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Physics Help!

Einstein theorized that the Earth traveled in a straight line around the sun due to the indentation of the fabric of space-time around the sun because of it's sheer mass. Does this mean that if I tried to run in a straight line past an extremely massive object (a gravitational singularity, lets say), I would actually run around it rather than past it?
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Just quoting in Puddles the Monkey so she can move the thread if needed :h:

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