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

1. Jun 21, 2015

### Josh S Thompson

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.

2. Jun 21, 2015

### shortyjat

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. Jun 21, 2015

### ShayanJ

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.

4. Jun 21, 2015

### davenn

5. Jun 21, 2015

### Drakkith

Staff Emeritus
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. Jun 21, 2015

### shortyjat

Gotcha. Thanks!
Gotcha. I checked out your explanation in another thread and it was much more thorough than the explanation given to me.

7. Jun 21, 2015

### Josh S Thompson

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 percieved acceleration i.e.one object hits the ground first.

8. Jun 21, 2015

### davenn

what do you mean by this ??

9. Jun 22, 2015

### Drakkith

Staff Emeritus
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. Jun 22, 2015

### ZapperZ

Staff Emeritus

Zz.

Last edited by a moderator: May 7, 2017
11. Jun 23, 2015

### Josh S Thompson

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. Jun 23, 2015

### Drakkith

Staff Emeritus
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. Jun 23, 2015

### Josh S Thompson

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. Jun 23, 2015

### davenn

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

Last edited: Jun 23, 2015
15. Jun 23, 2015

### Josh S Thompson

I'm not trying to read a book bro

16. Jun 24, 2015

### Josh S Thompson

Ok this is what im 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. Jun 24, 2015

### davenn

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

18. Jun 24, 2015

### Josh S Thompson

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)

19. Jun 24, 2015

### Drakkith

Staff Emeritus
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.

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. Jun 27, 2015

### paulfr

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.