Why do things accelerate due to gravity at the same rate?

In summary, the force of gravity between two objects is dependent on their masses and the distance between them. However, the acceleration due to gravity does not depend on the mass of the object and is the same for all objects. This is known as the weak equivalence principle. While it may appear that a heavier object would accelerate faster, in reality, the difference is so small that it is negligible and both objects will hit the ground at the same time when dropped from the same height. This is due to the fact that the Earth itself is also accelerating towards the objects, making the acceleration of the objects appear to be the same.
  • #1
Josh S Thompson
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If you use Newtons gravity equation; F=M1*M2/d^2. The force is dependent on the mass of two bodies so how could the mass cancel? Also, for example If I had a bowling ball and a ball the mass of the sun and droped them 100 feet above Earth The two balls would not accelerate at the same rate because one ball is so massive that it have much more force.
 
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  • #2
Things don't accelerate due to gravity at the same rate. What you're referring to, I think, is when people say that dropping a bowling ball and a marble from a building, both will hit the ground at the same time. People say this because the mass of both the bowling ball and the marble are negligible in comparison to the mass of the earth. Essentially, the bowling ball IS accelerating faster, however the difference is so small that it doesn't really matter.
 
  • #3
Using Newton's 2nd law and his law of acceleration, we have ## m\vec a=-G \frac{m M}{r^2}\hat r \Rightarrow \vec a=-G \frac{M}{r^2}\hat r ##. So the acceleration of an object due to gravity doesn't depend on the mass of the object, so its the same for all objects.
Actually the reason is that the gravitational and inertial masses of an object are equal. Otherwise we couldn't cancel them above and acceleration would depend on the mass of the object.
This is called weak equivalence principle.
 
  • #5
shortyjat said:
Things don't accelerate due to gravity at the same rate. What you're referring to, I think, is when people say that dropping a bowling ball and a marble from a building, both will hit the ground at the same time. People say this because the mass of both the bowling ball and the marble are negligible in comparison to the mass of the earth. Essentially, the bowling ball IS accelerating faster, however the difference is so small that it doesn't really matter.

This is not correct. In the absence of air resistance, both the bowling ball and the marble have the exact same acceleration. What's different is that the Earth accelerates at a higher rate under the influence of the bowling ball's gravity than the marble's.
 
  • #6
Drakkith said:
This is not correct. In the absence of air resistance, both the bowling ball and the marble have the exact same acceleration. What's different is that the Earth accelerates at a higher rate under the influence of the bowling ball's gravity than the marble's.
Gotcha. Thanks!
Drakkith said:
This is not correct. In the absence of air resistance, both the bowling ball and the marble have the exact same acceleration. What's different is that the Earth accelerates at a higher rate under the influence of the bowling ball's gravity than the marble's.
Gotcha. I checked out your explanation in another thread and it was much more thorough than the explanation given to me.
 
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  • #7
Drakkith said:
This is not correct. In the absence of air resistance, both the bowling ball and the marble have the exact same acceleration. What's different is that the Earth accelerates at a higher rate under the influence of the bowling ball's gravity than the marble's.
Thank you I agree with this, so essetially you can say if the objects are in the same location they accelerate at the same rate because Earth accelerates to one point. But if the objects are far away there would be a difference in the perceived acceleration i.e.one object hits the ground first.
 
  • #8
Josh S Thompson said:
But if the objects are far away there would be a difference in the perceived acceleration

what do you mean by this ??
 
  • #9
Josh S Thompson said:
Thank you I agree with this, so essetially you can say if the objects are in the same location they accelerate at the same rate because Earth accelerates to one point. But if the objects are far away there would be a difference in the perceived acceleration i.e.one object hits the ground first.

I think you're saying that a larger object dropped from a large distance would hit the ground first because the Earth accelerates faster towards it. If we were to set up two different situations where M1 and M2 are dropped from identical distances, then yes, that would be correct.
 
  • #10
Josh S Thompson said:
If you use Newtons gravity equation; F=M1*M2/d^2. The force is dependent on the mass of two bodies so how could the mass cancel? Also, for example If I had a bowling ball and a ball the mass of the sun and droped them 100 feet above Earth The two balls would not accelerate at the same rate because one ball is so massive that it have much more force.

Read the FAQ:
https://www.physicsforums.com/threads/why-is-acceleration-due-to-gravity-a-constant.511172/

Zz.
 
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  • #11
davenn said:
what do you mean by this ??

If you in the middle of the objects that are far away from each other but the objects are equal distance above Earth it would look like the heavier object accelerates faster and it would hit ground first
 
  • #12
Josh S Thompson said:
If you in the middle of the objects that are far away from each other but the objects are equal distance above Earth it would look like the heavier object accelerates faster and it would hit ground first

Only if you dropped them separately and measured the impact time for each one. If you drop them together then they still hit the ground at the same time.
 
  • #13
Drakkith said:
Only if you dropped them separately and measured the impact time for each one. If you drop them together then they still hit the ground at the same time.

what you mean, all other things constant the heavier object would hit the ground first if you dropped them together because there is more force between them.
 
  • #14
Josh S Thompson said:
what you mean, all other things constant the heavier object would hit the ground first if you dropped them together because there is more force between them.

did you not read Drakkith's post in that thread I linked to in post #4 ?

if you did you shouldn't still be asking these same questions over and over

Again ...
negating atmospheric drag ( resistance) 2 objects, regardless of difference in mass, if dropped at the same time, will fall and hit the ground at the same time
They are BOTH being subject to the same gravitational force
Their individual masses are irrelevant

Dave
 
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  • #15
davenn said:
did you not read Drakkith's post in that thread I linked to in post #4 ?

if you did you shouldn't still be asking these same questions over and over

Again ...
negating atmospheric drag ( resistance) 2 objects, regardless of difference in mass, if dropped at the same time, will fall and hit the ground at the same time
They are BOTH being subject to the same gravitational force
Their individual masses are irrelevant

Dave
I'm not trying to read a book bro
 
  • #16
davenn said:
did you not read Drakkith's post in that thread I linked to in post #4 ?

if you did you shouldn't still be asking these same questions over and over

Again ...
negating atmospheric drag ( resistance) 2 objects, regardless of difference in mass, if dropped at the same time, will fall and hit the ground at the same time
They are BOTH being subject to the same gravitational force
Their individual masses are irrelevant

Dave
Ok this is what I am saying

"The general form of the equation for the force of gravitation is: F = GM1M2/r2 This means that the force, which is the same magnitude for both objects" (Drakkith)

if the force is acting on both objects equally why can't you say the F acting on the Earth from gravity is MA, then set it equal to the force of gravity between two objects

MA=M*m*G/(r^2) = A = m*G/(r^2)
M=mass of earth
A=acceleration of earth
m=mass of an object
r=distance
G=constant

Then the acceleration of Earth would be dependent on the mass of an object
and you could say a heavier object does fall to Earth faster
because we are on Earth and it would be hard to notice Earth moving.
And the Earth would touch the heavier object first
 
  • #17
Josh S Thompson said:
Then the acceleration of Earth would be dependent on the mass of an object
and you could say a heavier object does fall to Earth faster
because we are on Earth and it would be hard to notice Earth moving.
And the Earth would touch the heavier object first

but as your have been told repeatedly ... the mass of the object isn't considered and doesn't need to be

PLEASE READ that post from Drakkith
 
  • #18
davenn said:
but as your have been told repeatedly ... the mass of the object isn't considered and doesn't need to be

PLEASE READ that post from Drakkith
I did read it and the part where he plugs in the F with MA, I say why can't you say the force acting on the Earth is equal to MA

M=mass of earth
A=acceleration of earth
m=mass of an object
r=distance
G=constant

M*m*G/(r^2) = force acting on earth

MA = definition of a force

MA=M*m*G/(r^2) =

A = m*G/(r^2)

Read that Dave
 
  • #19
Josh S Thompson said:
Ok this is what I am saying

"The general form of the equation for the force of gravitation is: F = GM1M2/r2 This means that the force, which is the same magnitude for both objects" (Drakkith)

if the force is acting on both objects equally why can't you say the F acting on the Earth from gravity is MA, then set it equal to the force of gravity between two objects

MA=M*m*G/(r^2) = A = m*G/(r^2)
M=mass of earth
A=acceleration of earth
m=mass of an object
r=distance
G=constant

Then the acceleration of Earth would be dependent on the mass of an object
and you could say a heavier object does fall to Earth faster
because we are on Earth and it would be hard to notice Earth moving.
And the Earth would touch the heavier object first

Sure. But here's where we have to be careful with terminology and word choice. When you say that the heavier objects falls to Earth faster, most of us interpret that to mean that the acceleration of the object under the force of Earth's gravity is more for M1 (heavier mass) than for M2 (lighter mass), which is NOT true. Both objects experience the same acceleration towards the Earth from Earth's gravity.

Now, if you want to account for the slight acceleration of the Earth towards the objects, then for clarity's sake we need to use an inertial coordinate system to compare everything to and not the accelerating frame of the Earth.

Josh S Thompson said:
I did read it and the part where he plugs in the F with MA, I say why can't you say the force acting on the Earth is equal to MA

It is equal to MA. For a 200 kg mass placed just above the surface of the Earth, the force exerted on the Earth by the mass is 1962 Newtons and the acceleration would be 3.29 x 10-22 m/s2. So 1962 N = (5.97 x 1024 kg) * (3.29 x 10-22 m/s2). F=MA.
 
  • #20
The bowling ball feels a greater Force from the Gravitational Mass of the Earth
than the marble as calculated with Newton's Universal Law of Gravitation.
But it also has more Inertial Mass, the tendency to resist a change in motion.

The two effects balance so that the bowling ball accelerates at exactly the same
rate as the marble.

I believe the argument that they accelerate slightly differently due to
their much smaller mass than that of the Earth is invalid.
Newton's Universal Law + Newton's 2nd Law F=ma show their
accelerations to be identical and independent of their mass.
 
  • #21
paulfr said:
The bowling ball feels a greater Force from the Gravitational Mass of the Earth
as calculated with Newton's Law of Gravitation.
But it also has more Inertial Mass, the tendency to resist a change in motion.

The two effects balance so that the bowling ball accelerates at exactly the same
rate as the marble.

While this is a perfectly acceptable qualitative explanation to give a conceptual understanding, note that to be able to say "... the two effects balance..." requires a quantitative explanation. There is no way to know that they EXACTLY "balance" each other such that the acceleration remains the same until one proves it via mathematics.

Zz.
 
  • #22
paulfr said:
I believe the argument that they accelerate slightly differently due to
their much smaller mass than that of the Earth is invalid.
Newton's Universal Law + Newton's 2nd Law F=ma show their
accelerations to be identical and independent of their mass.

It depends on whether you're considering the acceleration relative to the surface of the earth, or relative to a fixed point in space. These are the same thing if the Earth doesn't move, which will be the case if the gravitational force is small enough that its effect on the Earth is negligible.
 
  • #23
Drakkith said:
This is not correct. In the absence of air resistance, both the bowling ball and the marble have the exact same acceleration. What's different is that the Earth accelerates at a higher rate under the influence of the bowling ball's gravity than the marble's.
Being a bit of a pedant I don't reckon this is completely true. With the absence of air resistance the marble is ever so slightly attracted to the bowling ball and the bowling ball is accelerating at an even slower rate towards the marble.
The three body problem springs to mind, inconvenient but true.http://www.askamathematician.com/2011/10/q-what-is-the-three-body-problem/
 
  • #24
wow... thank you to all of your ideas everyone. I understand it now. :):smile:
 
  • #25
Buckleymanor said:
Being a bit of a pedant I don't reckon this is completely true. With the absence of air resistance the marble is ever so slightly attracted to the bowling ball and the bowling ball is accelerating at an even slower rate towards the marble.

Of course. I was ignoring the attraction the two balls had to each other because it doesn't change how fast the two accelerate towards the Earth or vice versa.
 
  • #26
Drakkith said:
Of course. I was ignoring the attraction the two balls had to each other because it doesn't change how fast the two accelerate towards the Earth or vice versa.
It does the marble takes a longer slightly more arced (geodesic) path towards the Earth than the bowling ball.
 
  • #27
Buckleymanor said:
It does the marble takes a longer slightly more arced (geodesic) path towards the Earth than the bowling ball.

If we're going to get this detailed then we might as well bring back air resistance. The point was that the mass of the object does not affect the acceleration of the object under gravity.
 
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  • #28
Drakkith said:
If we're going to get this detailed then we might as well bring back air resistance. The point was that the mass of the object does not affect the acceleration of the object under gravity.
Of course it does, let's go back to the O.P which mentions a ball with the mass of the Sun and a bowling ball.
They don't have the same acceleration nor does the marble and the bowling ball which was introduced in a later post.
Air resistance was not introduced by the O.P.
Some of these effects are negligible but what is the point of totally ignoring them.
I did mention I was a bit of a pedant but it is o.k to go into some detail if you want to get a clearer picture of what happens.
 
  • #29
Buckleymanor said:
Of course it does, let's go back to the O.P which mentions a ball with the mass of the Sun and a bowling ball.
They don't have the same acceleration nor does the marble and the bowling ball which was introduced in a later post.

Yes they do. That's exactly what we've been showing here in this thread.
If you're thinking of geodesics as in General Relativity geodesics, then that is simply beyond the scope of this thread, as we are discussing classical gravity. General relativity would be far beyond the OP's knowledge level.
 
  • #30
Shyan said:
Using Newton's 2nd law and his law of acceleration, we have ## m\vec a=-G \frac{m M}{r^2}\hat r \Rightarrow \vec a=-G \frac{M}{r^2}\hat r ##. So the acceleration of an object due to gravity doesn't depend on the mass of the object, so its the same for all objects.
Actually the reason is that the gravitational and inertial masses of an object are equal. Otherwise we couldn't cancel them above and acceleration would depend on the mass of the object.
This is called weak equivalence principle.

Er, only that's not a reason is it? It's not a scientific explanation of any fact. It's nothing but a restatement of the fact (that "the acceleration of an object due to gravity doesn't depend on the mass of the object, so its the same for all objects.").

All it does is fix things right with the taught concepts and principles of mechanics? - (that I'm never sure don't contain some circularity or unobservables)
 
  • #31
epenguin said:
Er, only that's not a reason is it? It's not a scientific explanation of any fact. It's nothing but a restatement of the fact (that "the acceleration of an object due to gravity doesn't depend on the mass of the object, so its the same for all objects.").

All it does is fix things right with the taught concepts and principles of mechanics? - (that I'm never sure don't contain some circularity or unobservables)
If you read OP's question, you'll see that it wasn't as obvious for him\her.
 
  • #32
What we have here is a failure to communicate - Josh S Thompson you do not express yourself clearly, and you don't listen to what people say. But to be fair, some of the people providing answers aren't listening to what YOU say either:

Josh S Thompson said:
If I had a bowling ball and a ball the mass of the sun ...

In this case we clearly do need to take into account the acceleration of the Earth which. So to answer your original question (actually it wasn't a question, but let's ignore that for a moment,
Josh S Thompson said:
The two balls would not accelerate at the same rate
From the point of view of an independent observer (more technically, an inertial frame of reference), the two balls would each accelerate towards the Earth at ## \frac{Gm_E}{r^2} ## where ## m_E ## is the mass of the Earth. However, just as the acceleration of the ball depends only on the mass of the Earth (and the distance between them), the acceleration of the Earth depends only on the mass of the ball. In the case of the bowling ball this is negligible, but for a ball the mass of the Sun it is much larger than that of the Earth - this is an important property of a celestial body known as its standard gravitational parameter: you can find some of these (including for the Earth and for the Sun) in this Wikipedia article.

So whereas if we drop a bowling ball from 100 ft we can ignore the motion of the Earth and calculate that the ball accelerates at about 9.8 ms-1 and hits the surface in 2.5 s, if it were possible to place an object the size of a bowling ball but the mass of the Sun 100 ft above the surface of the Earth and release it, we can ignore the motion of the solar mass object and calculate that the Earth would accelerate at about 3,300,000 ms-1 and collide in 0.0043 s.

So from the point of view of an observer on the surface of the Earth, the Sun would indeed accelerate 330,000 times faster than the bowling ball.
 
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  • #33
Buckleymanor said:
It does the marble takes a longer slightly more arced (geodesic) path towards the Earth than the bowling ball.
That doesn't affect the downwards component of acceleration, or the time it takes to collide.
 
  • #34
One of the reasons (and possibly the main reason) people have a hard time understanding the universality of free fall is that they confuse relative acceleration (acceleration relative to one of the accelerating bodies) with acceleration relative to the inertial frame of reference. This is what Nugatory was referring to in his post #22. The UFF is only valid when using an inertial frame of reference.
 

FAQ: Why do things accelerate due to gravity at the same rate?

1. Why do objects of different masses accelerate at the same rate due to gravity?

According to Newton's law of universal gravitation, the force of gravity between two objects is directly proportional to their masses and inversely proportional to the square of the distance between them. This means that the acceleration due to gravity is the same for all objects, regardless of their mass, because the mass cancels out in the equation.

2. How does the mass of an object affect its acceleration due to gravity?

The mass of an object does not affect its acceleration due to gravity. As mentioned before, the mass of an object cancels out in the equation for gravitational force, so the acceleration due to gravity remains constant for all objects.

3. Why is the acceleration due to gravity on Earth approximately 9.8 meters per second squared?

The acceleration due to gravity on Earth is approximately 9.8 meters per second squared because of the mass and radius of the Earth. The larger the mass of an object and the closer the distance between two objects, the stronger the force of gravity. The Earth's mass and radius create a gravitational force that results in an acceleration of 9.8 meters per second squared.

4. How does the acceleration due to gravity change on other planets?

The acceleration due to gravity on other planets varies based on their mass and radius. For example, on Mars, the acceleration due to gravity is approximately 3.7 meters per second squared, while on Jupiter it is about 24.8 meters per second squared. This is because these planets have different masses and radii compared to Earth.

5. Is the acceleration due to gravity always constant?

No, the acceleration due to gravity is not always constant. It can vary based on the location and distance from the source of gravity. For example, the acceleration due to gravity is lower at the top of a mountain compared to sea level because the distance from the center of the Earth is greater. Additionally, the acceleration due to gravity can also be affected by other factors, such as air resistance or the presence of other massive objects.

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