I have been reading an article about a theory of gravity that involves space being curved or warped.(adsbygoogle = window.adsbygoogle || []).push({});

An example was given where a heavy weight, representing the sun, is placed in the centre of a trampoline, and a golf ball, representing the earth, is caused to circle the centre of the trampoline due to the depression caused by the heavy weight.

I have two questions I would like to ask.

1) What is the name given to the shape of the curve that is produced in

space by a mass ?

I remember studying Conic Sections when I was at school and just

as you can derive many different parabolic curves from one cone, they

are all called a parabola.

Equally, although different masses will cause different curvatures of

space, I presume that all these curves will come under just one name.

Just as I am able to understand the relationship between a parabola and

a cone, my wish is to look up the definition of this name in order to

understand what the underlying relationship of the curve is.

( I understand that space can be looked upon as being a three

dimensional surface curved through four dimensional space. This is

analogous to the two dimensional surface of the trampoline being curved

through three dimensional space. )

2) At what point, and how, does the trampoline analogy break down ?

My understanding, from the article, is that the direction that the

earth takes in space, is completely controlled by the curvature of the

space itself.

I can certainly understand that the curvature will influence the

direction the Earth takes but not control it. From the trampoline example,

there are essentially two things controlling the direction of the golf ball.

One is the curvature of the trampoline and the other ( ignoring friction )

is the force of gravity acting downwards on the ball. However, as far as I

can see, there is no equivalent in the Sun-Earth system to gravity acting

downwards on the golf ball.

If we imagine our three dimensional universe to be the three

dimensional surface of a four dimensional sphere then, to continue the

analogy with the trampoline, the force of gravity acting on the golf ball

would be equivalent to a force acting on matter towards the centre of

the four dimensional sphere. Thus, this force pulls the Earth down into

the depression caused by the Sun and the Sun is also pulled on by this

force.

The implication, from the article, is that the direction that the

earth takes in space, is completely controlled by the curvature of the

space that the earth travels through. How can this be ?

( Perhaps I should note here that I may be having difficulty with

the fact that the depression in the surface of the trampoline is negatively

curved. Certainly, if we were dealing with a positively curved surface, ie.

a sphere around the sun that the Earth travelled on, then there would be

no doubt that the Earth would be forced to orbit the Sun on a geodesic.)

I apologise about being so long winded with my questions. However, my feeling is that, if I am able to articulate where my thinking lies, then you will more easily be able to comment on my misunderstandings and point me to where I can do further reading.

I hope I have chosen the correct forum to post to and I hope my questions aren’t too basic for this forum.

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# Does the shape of the curve, that is produced in space by a mass, have a name ?

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