By newton third law of motion, we know that if a rocket ship pushes down on the ground, the ground will push back up on the rocket ship with twice as much force

We don't know that at all. The 3rd law says that the REaction is opposite and EQUAL to the action. We don't know where that "twice as much" comes from.

By Newton's third law of motion, we know that if a rocket ship pushes down on the ground, the ground will push back up on the rocket ship with twice as much force ... Suppose an object has 20 N of tension force pulling it upward and 40 N of gravitational force pulling it downward.