What would happen to the moon the density of earth was suddenly halved?

physics.md

radius r =
       384000 km
       384000000 m

period p =
       27.3 days
       2358720 s

moon's speed =
       d / t
       2πr / p
       2π 384000000 / 2358720
       1023 m/s



fucked-up-earth's mass M =
       5.972 * 10^24 kg * 0.5
       2.986 * 10^24 kg

gravitational constant G =
       6.67 * 10^−11 m^3kg^−1s^−2

escape velocity of fucked-up-earth:
       sqrt(2 * G * M / r)
       sqrt(2 * 6.67*10^−11 * 2.986 * 10^24 / 384000000)
       1019 m/s

1023 > 1019
       The moon would just escape earth's gravity and drift away slowly, disregarding other factors.
       Would be flung far away from eath at a low speed, meaning that Sun's gravity may become significant.
       The effects then would depend on which way it was flung.