Student or Learner
What does this idiom mean "Like booster falling from a rocket"
In this instance the mentioned in your poster sentence is a quite ordinary expression. It is not an idiom. The word "booster" have a few meaning, as 1) device for increasing power or effectiveness; 2) a radio-frequency amplifier, but in your case, you have to use the mentioned below meaning:
the primary stage of a multistage rocket that provides the main thrust for launch, liftoff, and initial flight.
an auxiliary or initial propulsion system that travels with a missile or aircraft and that may or may not separate from the parent craft when its impulse has been delivered. A booster system may contain, or consist of, one or more units.
Further you might go on with your work alone.