The Enterprise is 267,000km from Earth when she drops out of warp, the moon is 384,405km away. The Enterprise is 117,405km closer to the Earth. The pull is stronger.
Don't claim shit science when you didn't even take 10 seconds to find that out.
I took less than 10 seconds. I did the calculations. It's not "shit science".
I already said the net field is directed toward the Earth. But it is so small that it is effectively 0.
Field from Earth:
F_e = GM_e/r_e^2 = (6.67e-11)(6e24)/(272e6)^2 = 0.005 N/kg
Field from the Moon:
F_m = -G M_m /r_m^2 - (6.67e-11)(120e8)^2 = -0.0003 N/kg
Net field: basically 0.005 N/kg toward Earth.
So, 0.005 N/kg is non-zero, but not significant.
Never accuse me of "shit science," Herbert.