Curved space time is not the same as centripetal force. However, one can use centripetal force as an easier concept to understand planetary motions. Sorry if I didn't make that clear. Centripetal force is a true force. You need a force to accelerate a mass. However, gravity is an imaginary 'force'.
The planets are moving in a straight line in curved space-time.
We could also explain it with conservation of angular momentum and/or Keplar's Laws.
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