Can Earth Rise Upwards to Touch an Apple?

[Nemika]

This is a really silly question though...

Newton said that the apple fell on the ground due to gravity but can we say that the Earth rose upwards to touch the apple. Is it possible to prove this by any physics law?

Thnx for any reply.

 

[nasu]

Yes, the Earth is also attracted by the apple and moves "up" a little.
There is nothing to prove, really.

 

[ZapperZ]

This is a really silly question though...

Newton said that the apple fell on the ground due to gravity but can we say that the Earth rose upwards to touch the apple. Is it possible to prove this by any physics law?

Just look at the equation for the universal law of gravity that Newton formulated! The equation is symmetric if you interchange the masses.

If the apple is the same size and mass as the earth, and you let both of them go, they will both smash into each other at the half-way point between them.

Zz.

 

[QuantumPion]

This is a really silly question though...

Newton said that the apple fell on the ground due to gravity but can we say that the Earth rose upwards to touch the apple. Is it possible to prove this by any physics law?

Thnx for any reply.

I'm not an expert in this area and might be wrong, but I thought that this is sort of the basis for General Relativity - the apple in freefall is inertial, and the Earth, due to the curvature of space-time, is accelerating upward to meet it, or something like that.

 

[Nemika]

Yes, the Earth is also attracted by the apple and moves "up" a little.

But how does this happen?
How can a tiny apple generate enough force to move "up" earth even a little?

 

[nasu]

The forces between the two are the same. The force attracting the apple towards the Erath has the same magnitude as the force attracting the Earth towards the apple.
The magnitude depends on both masses.
And there is no such thing as "enough force". Any force will produce some acceleration. If the force is small and the mass is huge, the acceleration is small too. Maybe to small to observe or measure.

 

[Drakkith]

But how does this happen?
How can a tiny apple generate enough force to move "up" earth even a little?

Note that the equation for acceleration is A = F/M. Any amount of force will cause at least a small amount of acceleration, no matter what the mass of the object being accelerated is.

 

[anorlunda]

But how does this happen?
How can a tiny apple generate enough force to move "up" earth even a little?

It depends on what you mean by little. The mass of Earth is about $$6 X 10^{24}$$ kg. The mass of an apple is about 0.1 kg. Therefore, for every one meter the apple falls, the Earth will rise about 0.000000000000000000000000016 meters. That is very small indeed but more than zero.

 

[Nemika]

Thnx for the replies and now I know that the Earth does move a little bit.

But I meant to say that is it totally possible that the apple was completely stationary and it was the Earth which accelerated towards it and finally collided with it (though the impact on Earth would be very less).

Because I think according to general relativity, from the apple's frame of reference it is stationary and the Earth is accelerating towards it.

Is this statement correct? And if yes, please can you explain how this is possible?

 

[A.T.]

Because I think according to general relativity, from the apple's frame of reference it is stationary and the Earth is accelerating towards it.

Is this statement correct? And if yes, please can you explain how this is possible?

The force for the proper acceleration of the Earth's surface is supplied from below, by the layers of Earth underneath, not by the apple.

You are confusing two different models of gravity here? This might help:

 

[RMM]

It seems to me, that your question is headed for the equality of inertial and gravitational mass.
In par. 20 of the general Relativity Theory Einstein describes the identity of slow and heavy mass as an argument for the general principle. Einstein describes thereby an idea that you can imagine yourself:
"We must note carefully that the possibility of this mode of interpretation rests on the fundamental property of the gravitational field of giving all bodies the same acceleration, or, what comes to the same thing, on the law of the equality of inertial and gravitational mass. If this natural law did not exist, the man in the accelerated chest would not be able to interpret the behavior of the bodies around him on the supposition of a gravitational field, and he would not be justified on the grounds of experience in supposing his reference-body to be “at rest.”

Nobody can explain HOW this equality would found in real world. There are a few theories that support the idea that all matter expands and that there for the expanding Earth causes acceleration in a way that is explained in this drawing:

 

[A.T.]

There are a few theories that support the idea that all matter expands and that there for the expanding Earth causes acceleration in a way that is explained in this drawing:

I have never seen any scientifically accepted theories based on the expansion that you mention. Usually it's just an misunderstanding of General Relativity.

In GR's curved space-time, proper acceleration of the surface away from the center doesn't imply expansion of the Earth. It just means that the surface doesn't have a geodesic worldline in the curved space-time. The world line bends upwards, just like the one of the green apple in the video above, but the distance to the center (Earth radius) is constant.

 

[RMM]

It seems to me that in the animated video at 1.13 min. the worldline is expanding (at least the cilinder changes to an expanding model). Is that correct? If yes:What does this expanding mean? Is this the bending space? What does it really mean?

 

[A.T.]

It seems to me that in the animated video at 1.13 min. the worldline is expanding (at least the cilinder changes to an expanding model). Is that correct?

Nothing changes about the model or the intrinsic space-time geometry at 1:13 min. Rolling the diagram together is just an alternative way to visualize it.

What does this expanding mean?

Not sure what you mean by "expanding". That the cone is wider at the bottom? The distances along the time dimension depend on the radial spatial position. This corresponds to gravitational time dilatation: Clocks lower in the gravitational field tick slower. See the illustrations here:

http://www.physics.ucla.edu/demoweb..._and_general_relativity/curved_spacetime.html

 

[RMM]

Wow. Thank you for your persistence.

 

[Vanadium 50]

. There are a few theories that support the idea that all matter expands and that there for the expanding Earth causes acceleration in a way that is explained in this drawing:

These theories are not predicted by scientists - they are produced by crackpots and the occasional comic book artists, I am afraid. Apart from the problem of why the sun hasn't expanded into the Earth by now, you have the problem of orbits. This model says orbits are impossible.