The mass of the Earth is about 81 times greater than the mass of the Moon. Due to this large mass difference, the acceleration of the Earth towards the Moon is extremely small compared to the acceleration of the Moon towards the Earth. This small acceleration of the Earth is not easily noticeable.
Given the significant mass difference between the Earth and the Moon, why don’t we observe the Earth moving towards the Moon in a noticeable way?
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Despite the mass difference, Earth and Moon’s mutual gravitational pull results in their orbit around a common center of mass, the barycenter, located inside Earth. This balanced orbital motion prevents noticeable movement towards each other, maintaining a stable distance and causing only minor, observable effects like tides and slight shifts.