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    1.1    Gravity is needed to explain gravity

The image of Figure 1 is used to represent curved space, which is a two dimensional representation of 3-D space.  This is perfectly acceptable, since most gravitational motion happens in 2-D.

curved space time
Figure 1  Curved Spacetime

The problem with this image is that to represent motion we need to take into account our daily experience with gravity on Earth.  In effect, gravitation is two effects:  Warping of space-time and pulling object in.   Figure 2 shows what motion looks like in curved space with a downward gravitational pull.


Motion in curved space with gravitational downward pull

Figure 2:  Motion in curved space with gravitational downward pull

In essence, gravitation pulls objects moving in curved space in, towards the massive object that creates the ‘warping of spacetime’ (otherwise called gravitational field).  When we do not consider the inward gravitational pull of the motion of an object in curved space, the motion looks as shown in Figure 3.  The object’s motion is not a straight line, but the curvature of the path is not what we are used to seeing in a gravitational field.

 

Motion in curved space without gravity’s inwards pull

Figure 3:  Motion in curved space without gravity’s inwards pull

This is also illustrated in Figure 4, where a blue object is at rest in curved space-time.  This object starts to move towards the massive object creating the warping of space because, from our daily experience, Earth’s gravity pulls things down.  Because the blue object is on a slope on curved space, it will move down towards the hole where the massive object is.

 

Falling object in curved space

Figure 4:  Object at rest in curved space


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