Verified answer

You need to assume the moons mass is insubstantial and assume G as in

a = GM/r^2

G= 6.67300 × 10-11 m3 kg-1 s-2

v = r *2 pi / 27.3 days

= 1023 m/s

a=v^2/r = GM/r^2

M= v^2r/G

M= 1023^2 * 3.84x10^8 /6.67300 × 10^-11

M= 4.84 x10^24 kg

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