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Offline PAOLO137

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Geodesics around a planet
« on: 23/09/2011 14:18:18 »
I tried to figure out the shape of geodesics around a heavy round body far away from any other matter  (say the earth with some approximation). Since I keep the famous apple in my hand and then let it free it will follow a straight line towards the center of the planet. Does it mean that the apple is following a geodesic? Has anybody found a simple way of explaining how to figure out space curvature to the layman?

For example, the idea of explaining Minkowski space letting one space dimension out, and using the well
known double cone picture is fantastic. Nothing similar can be envisaged for space curvature?Thank you,
Paolo de Magistris, Rome.


 

Offline MikeS

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Geodesics around a planet
« Reply #1 on: 24/09/2011 09:12:24 »
I tried to figure out the shape of geodesics around a heavy round body far away from any other matter  (say the earth with some approximation). Since I keep the famous apple in my hand and then let it free it will follow a straight line towards the center of the planet. Does it mean that the apple is following a geodesic? Has anybody found a simple way of explaining how to figure out space curvature to the layman?

For example, the idea of explaining Minkowski space letting one space dimension out, and using the well
known double cone picture is fantastic. Nothing similar can be envisaged for space curvature?Thank you,
Paolo de Magistris, Rome.

Paolo
Yes, the apple is following a geodesic in space-time even if that geodesic is a straight line.
To the best of my knowledge the answer is no.
But I have a way of envisioning space time curvature that works for me and it's as follows:-
All mass has an associated gravitational field.
Gravity is equivalent to acceleration.
Gravity is mass accelerating through time (space-time).
The Earth (mass) accelerates through time (space-time) because time is being continuously dilated the closer you get to the surface.

This is not a mainstream view but it works for me.
Imagine the Earth being surrounded by concentric shells (like Russian dolls) of time.  These shells are continually collapsing onto the Earth, one after another.  This is the passage of time (dimension of time) in terms of the three spacial dimensions.  It's not strictly correct as time is not a separate dimension but is 'mixed' up with the other dimensions. Each 'shell' of time is a hollow sphere and around its equator (diameter), at right angles to its diameter parallel lines (like lines of longitude) eventually cross at two places (the imaginary poles).  Each sphere has an infinite number of equators all of which have these 'lines of longitude'.  If we think of time as being quantatized then we have a finite but very large number of shells or spheres.  The equators of which are all randomly orientated.  The crossing of parallel lines represents curved space-time.  As the 'shells' collapse, so this represents both the passage of time and gravity.  This has actually taken far longer to explain than to visualize, just think of collapsing concentric shells and a ball of string.

I hope this has helped.
« Last Edit: 24/09/2011 12:51:52 by MikeS »
 

Offline jartza

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Geodesics around a planet
« Reply #2 on: 25/09/2011 02:20:38 »
Here are 3 planets, lined up on a straight line, in flat (not curved) space:

O   O   O

On the leftmost planet stands a person, with a laser gun, his task is to shoot a laser beam to the rightmost planet. As the planets have quite strong gravity fields, the shooter must point the gun a little bit upwards, then the beam takes a curved path to he rightmost planet.



Now, let's pull a wire from the leftmost planet to the rightmost planet, like this:
And let's make it an extremely tight wire.
__________
O   O    O



A person near the wire will say that the wire sags just a little bit, because of gravity.

A person observing the wire from far away position says that the wire arches upwards, away from the planets. (same kind of arch as the path of the laser beam)


So, watching the wire or the beam a distant observer can perhaps get some kind of idea how space is curved near the planets.

 

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Geodesics around a planet
« Reply #2 on: 25/09/2011 02:20:38 »

 

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