My players gave me the same question (if the ship only has 1G can we take off from larger worlds than Earth?), And this was my response:
The spacecraft's engines do not move the ship by repelling or emission of matter / energy generating a force should be balanced against the force of gravity on the planet, but by manipulating the field of bosons (gravitational field, usually). The radiation resulting from these manipulations at the subatomic level is what causes the blue glow of the "thrusters" (actually, the engine section than remains off the ship, usually aft).
Older versions of the engine (and the grav vehicle engines.) Needed a gravitational field against which "push", so his performance plummeted once out of the planet's gravity (explained quite well in " hard times ")
Modern engines "produce" a field of bosons that replaces the planet's gravitational field (or generates a new, if not exist). Therefore, the external gravity does not compute when it comes to change the motion of the ship (as long as the motors are active.)
The only question is whether there is a gravitational field strong enough to "overcome" the physical manipulation of the engines of the ship (black holes, neutron stars, low orbits around O and B type stars, etc). However, I doubt that my players want to risk his characters in such a mission, so that the explanation was enough to satisfy and continue with the game ...