So now we have a three-dimensional representation of space-time.
A star in this model would put a dent in space-time. It would cause the space around itself to curve.
This curvature would affect the path of an asteroid as it approached the star. The asteroid might be deflected by the curvature, or, if it travelled close enough to the star, the curvature could capture it, causing it to orbit the star.
The asteroid would not be pulled by the star's gravity. It would just follow the path of least resistance. It would follow what it "feels" is a straight line.
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