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Author Topic: does the earth bend up to meet a falling object or does object press it down?  (Read 4558 times)

Offline Alinta

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Hi all,

Ok another beginner question.

I have read somewhere that if an object falls to the ground (let's just say on a small scale - a human falling over), the earth (in a very very small way) bends up to meet it. I think I read that this was an affect of gravity. Though I've also read that sound waves are caused by the object bending the earth back down in a small way, causing a compacting that creates a displacement wave (and another kind of wave that I forget).

So does the earth end up bending up to meet the object, then bending down once the object collides? And is this bending up something that is recordable (albeit in a very small way) or is it a way to explain space-time curvature?

Or does this not count for the small scale example?

Cheers
Alinta


 

Offline evan_au

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If we take the example of a skydiver jumping out of an aeroplane:
  • The skydiver accelerates down towards the center of the Earth, due to the force of gravity
  • According to Newton's Laws of Motion, the Earth feels an equal and opposite force attracting it upwards towards the skydiver
  • Newton worked out that F=ma, where:
    • F=Force (ironically measured in Newtons, in the metric system)
    • m=mass of the object (either the mass of the skydiver or the mass of the Earth)
    • a=acceleration of the object (either the skydiver or the Earth)
  • Since the Earth's mass is immensely more than the skydiver, the acceleration of the Earth is miniscule compared to the skydiver, and so we usually just ignore it.
An Example (If I've done the calculations right):
  • Lets say the skydiver weighs 100kg (with parachute), and the Earth has a mass of 6 1024 kg
  • The Force between them is about 1000 Newtons
  • The skydiver will fall 1km in about 14s (in a vacuum)
  • In this same time, the Earth would move up to meet him by 1.6x10-6 m, or a couple of wavelengths of visible light.
  • ...of course, the parachute won't be of much use to him in a vacuum.
So the whole Earth does rise up to meet you, but not by an amount you could easily measure...
« Last Edit: 07/03/2013 16:44:15 by evan_au »
 

Offline evan_au

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PS: The above calculations assume that the Earth is a completely rigid object.

In fact, the Earth is slightly "stretchy" (if you could call rock "stretchy"), and so the area immediately under the skydiver will feel a stronger gravitational attraction to the skydiver than the far side of the Earth.

This area under the skydiver will bend up to meet him - but again, this upwards deformation will be very tiny, and will be immediately reversed when the skydiver hits the ground.

This difference in attraction between different parts of the Earth is called a "tide", but it usually takes something the size of the Sun or Moon to produce a noticeable tide.
 

Offline syhprum

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I have tried to explain to my teachers that the 1 Kg cannon ball falls from the tower slightly less fast than the 100 Kg because once you have taken the 100 kg with you up in the tower the mass attracting to the Earth is slightly reduced but they take a lot of convincing.
 

Offline Pmb

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The best way to describe this is by the equivalence principle which states that a uniform gravitational field is equivalent to a uniformly accelerating frame of reference. That means that there exist no experiment that can distinguish the two. If you were at rest in an inerial frame and a platform was accelerating up from below your feet to meet you then you'd be unable to distinguish it from actually falling in a gravitational field to the stationary earth's surface. So it's neither correct nor incorrect to say that one view is right and the other wrong since there's no experiment which can distinguish between the two situations. Either frame of reference is a valid frame. If you're at rest on the earth then the falling body rushes down to meet the earth. If you're in the frame falling in the earth's gravitational field then the earth's surface is rushing up to meet you.

So when you ask these questions you need to specify with which frame of reference you're referring to.
 

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