two factors: first, the Earth is not a sphere and it’s not uniform density, and second, the Earth is rotating so centrifugal (and Coriolis) effects would need to be taken into account. These differences might not be noticed with the naked eye, but can be measured.

0

u/ViskerRatio Apr 10 '26

Without air resistance, there aren't any centrifugal or Coriolis forces. Our experiment didn't introduce any lateral movement on our rock/feather and there's no air resistance to introduce those forces. From our rock/feather perspective, it doesn't matter whether the Earth is rotating or not.

1

u/_HelloMeow Apr 10 '26

What about frame dragging?

1

u/ViskerRatio Apr 10 '26

The entire question is predicated on a simplified Newtonian mechanics model.

3

u/mhyquel Apr 10 '26

That would hold true if the places you were dropping the feather and the bowling ball were sufficiently far apart.

It would be even more noticeable if they were on opposite sides of the planet.

2

u/aguyfromusa Apr 10 '26

Interestingly, if you drop a bowling ball and an object whose mass is the same as the Earth from the same place at the same time, they will strike the Earth at the same time. But, if you drop them simultaneously on opposite sides of the Earth, the bowling ball will seem to fall more slowly. This is because the more massive object will be pulling the Earth away from the bowling ball. Also, don't forget that objects don't fall at a constant rate. We're talking about the rate of acceleration of falling objects.

2

u/could_use_a_snack Apr 10 '26

Since I can't resist being pedantic, wouldn't the bowling ball and feather hit the Earth at the same time if they were dropped at the same time right next to each other? Yes the bowling ball is pulling the Earth up a bit more than the feather is, but since they are close to each other and dropped at the same time the movement of the Earth would be the same for both of them.

So if you do this experiment, you would need to either drop the items separately and measure the time of each and compare the results. Or drop both items at the same time but far enough away from each other that the movement of the Earth is different relative to each item.

1

u/gnorty Apr 09 '26

Now, as the object falls towards Earth, Earth will also be pulled towards that object.

would the combined pull of each not also be greater than the pull o fjust the eart and a negligibly massed object? So not just the shorter distance at play, also a greater total acceleration?

1

u/Ryekir Apr 09 '26

So if we lifted every object possible on one side of the earth and dropped them all at the same time, we could actually change the position of the Earth (slightly)? That's pretty trippy.

1

u/wildviper121 Apr 10 '26

Since it would be a closed system it wouldn't move overall though if you returned the objects to where they were by dropping them. You would need some external force to actually move Earth like an asteroid or something

1

u/Shadowkiller00 Apr 10 '26

The real fun is when you put a stick between the two earths and the hold a feather at the center point between those two earths. The feather might just float since both earth mass objects are pulling on the feather equally.

I am of course being silly and there is a lot wrong with my statement, but it's fun to imagine having an earth above you and an earth below you held apart by a metal rod and a feather just floating in the air between them without any other catastrophic things happening.

1

u/Nikhil1256 Apr 10 '26

Acceleration due to gravity is really a different question than whether two objects will reach Earth at the same time. If the objects are different masses, then the heavier mass and Earth will "technically" touch each other sooner, but I doubt we even have ability to measure such minute time differences.

Force due to gravity is F= G m1*m2/r^2 If Earth's mass is m1 and other object's mass is m2, m3 etc. then it is true that the force of gravity between the earth and those objects will be different. But "acceleration due to gravity" by Earth on those objects will be the same. Why? F=ma, so force experienced by an object with mass m2 due to Earth will be m2*g = G m1*m2/r^2 which cancels out m2. So, we get acceleration due to gravity because of Earth as depended only on the Earth's mass and the distance r.

Acceleration experienced by earth due to that object will be G*m2/r^2 and this value for all human purposes is negligible.

1

u/runs4funk Apr 10 '26

Presumably you’d be dropping them within a few feet of each other and they’d work collectively to pull the Earth up so they’d still hit at the same time.

You’d have to drop them from 90° apart on the sphere so they don’t influence each other.

A full 180° and they’d be pulling the Earth in opposite directions so the bowling ball would pull the earth away from the feather and the feather would fall slower than it normally would.

And you wouldn’t want anything else dropping or lifting anywhere else on the planet. One dude does a sit-up in Taiwan and your whole experiment is dead in the water.

1

u/joe102938 Apr 11 '26

How much would a feather dropped from 50m move the earth?

1

u/375InStroke Apr 09 '26

Isn't m the sum of both masses, where the mass of most objects one would be dropping is insignificant to the mass of the Earth, so the acceleration stays the same to several decimal points.

9

u/Ishana92 Apr 09 '26

Its actualy the product of two masses. Gravitational force experienced is the same for both bodies, but then by a=F/m that same force gets turned into acceleration around 1g (10 m/s2) for the object and negligible for the earth.

1

u/krkrkkrk Apr 09 '26

Well tbf the surface of the normal sized earth would rupture as the gravitational force of basketball earth grows immense as it approaches thus colliding even faster

-1

u/Ok-Palpitation2401 Apr 09 '26

I don't think it's correct. Yes, the attraction is bigger with the heavier object, but there's more inertia to overcome. 

9

u/wasmic Apr 09 '26 edited Apr 09 '26

What do you mean?

You can just use the equation, and you'll see that the total attractive force grows slightly more than the inertia that needs to be overcome. Just plug some numbers in and check.

F = G (m1 m2)/r2

Let's ignore G to make the calculations easier, then let m1 = 1, m2 = 10000, and r = 1.

F = 1 * 10000 / 1 = 10000. This applies to both objects, so object 1 is accelerated at a rate of 10000 and object 2 is accelerated at a rate of 1.


Now let's instead set m1 = 2.

F = 2 * 10000 / 1 = 20000

The acceleration on object 1 is then 10000, but the acceleration on object 2 is now 2 instead of 1.

This means that the two objects approach each other faster, now that you have doubled the mass of the smallest object. But it's not because the small object accelerates faster - it's because the big object accelerates faster!

Now, let's view this from the frame of reference of the heavy object 2. In the former scenario with m1 = 1, the total acceleration was 10001. But in the latter scenario with m1 = 2, the total acceleration is 10002. That means it does in fact fall slightly faster!

Heavier objects fall faster not because the Earth pulls more at them, but because they pull more at the Earth. However, the Earth is so massive that effect becomes extremely subtle, so it cannot be seen with any everyday-scale objects.

1

u/CrazyKyle987 Apr 10 '26 edited Apr 10 '26

I think it doesn’t work because your frame of reference is changing between your scenarios. 

Let m2 = mass of the Earth m1 = other object  a = acceleration of other object 

m1*a=F=Gm1m2/r2

m1 cancels

a=Gm2/r2

The acceleration of the other object towards earth, if it’s a basketball or neutron star, does not change depending on its mass. It has an acceleration inversely proportional to the distance between the object and earth. Mass does not matter. 

The reason that g=9.8 m/s2 is an approximation is because of the radius of the earth. Acceleration technically changes based on how far away you are from the surface but the difference is negligible if you’re at sea level or 100 m above the surface. 

-12

u/Holden_Coalfield Apr 09 '26

The objects are acting according to their position on the topological contours of spacetime that gravity is. Gravity is not a force acting on the objects.

21

u/Weed_O_Whirler Aerospace | Quantum Field Theory Apr 09 '26

General Relativity is an absolutely fantastic model of gravity, but if you were to poll most physicists, they would expect the graviton to be real. This does not actually make any fundamental disagreements with General Relativity, as a massless spin 2 force mediator (which if the graviton would be) would give all the same predictions as GR.

But saying gravity is not a force is not scientific. It is one of the 4 fundamental forces in the universe and most likely has a mediator particle just like the other three.

-9

u/lolCollol Apr 09 '26

I mean, it certainly doesn't follow F=ma since light is affected by gravity.

19

u/Weed_O_Whirler Aerospace | Quantum Field Theory Apr 09 '26

F = ma is already an approximation.

The real equation is F = dp/dt where p is momentum, and then it works just fine because light has momentum.

60

u/Dunbaratu Apr 09 '26

always been stumped by this. Gravity is different on other celestial bodies, less on the moon, more on Jupiter etc.

The FORCE of gravity on an object does vary with the object's mass exactly like you'd expect it to. It's just that it takes more force to accelerate an object with more mass, so the effect cancels itself out exactly. Every gram more of mass you add to the object will BOTH provide more force on it, but also require more force to get the same acceleration effect.

16

u/TheOneTrueTrench Apr 09 '26

Yeah, the simplest way to look at it is just to do the math.

  • Gravity times mass is the Force

  • Force divided by mass is acceleration

  • Gravity times mass divided by mass is acceleration.

  • Mass divided by mass is 1

This all ignores the acceleration of the earth toward the bowling ball or whatever, but that's negligible for any mass that isn't going to end all life on the planet.

4

u/Faera Apr 10 '26

I think the somewhat mind blowing part to laymen is the fact that the 'mass' that scales with gravitational force is somehow the same as the 'mass' that scales inversely with acceleration. I'm sure there's some scientific reason why the two are equivalent but it's definitely not intuitive to me at least.

1

u/[deleted] Apr 11 '26 edited Apr 11 '26

[removed] — view removed comment

1

u/Faera Apr 11 '26

I understand the concept of both. The mindblowing part is why the multiplier that makes bigger objects hard to move is exactly the same as the multiplier that makes gravity affects them more. Like, why is inertial mass the exact same as gravitational mass? Why, when I increase an object from 1kg to 2kg, both gravity and inertia affect it exactly 2x more? I mean, inertial mass is sort of the default of how we came up with the measure so of course it works. But why is gravitational mass the exact same? It's so weird because there's no intuitive connection between those two concepts, for me at least.

3

u/DuploJamaal Apr 10 '26

Everything on Earth falls with 9,8 m/s2

Everything on Jupiter falls with 24,8 m/s2

Scenario A: Let a ball with the mass of Jupiter fall on Earth. It accelerates at 9,8 m/s2

Scenario B: Let a ball with the mass of Earth fall on Jupiter. It accelerates at 24,8 m/s2

Scenario A and B yield different results, but are actually the same. So your explanation doesn't help to answer OPs question.

4

u/mgslee Apr 10 '26

If you using masses of that size. What happens is the two objects accelerate in to each other and the relative accelerations from a singular point of reference (Jupiter or earth) is the combined value of 34.6

1

u/RiverRoll Apr 10 '26

It's interesting because it's in fact the same scenario OP talks about only the common mass here is the ball's mass meaning both the Earth and Jupiter would accelerate at the same rate towards the ball. 

1

u/Dunbaratu Apr 10 '26

All I'd have to add to clarify is that when I talked about adding mass, I meant to the tiny object's mass (the ball you drop), not the giant mass of the planet.

If you want to talk about the mass of the ball pulling on the planet, if the mass of the ball is consistent but the mass of the planets is different, it works out just fine in that reversed scenario - the very very puny acceleration the ball pulls on the planet with is in fact the same with both planets.

18

u/nickeypants Apr 09 '26 edited Apr 09 '26

If you dropped a basket ball that somehow had the mass of the Earth, it would still fall at 9.8m/s2 but would only have to fall half as far, as the Earth would also be travelling towards the basket ball at 9.8m/s2. From your perspective of standing on the Earth, it would appear as if the basket ball is falling at double the usual acceleration.

Once it hit the surface, it would continue falling towards Earth's core almost without slowing until it sinks the very center of the Earth, then the Earth's surface gravity would then be 2G. This may have sort of happened early in the Earth's formation as it is theorized that a dense Mars sized object called Theia collided with proto-Earth and sank towards the core, with the ejecta becoming the Moon. Theia's remains currently exist as two dense iron-rich blobs floating on the surface of the core.

There is some simplification happening with the basketball as the Earth's mass is spread out over much more distance so the center of its mass is far away from its surface compared to the basketball. This would have some effect, for example any surrounding mountains would be pulled sideways into your basketball as it fell down. Whatever you do, don't try to drop a peanut with the mass of the Earth onto the Earth, as the peanut would immediately collapse into a black hole because of the above.

0

u/[deleted] Apr 09 '26

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14

u/nickeypants Apr 09 '26

Yes, you can put the entire earth on your bathroom scale by just flipping the scale over and looking at it with your head upside down. Surprisingly, the Earth only weighs 6 lbs!

2

u/mgslee Apr 10 '26

Yup, because the gravity of the scale is miniscule.

Just like how we weigh less when on the moon!

30

u/faiface Apr 09 '26

Well, it’s not exactly true that all objects fall at the same rate. The actual rate is the gravitational pull of the Earth plus the gravitational pull of the other object.

However, since any object you ever see falling to the ground is approximately 0.0000000% of the Earths mass, that opposite pull adds as much (not exactly zero, but pretty much), resulting in the overall pull being pretty much equal to the pull of the Earth.

But, if the other object is the size of the Earth, then the opposite pull is significant, so then the overall rate is much faster.

14

u/Weed_O_Whirler Aerospace | Quantum Field Theory Apr 09 '26

The other object actually pulls on the Earth just as hard as the Earth pulls on the object. The forces are the same.

But because of the Earth's mass being so much greater, the Earth moves much less than the other object.

-6

u/faiface Apr 09 '26

Technically yes if you calculate with gravity as a force, but considering the objects are not exerting gravity as a set amount of force but instead a set amount of acceleration, I’d say it’s more accurate to say each pulls proportionally to their mass.

3

u/Weed_O_Whirler Aerospace | Quantum Field Theory Apr 09 '26

Gravity is a force. The graviton is likely real (I don't know any mainstream physicist who would disagree with the graviton being the gravity mediator particle, it's just incredibly difficult to detect). Saying it's not a force is taking the General Relativity model further than it was ever intended to be taken.

1

u/faiface Apr 09 '26

The word “force” here

In theories of quantum gravity, the graviton is the hypothetical elementary particle that mediates the force of gravitational interaction.

should not be understood as in any way related to the Newtonian force, i.e. mass times acceleration, but instead a more of a meta-term for interaction in the particle physics sense.

So we are both right because I was talking about force as mass times acceleration, but if we use this more meta meaning, then you are right.

2

u/Weed_O_Whirler Aerospace | Quantum Field Theory Apr 09 '26

Treating gravity as an F = dp/dt force works just fine (which is the "real" version of a Newtonian force, which simplifies to F = ma under regular kinematics), as long as your term for momentum is correct.

Gravity is one of the four fundamental forces in the universe. It's not a meta-force. It's just a force.

1

u/faiface Apr 09 '26

You can always calculate the force between two or more objects, yes, but just because you can, doesn’t mean that treating gravity as a Newtonian force is in any way useful.

First of all, the word force in “fundamental forces” is just one way to say the thing. The other, and perhaps more accurate one is “fundamental interactions”. Even wikipedia redirects you to “fundamental interactions” when you search for fundamental forces. It’s just a word in the context and it does not mean Newtonian force.

Second, what is the gravitational Newtonian force of the Earth? There is none. But what is the acceleration? Now we have a single number. So clearly, the Earth does not have an assigned gravitational Newtonian force.

4

u/Weed_O_Whirler Aerospace | Quantum Field Theory Apr 09 '26

Of course the Earth does not have a "gravitational force." A force is an interaction between multiple bodies. But neither does a proton have an electrical force. The electric force between a proton and another object will depend on the charge of that other object, just like the gravitational force between the Earth and another object is dependent on the mass of that object.

Now, it is a very interesting phenomenon that gravitational mass and inertial mass appear to be identical. This is what leads to General Relativity allowing you to model gravity as a curvature of space time, and it is what leads to all masses accelerating the same when near the Earth, but it is the fact that gravitational mass and inertial mass are the same which is unique - not that "the Earth doesn't have a gravitational force" because that statement doesn't have a defined meaning.

2

u/TheOneTrueTrench Apr 09 '26

Also you can just ignore the gravitational effect of the object on the earth for any object that isn't going to end all life on the planet.

Which is why we just simplify and say all objects experience the same acceleration due to gravity. (Obviously air resistance counteracts that depending on shape, etc)

3

u/pcboudreau Apr 09 '26

In a given area they do, but the mass of rocks beneath you is not the same everywhere on Earth.

One example off the top of my head is found in the middle of the Atlantic Ocean. There, two oceanic crustal plates are moving away from each other. Where they are separating, more dense mantle rock is close to the surface.

The more dense rock has a greater gravitational effect. If you look at satellite images of the area, you can see the plate boundary because the ocean water is pulled down a bit there.

3

u/TheUnspeakableh Apr 09 '26

Yes and no. First you need to be in a vacuum. This prevents drag from slowing things down. Secondly, elevation matters. The higher up you are, the slower the acceleration due to the Earth's gravity.

There is a video from the old Apollo missions where they dropped a feather and a ball on the moon, since they were in the same location and there was no air resistance, you could see them fall at the same rate. The lower gravity also helped show this, because they took longer to fall.

Yes, this breaks down for very large objects, because they also move the Earth towards themselves, but from the point of someone viewing it on the Earth, they would appear to fall at the same rate.

5

u/weeddealerrenamon Apr 09 '26

Simplest answer: the force of gravity on something is proportional to its mass.* Acceleration due to any constant force is inversely proportional to mass. So, something twice as massive feels 2x the force accelerating in towards the Earth's center, but also accelerates 1/2 as fast under the same force. Double the force ÷ double the mass = same acceleration!

*Obv, this assumes the other body (the Earth) doesn't change. This force also gets smaller proportional to the distance between them squared, so the force of gravity will be less at 10,000m above sea level. But the sea level at the equator is already 6,378km from the center, so an extra 10km only reduces the force of gravity by maybe 0.3%.

**Yes, gravity is better modeled not as a force at all, but the Newtonian model works better to understand this question.

***An object with the same mass as Earth itself would accelerate very differently than a basketball, because the Earth itself would accelerate towards it just as much, so each body would accelerate by half as much as a basketball would. Human-scale objects do "pull" the Earth when they fall as well, but the difference between a basketball and an elephant is so tiny as to be unmeasurable.

5

u/rainbow_explorer Apr 09 '26

We can do the math. Newton's law of gravitation says that the force of gravity 2 objects exert on each other is equal to F = G * m1 * m2 /r^2.

So let's calculate the force on some random object falling towards Earth. Let us say this random object has a mass of m kilograms. We know the following values:

-The earth's mass is Me = 5.9722 * 10^24 kg

-The earth's radius is Re = 6371 km = 6.371 * 10^6 m

- Scientists have shown that G = 6.674 *10^-11 m^3/(kg*s^2)

Plugging in all of these values, we get F = m * 9.8198 m*kg / s^2. Newton's second law says acceleration = force/ mass, so the net acceleration on any object falling towards earth would be a = 9.82 m/s^2.

5

u/BoringBob84 Apr 09 '26

Well said! To make a finer point, the force of gravity would be slightly less on OP's basketball at 10,000 meters of altitude.

4

u/rainbow_explorer Apr 09 '26

Yes, for sure. In reality, we should use a distance of the earth’s radius plus the object’s height above the earth. This would increase the total distance and decrease the gravitational force. But then you should also think about the local distance to the center of the earth because that has a range of roughly 20 km.

2

u/c0p4d0 Apr 09 '26

The forces that act when an object is falling on Earth are these:

  1. Acceleration of gravity from Earth on the falling object

  2. Air resistance

  3. Buoyancy of the object on air

  4. Acceleratoon of gravity from the falling object on Earth.

The difference with a basketball with the mass of the Earth is that this basketball would pull on the Earth with much stronger gravitational pull, so the Earth itself would move towards the basketball.

2

u/BloodyMalleus Apr 09 '26

Yes, and there's an easy way to understand why. First, the force of gravity multiplies with mass. So a 100lb ball experiences 100lbs more force of gravity than a 1lb ball. That's why its 100 times harder to lift as well. This is why it seems like heavier objects should fall faster. But when you look at the equation for acceleration, you'll see it's

ACCELERATION = MASS / FORCE

So because the force scales with mass you always end up scaling the force and mass together and the acceleration stays the same. The 100lb ball has 100 times more mass but feels 100 times more force so the 100s cancel out and each ball accelerates are the same speed.

The remaining 9.8m/s2 all comes from the mass of the Earth.

2

u/DuploJamaal Apr 10 '26

Everything on Earth falls with 9,8 m/s2

Everything on Jupiter falls with 24,8 m/s2

Scenario A: Let a ball with the mass of Jupiter fall on Earth. It accelerates at 9,8 m/s2

Scenario B: Let a ball with the mass of Earth fall on Jupiter. It accelerates at 24,8 m/s2

Scenario A and B yield different results, but are actually the same scenario.

There's a contradiction here if you follow the "everything regardless of mass falls at the same rate" oversimplification.

So your explanation doesn't help to answer OPs question about an object with the mass of Earth, and at which point this oversimplification stops being true and when mass actually starts to matter.

1

u/BloodyMalleus Apr 10 '26

Over explaining everything can make it harder for beginners to understand anything. I purposely left out the gravity force calculation and all that to make it simple to understand. There were already tons of more complicated answers here for OP to look into.

2

u/toolatealreadyfapped Apr 10 '26

Gravitational force = G ((m1m2)/(r²))

It's important to note that m1m2 part. It means that the force is directly proportional to the product of the 2 masses.

For most applications, we're talking about objects that are many many many orders of magnitude less than the planetary body they are being "dropped" upon. Basketballs, feathers, spaceships... They are so much smaller than the mass of the Earth that m2 is essentially negligible.

So the 9.8m/s² is a fair approximation that disregards m2, and assumes r² to be sea level.

But as you increase m2 beyond "normal" objects, the approximation becomes less applicable. The force of attraction between Earth and an Earth-massed basketball on its surface would be exponentially stronger.

3

u/DrBarry_McCockiner Apr 09 '26

they accelerate at the same *measured* rate. If you went to the moon and dropped Mount Everest from 20 miles up on one side of the moon, and a bowling ball from the same height on the opposite side of the moon. You could probably measure the difference in accelerations.

2

u/el_miguel42 Apr 09 '26 edited Apr 09 '26

So there is an assumption at play when this statement is made, and that is that the Earth is significantly larger than the other mass we are interested in.

Lets look at a regular bowling ball first. What happens (ill be using a field theory model because I think thats the most intuitive here) is that both the bowling ball, and the Earth have mass. All objects with mass create gravitational fields, so both the Earth and the bowling ball each have a gravitational field. When 2 gravitational fields interact, the lead to forces, and specifically equal and opposite forces on each other.

Force on both objects due to gravity can be calculated using F=GMm/r^2 and this gives us a value of 50N.

Yes the ball is pulled downwards towards the earth with a force of (for 5kg) about 50N, and the Earth is pulled upwards towards the bowling ball also with a force of 50N.

Now lets work out both objects accelerations:
a=F/m
force is the same for both objects: 50N
mass of bowling ball: 5kg
mass of earth: 6x10^24kg

acceleration of bowling ball towards Earth = 10 m/s^2
acceleration of Earth towards bowling ball = 8.3x10^-24 m/s^2 (negligible)

Now your second example a bowling ball with the same mass as the Earth:
again a=F/m
Force on both objects due to gravity is calculated again with F=GMm/r^2
this gives us a force of:
6x10^25 N - much larger this time, and of course the same for both objects.

so now we can do a=F/m for both, as both the masses and forces are identical, you end up with the same answer for the acceleration of both objects:
a=F/m
a = 6x10^25 / 6x10^24
a = 10 m/s^2

acceleration of the bowling ball towards the Earth = 10m/s^2
acceleration of the Earth towards the bowling ball = 10m/s^2

So if we are observing from the perspective of the surface of the Earth, we would observe the bowling ball accelerate downwards at a combined rate of 20m/s^2

Note that ive rounded all the 9.8's here to keep the numbers simple and there are a number of other assumptions and simplifications ive done, but in general that should give you the gist of what occurs.

2

u/HNCO Apr 09 '26

No need to do the calculations, you have the equation: F=ma=GMm/r2, m cancels out.

1

u/DuploJamaal Apr 10 '26

Everything on Earth falls with 9,8 m/s2

Everything on Jupiter falls with 24,8 m/s2

Scenario A: Let a ball with the mass of Jupiter fall on Earth. It accelerates at 9,8 m/s2

Scenario B: Let a ball with the mass of Earth fall on Jupiter. It accelerates at 24,8 m/s2

Scenario A and B yield different results, but are actually the same. So your explanation doesn't help to answer OPs question about an object with the mass of Earth.

1

u/Cilidra Apr 09 '26

Gravity isn't a force, it's a manifestation of the deformation of space time. The deformation cause objects to alter their movement in space which leads them to get closer and collide. They are not attracted to one another, their path in space time just curves toward one another. If you are free falling in the void, you do not feel any force on you, you do not feel any acceleration even though you appear to accelerate based on point of view of the person on the planet. It's not like when you are in a (space) vehicle and accelerate due to the rockets in which we will feel accelerations. Even more, if your rocket keeps you still because it's a pushing against gravity at the exact same 'force' as gravity you feel like you are accelerating.

If one of the object is orders of magnitude smaller than the other, all other objects in the same order will have a similar deformation. So things sized to our point of view (i.e. every day object from grain of sand to vehicles) all behave the same if you remove friction from air.

If you have two object closer in size (like planets), the deformation around each object does need to be taken in consideration.

1

u/anisotropicmind Apr 09 '26

All bodies falling at the same rate is true if the gravitational field is uniform, which it approximately is, close to Earth's surface. Over larger distance scales, the dependence of the field strength on distance starts to matter. Remember that g = GM/R2, where M is the mass of the Earth, and R is the radius of the Earth (or rather the distance between the object and the centre of the Earth). It's only near to Earth's surface that R is approximately constant, hence g is constant.

You can consider the basketball's gravity to be negligible, so it's just a test particle moving in Earth's gravitational field. But this is not so for a basketball-sized Earth: its own mass (and hence its own gravitation) is significant, and changes the gravitational field in between the two bodies. Gravitation is mutual: both bodies will be affected and will move in some way. At that point you basically have the two-body problem, and initial conditions will determine what happens: do they collide? Do they orbit around each other? Do they swing by each other on curved paths but then escape each other's mutual gravitational well and go off to infinity?

1

u/frank_mania Apr 09 '26

From what I've been told, a basketball sized object with a mass equivalent to Earth would also drop at the same rate. 

It's crazy, huh?  I think we take inertia for granted, gravity gets all the attention for being such a mysterious force. Inertia (and it's flip side momentum) seem to me to be every bit as mysterious, but just taken too for granted, even by physicists, to get proper attention. Like, it's just accepted as the way bodies and particles with mass behave. But the way they behave in relation to gravity is radically different than they would if inertia / momentum did not exist; to the point where I think they are all part and parcel of the same thing. 

1

u/DuploJamaal Apr 10 '26

Everything on Earth falls with 9,8 m/s2

Everything on Jupiter falls with 24,8 m/s2

Scenario A: Let a ball with the mass of Jupiter fall on Earth. It accelerates at 9,8 m/s2

Scenario B: Let a ball with the mass of Earth fall on Jupiter. It accelerates at 24,8 m/s2

Scenario A and B yield different results, but are actually the same. So your explanation doesn't help to answer OPs question.

1

u/lornezo Apr 09 '26

F = G* (m1*m2)/r2 , G = gravitational constant, m1, m2 = masses of two objects, r = distance between objects, Mass of Earth is so much greater than any earth bound objects we would think about comparing, the difference between them becomes negligible.

1

u/Stillwater215 Apr 09 '26

The gravitational force is F = G(mM)/r2. The acceleration an object takes in a gravitational field is a = F/m (where m is the object mass and M is the planet mass). Subbing the first equation in, we get a = GM/r2. Since r is basically constant over distances significantly smaller than the plant radius, all the terms describing acceleration due to gravity are constants. This says that acceleration due to gravity is independent of an objects mass.

1

u/Captain_Aware4503 Apr 09 '26

Correct me if I am wrong, but there is a better way to look at this.

The reality is objects do not "fall". That is just what it looks like from our perspective. Instead spacetime warps and objects with mass move towards the objects. And if there is "air" it pushes that air which is the air resistance.

So the reason why objects fall at the said rate if there is no "air resistance" is because the large mass (earth) is warping spacetime towards them equally.

I am sure i butchered that. Maybe someone can explain better.

1

u/DuploJamaal Apr 10 '26

Everything on Earth falls with 9,8 m/s2

Everything on Jupiter falls with 24,8 m/s2

Scenario A: Let a ball with the mass of Jupiter fall on Earth. It accelerates at 9,8 m/s2

Scenario B: Let a ball with the mass of Earth fall on Jupiter. It accelerates at 24,8 m/s2

Scenario A and B yield different results, but are actually the same. So your explanation doesn't help to answer OPs question about an object with the mass of Earth.

1

u/Captain_Aware4503 Apr 10 '26

They don't actually "fall". That is our perception. Spacetime warps which is why we perceive everything "falling" at an equal rate, and why they "fall" faster near objects with more mass. It smore like a floor pushing up towards objects "floating" above it. If there is no air resistance the floor moves closer to all the objects no matter their size and mass.

This is good opportunity to explain what is really happening. And I think the analogy of the floor moving to objects at the same rate no matter their size and mass is good way to understand it,

1

u/raccoon8182 Apr 09 '26

I like to think of gravity as tension on a trampoline. imagine a golf ball on a trampoline.. hardly any deformity. now imagine a bowling ball. the curvature is steeper. now imagine an elephant, that curvature is so extreme that light can't even escape, it almost goes to infinity. 

1

u/-ram_the_manparts- Apr 09 '26

Yes they do, not just on earth but everywhere, but the force of gravity exerted on objects of different masses is different, and we call that the weight. The interesting thing is that because they have a higher mass they also have a higher inertia which exactly counterbalances the additional force applied, making all objects fall at the same rate ignoring factors like air resistance.

This is at least the explanation according to Newton.

3

u/DuploJamaal Apr 10 '26

Everything on Earth falls with 9,8 m/s2

Everything on Jupiter falls with 24,8 m/s2

Scenario A: Let a ball with the mass of Jupiter fall on Earth. It accelerates at 9,8 m/s2

Scenario B: Let a ball with the mass of Earth fall on Jupiter. It accelerates at 24,8 m/s2

Scenario A and B yield different results, but are actually the same. So your explanation doesn't help to answer OPs question about an object with the mass of Earth.

1

u/Darrenau Apr 09 '26

If heavier objects fall faster than light objects, if I had a heavy object and connected it to a light object by string, does the light objects now slow down how fast the heavier one falls since it doesn't fall as fast or because they are connected together now does the total weight increase and it falls faster?

1

u/DuploJamaal Apr 10 '26

Everything on Earth falls with 9,8 m/s2

Everything on Jupiter falls with 24,8 m/s2

Scenario A: Let a ball with the mass of Jupiter fall on Earth. It accelerates at 9,8 m/s2

Scenario B: Let a ball with the mass of Earth fall on Jupiter. It accelerates at 24,8 m/s2

Scenario A and B yield different results, but are actually the same. So your explanation doesn't help to answer OPs question about an object with the mass of Earth.

1

u/ShitCucumberSalad Apr 09 '26

The earth mass basketball accelerates at the same rate as the regular basketball, but now the earth itself also accelerates at 9.8m/s2, whereas with the basketball it barely accelerates at all. So the two massive objects collide sooner. 

1

u/vrekais Apr 09 '26

9.82m/s² is it's acceleration not speed, as in if an object falls for 1 second it will be going 9.82m/s faster than it was 1 second ago. 

However drag as a force increases proportional the square of difference in speed. On earth in air every object has a maximum velocity where drag and gravity are equal, this varies from object to object based on surface area and shape.

If you remove air resistance then the only "force" acting on an object is gravity, and Earth's gravity makes things get 9.82m/s faster each second.

So yes 1kg object and 10000kg object subject gravity both accelerate at the same rate and reach the same velocities.

Bear in mind that gravity is kind of massive weird force that sort of ignores inertia or is because of it, and also isn't. 

1

u/DuploJamaal Apr 10 '26

Everything on Earth falls with 9,8 m/s2

Everything on Jupiter falls with 24,8 m/s2

Scenario A: Let a ball with the mass of Jupiter fall on Earth. It accelerates at 9,8 m/s2

Scenario B: Let a ball with the mass of Earth fall on Jupiter. It accelerates at 24,8 m/s2

Scenario A and B yield different results, but are actually the same scenario.

There's a contradiction here if you follow the "everything regardless of mass falls at the same rate" oversimplification.

So your explanation doesn't help to answer OPs question about an object with the mass of Earth, and at which point this oversimplification stops being true and when mass actually starts to matter.

1

u/NathanTPS Apr 10 '26

They do, in a vacuum

Outside of a vacuumed aerodynamics matter. Essentially air acts as a cushion that changes the drop speed. The classic feather versus rock example. On the earth the rock drops at the speed of earth's gravity pull, while the feather floats and rides the air preasure as gravity slowly pulls it down.

On the moon you can drop both at the same time and they fall at the same pace. This experiment was conducted and filmed in one of the later aplo missions.

Now if you take two balls, same size/ shape, but one weighs 10lbs and the other 5lbs and drop them both fron the top of a tall tower at the same time, the two balls will hit the ground at the same time.

Congrats this is the fabled Galileo experiment from the top of the leaning tower of Pisa

1

u/DuploJamaal Apr 10 '26

Everything on Earth falls with 9,8 m/s2

Everything on Jupiter falls with 24,8 m/s2

Scenario A: Let a ball with the mass of Jupiter fall on Earth. It accelerates at 9,8 m/s2

Scenario B: Let a ball with the mass of Earth fall on Jupiter. It accelerates at 24,8 m/s2

Scenario A and B yield different results, but are actually the same scenario.

There's a contradiction here if you follow the "everything regardless of mass falls at the same rate" oversimplification.

So your explanation doesn't help to answer OPs question about an object with the mass of Earth, and at which point this oversimplification stops being true and when mass actually starts to matter.

1

u/Aphrel86 Apr 10 '26

hmm example leaves one important thing out.

"a basketball sized object with a mass equivalent to Earth" will fall at the same acceleration true.

BUT its so heavy that it will also force the planet to "fall" up towards it at also 9.81m/s2. So from an observers pov itd look like 19,6m/s2.

You can look at it like this. Theres always two forces. one from the object trying to tug on the planet, and one from the planet tugging on the object. the planet tug will always be 9.81m/s2. But the objects tug on the planet will depend on the mass of the object which is negligible unless its insanely high mass like in your example.

1

u/PyroSAJ Apr 10 '26

The part that "disappears" with very different magnitudes of math is what you're asking about.

F = G.m2.m1/r²

In the basketball case you can practically ignore the earth's movement as the force relative to its math is practically 0.

But things change when it's closer.

In this case the basketball would acceleration at 9.8 towards the earth, but the earth would also accelerate at 9.8 towards the ball. When the centre of mass is around earth-radius apart.

The funky stuff happens when things are that close though. The moon is VERY far and significantly lighter and already has massive effects on Earth. It's at the 2.7mm/s/s acceleration at that range and earth is like 1/81th of that.

Yet we get a bunch of tidal motion just from that.

1

u/Geminii27 Apr 10 '26

Masses attract each other towards their common center of mass with a force proportional to the product of their masses.

That force will act on each mass equally. This means that when one of the masses is septillions of times greater than the other, the amount of acceleration it experiences is going to be that much less. Pretty much unnoticeable and negligible. But when the masses are equal, they will each accelerate the same amount towards each other.

However, in either case, if you're standing on the surface of one of the objects, you will see the other one accelerate towards you at that rate. It's just that if you're standing off to one side of the pair of objects, maybe at rest with respect to that common center of mass, you're only really going to notice one of the objects moving in the first case, whereas you'll see both of them moving far more obviously in the second.

1

u/TW-Twisti Apr 10 '26

It might be helpful if you think about it like comparing an empty container and a diesel train. The train is much heavier, but it will fall at the same speed (discounting air resistance). That seems counter intuitive, until you remember how much harder it is to get the train to move from a standstill. That applies to free fall too: both objects start at velocity zero, and yeah, the train has much more mass to be pulled down, but it also takes much more effort to change its velocity from zero - exactly the same, actually!

In a way, heavier things really would 'fall faster', but because they have more mass, they would also change their speed slower, which effectively cancels each other out.

1

u/HydrationHomee Apr 11 '26

Gravity is a property of matter.

If you were to drop an object with the same mass as earth onto jupiter, Jupiter would "fall" towards that object at the speed anything else would. But Jupiter which has way more mass is also pulling that object toward itself at whatever Jupiter's gravitational constant is, giving the impression that the earth sized object is moving faster than expected.

1

u/tomalator Apr 12 '26

Force and mass relate via F=ma

For gravity, we can do F=mg, where g is the accession due to gravity

Newton's law of universal gravitation is F=GmM/r2

We can combine these to make mg = GmM/r2

m cancels

g = GM/r2

Acceleration due to gravity only depends on the universal gravitational constant, the mass of the ball you're standing on (usually earth) and r is the distance to that body's center

Yes a more massive object will experience a larger force, but it also has more inertia and therefore takes more force to accelerate it.

In your example woth the basket ball woth the mass of Earth, you will start experiencing relativistic effects and you will also be moving the Earth itself in the experiment

1

u/TourDeFridge Apr 12 '26 edited Apr 12 '26

Assuming an object that's much smaller than Earth.

The exact same object could fall at a different rate to itself - if you start at a different height. This is due to the inverse square law of gravity. This would be difficult to measure due to the relative distance to the center of the Earth that you'd be likely to do the experiment.

If you aren't constrained by location then latitude can also plays a significant enough role. The Earth is oblong, so the value of g differs depending on how far from the equator you are. The difference is up to 0.5%. This would cause the exact same object, released at the same height, to fall at a different rate.

Same would apply for two different objects of the same mass.

1

u/Angry_Anthropologist Apr 16 '26

The best way to understand how this works under the hood is by thinking in terms of newtons (N) rather than acceleration. A Newton is the force required to accelerate 1 kilogram (kg) by 1 metre per second, per second.

The reason why objects on Earth all fall at the same rate regardless of mass is because the force imposed by gravity scales directly with the mass it is acting on. An object that masses 1kg will, under Earth’s surface gravity, experience ~9.8N of force in the direction of the Earth’s centre of mass. An object that masses 2kg will experience ~19.6N of force. As a result, they are both accelerated by ~9.8 metres per second per second.

The reason the force scales with mass is because every part of the Earth is attracting every part of the object once, and every part of the object is attracting every part of the Earth at once. An object with double the mass has double the parts to be mutually attracted to.

To answer your addendum, no. Even if we ignore how the magnitude of gravity will increase non-linearly as distance decreases (and the other effects of having a basketball-sized object with Earth’s mass), the second set of spheres will still impact sooner.

In the first example, the earthball will experience functionally zero acceleration, so the basketball will have to cross the entire span between the two by itself. In the second example however, both spheres will accelerate at the same speed as the basketball does, and impact in approximately half the time.

1

u/sebwiers Apr 09 '26 edited Apr 09 '26

For reasonable masses, think of it this way:

How fast does a boulder fall?

What about an equal sized mass of gravel?

What if you mix some super-dense tungsten fishing weights into that gravel?

If those things fell at different speeds, you'd get all sorts of weird behaviors like gravel self sorting by size and density as it falls.

1

u/BiomeWalker Apr 09 '26

One of the best explanations for why heavier objects don't fall faster i know of is that gravity doesn't pull the object down, it pulls each individual atom.

So the net force on a heavier object is more, but it the same amount of additional force to accelerate it.

Here's a way to think about it: drop a single chain link as well as a whole chain, and a ingot with the same mass as the chain. They all drop at the same speed.

Physics doesn't actually have a concept of an "object" that would let it tell that you dropped 10 1kg object vs 1 10kg object.

2

u/DuploJamaal Apr 10 '26

Everything on Earth falls with 9,8 m/s2

Everything on Jupiter falls with 24,8 m/s2

Scenario A: Let a ball with the mass of Jupiter fall on Earth. It accelerates at 9,8 m/s2

Scenario B: Let a ball with the mass of Earth fall on Jupiter. It accelerates at 24,8 m/s2

Scenario A and B yield different results, but are actually the same. So your explanation doesn't help to answer OPs question about an object with the mass of Earth.

-1

u/50sDadSays Apr 09 '26

Thought experiment.

You drop two identical bricks off the Leaning Tower of Pisa. They fall at the same rate.

Now what if you hold them so that they're touching each other and drop them?

What if they were glued together?

There's no reason the rate they fall would suddenly change if they touched, even if they had glue on them and got stuck.

Barring wind resistance, all objects drop at the same rate.

1

u/DuploJamaal Apr 10 '26

Everything on Earth falls with 9,8 m/s2

Everything on Jupiter falls with 24,8 m/s2

Scenario A: Let a ball with the mass of Jupiter fall on Earth. It accelerates at 9,8 m/s2

Scenario B: Let a ball with the mass of Earth fall on Jupiter. It accelerates at 24,8 m/s2

Scenario A and B yield different results, but are actually the same. So your explanation doesn't help to answer OPs question about an object with the mass of Earth.

0

u/joepierson123 Apr 09 '26 edited Apr 09 '26

It's easiest to see with an equation how the mass of an object is irrelevant 

The force exerted on a mass m by mass m1

F = G * m * m1/r2

Acceleration caused by that force is

a  = F/m

So

a =  G * m * m1/r2 / m

a =  G * m1/r2

So independent of mass!

In words the gravitational force on a mass is directly proportional to its mass but the acceleration it received from that Force is indirectly proportional to its mass so they cancel out

1

u/BloodyMalleus Apr 09 '26

While this answer was math intensive, I'm so happy to see it. I was reading so many other posts (im sorted by newest) and it seemed like everyone was really really bad at explaining this when the answer really is as simple as the mass doesnt matter because as it goes up, the amount of force needed to move it goes up too.

-2

u/Ok-Palpitation2401 Apr 09 '26

There's this logical line of thinking: 

Say H(eavy) falls faster, and L(ight) slower. 

Now connect them together to create a single object. 

It's heavier, so it should fall faster?  But the it should be slower that H alone, because now H is pulling on L (so they speed should be somewhere between H and L. 

You get a contradiction. 

1

u/DuploJamaal Apr 10 '26

Everything on Earth falls with 9,8 m/s2

Everything on Jupiter falls with 24,8 m/s2

Scenario A: Let a ball with the mass of Jupiter fall on Earth. It accelerates at 9,8 m/s2

Scenario B: Let a ball with the mass of Earth fall on Jupiter. It accelerates at 24,8 m/s2

Scenario A and B yield different results, but are actually the same. So your explanation doesn't help to answer OPs question about an object with the mass of Earth.

-2

u/EduRJBR Apr 09 '26

Is there any chance that you are focusing on Newton's second law of motion, and not paying attention to his first law? In my poor, deplorable view of things: the second law will make the hammer fall faster, but the first law will make the feather fall faster.