Gravity vs Inertia: Newton's Law of Gravitation Explained

[johnny_bohnny]

As it's stated in Newton's law of gravitation, every object with mass attracts all other object with a force which causes acceleration. So basically there are infinite number of forces in our universe which affect our planet as well. My question is, can an inertifal frame (which has the net force of zero) exist in these condition, and does inertia itself play a role in determining acceleration due to gravity. If we have two objects many many miles aparat, and one has a much greater mass, will the heavier object still accelerate relative to the lighter one.

 

[ZapperZ]

As it's stated in Newton's law of gravitation, every object with mass attracts all other object with a force which causes acceleration. So basically there are infinite number of forces in our universe which affect our planet as well. My question is, can an inertifal frame (which has the net force of zero) exist in these condition, and does inertia itself play a role in determining acceleration due to gravity. If we have two objects many many miles aparat, and one has a much greater mass, will the heavier object still accelerate relative to the lighter one.

Think about this: when and where was the last time you felt the effect of the gravity from Alpha Centauri?

Zz.

 

[johnny_bohnny]

Think about this: when and where was the last time you felt the effect of the gravity from Alpha Centauri?

Zz.

Never, of course. But does that mean that there is no acceleration between Earth and Alpha Centauri because of the great distance or something else?

Or to add a sub-question, why don't small objects like my desk and my ball for instance pull each other causing motion between them, since they also have gravity?

 

[A.T.]

Inertial frames are an idealization, and exist in nature only approximately.

 

[Matterwave]

Never, of course. But does that mean that there is no acceleration between Earth and Alpha Centauri because of the great distance or something else?

Or to add a sub-question, why don't small objects like my desk and my ball for instance pull each other causing motion between them, since they also have gravity?

Gravity is a VERY weak force! So between things which don't have much mass (anything smaller than say, asteroid sized), or things which are far away (e.g. Alpha Centauri) you probably wouldn't be able to feel any attraction at all. For things on your desk, the force between them is so tiny it's negligible.

Why not try to plug in some numbers and see for yourself? Newton's law of gravitation says:

$$F=\frac{G m_1 m_2}{d^2}$$

Where F is the force, G=6.67*10^-11 N*m^2/kg^2, m1 and m2 are the masses (express them in kilograms to get the right units), and d is the distance between the masses (express it in meters for the right units).

Try something like m1=1kg, m2=1kg, and d=1m.

 

[johnny_bohnny]

So inertial movement in practice is very debatable because of many gravitational forces from different masses?

 

[Nugatory]

So inertial movement in practice is very debatable because of many gravitational forces from different masses?

No, it's the other way around. In practice it is not in the least bit debatable because the gravitational forces are so negligible that for most practical purposes the world acts like the idealization.

 

[johnny_bohnny]

No, it's the other way around. In practice it is not in the least bit debatable because the gravitational forces are so negligible that for most practical purposes the world acts like the idealization.

So do there exist inertial frames in our universe, despite gravity? (if we look at the classical picture, without GR)

For instance is the Sun an example of an IRF?

 

[Matterwave]

So do there exist inertial frames in our universe, despite gravity?

For instance is the Sun an example of an IRF?

We've been giving you the same answer for the past several posts now...

There are APPROXIMATELY inertial reference frames all around. These frames are to a very good approximation, inertial. From a Newtonian viewpoint, the reference frame you are in right now, at your computer, is approximately inertial. The gravitational force from the Earth is being balanced by the normal force of the ground on which you stand. Your acceleration is very nearly 0.

In addition, the factors making your current frame of reference not exactly inertial, is not the gravity from all the other stars/objects in the universe, because all of these forces are being canceled out by the gravity of Earth and the normal force of the ground. The reason your frame of reference is not exactly inertial is due to the rotation of the Earth, and the rotation of the Earth about the Sun, and the rotation of the Sun about the center of the galaxy. The largest factor, the rotation of the Earth, still has negligible effects in comparison to much of your every day observations.

 

[dean barry]

Considering the classic equation :

a = ( G * ( m1 + m2 ) ) / d ²

The a refers to the total acceleration of both bodies.

The individual accelerations of m1 and m2 :

acceleration, m1 = ( m2 / ( m1 + m2 ) ) * a

acceleration, m2 = ( m1 / ( m1 + m2 ) ) * a

 

[johnny_bohnny]

We've been giving you the same answer for the past several posts now...

There are APPROXIMATELY inertial reference frames all around. These frames are to a very good approximation, inertial. From a Newtonian viewpoint, the reference frame you are in right now, at your computer, is approximately inertial. The gravitational force from the Earth is being balanced by the normal force of the ground on which you stand. Your acceleration is very nearly 0.

In addition, the factors making your current frame of reference not exactly inertial, is not the gravity from all the other stars/objects in the universe, because all of these forces are being canceled out by the gravity of Earth and the normal force of the ground. The reason your frame of reference is not exactly inertial is due to the rotation of the Earth, and the rotation of the Earth about the Sun, and the rotation of the Sun about the center of the galaxy. The largest factor, the rotation of the Earth, still has negligible effects in comparison to much of your every day observations.

Can anybody please explain the bolded part, how is this cancelling of forces achieved basically? Shouldn't any object still pull the Earth with objects that are on its surfaces because of its gravitational force, so what does cancelling out really mean?

And I've red that an apple falling to Earth still attracts Earth so that Earth moves towards the apple, why doesn't this effect get canceled out?

 

[johnny_bohnny]

Can anyone please explain the previously mentioned effect and its applications on Earth and other objects with mass, because I still haven't found a relevant answer.

 

[Matterwave]

In a Newtonian frame of reference, if you are sitting at your desk and the Earth were not rotating, you would NOT be considered to be accelerating. The force of gravity of the Earth pulls you down, the force of gravity of everything else pulls you very very little bit in other directions. The normal force exactly cancels all the left over forces (which is 99.99% going to be from the Earth).