May I ask, why is the g-value being used related to the earth and not the moon?
It's an artifact of the utterly obsolete English system of units, and shows why using them ought to be made a capital crime.
Although rocket specific impulse is typically quoted in seconds, this involves implicitly canceling pounds-force (lbf) with pounds-mass (lbm).
An I
sp of 300 seconds means that the engine can produce 1 pound-force of thrust from 1 pound-mass of propellant for 300 seconds. But a pound of force and a pound of mass are two completely different things. Only in standard earth gravity does a mass of 1 pound-mass exert a downward force of 1 pound-force, and these units remain the same regardless of the local gravitational acceleration and the actual weight in pounds-force of 1 pound-mass.
The
correct measure of rocket engine performance is effective exhaust velocity, which is what you get when you don't incorrectly cancel units. In SI, the units of I
sp are simply m/sec, which makes far more intuitive sense anyway.