Why is the weight of an object on the moon 1/6 th its weight on the earth?

Let ME be the mass of the Earth and m be an object on the surface of the Earth. Let RE be the radius of the Earth. According to the universal law of gravitation, weight WE of the object on the surface of the Earth is given by, 𝑊𝐸=𝐺𝑀ᴇ𝑚/𝑅ᴇ²
Let MM and RM be the mass and radius of the moon. Then, according to the universal law of gravitation, weight WM of the object on the surface of the moon is given by:
𝑊𝑀=𝐺𝑀𝑀𝑚/𝑅𝑀²
Now,
⇒𝑊𝑀𝑊𝐸=𝑀𝑀𝑅𝐸 2𝑀𝐸𝑅𝑀 2
Where,
𝑀𝐸=5.98×1024 𝑘𝑔
𝑀𝑀=7.36×1022 𝑘𝑔
𝑅𝐸=6.4×106 𝑚
𝑅𝑀=1.74×106 𝑚
⇒𝑊𝑀/𝑊𝐸=7.36×10²²×(6.4×10⁶) ² / 5.98×10²⁴×(1.74×10⁶) ²=0.165≈1/6
Therefore, weight of an object on the moon is 1/6 of its weight on the Earth.

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