Final answer:
Newton knew an unbalanced force was acting on the moon and a falling apple because he realized that the gravitational force that caused an apple to fall also extended to celestial bodies, keeping the moon in orbit. This universal law of gravitation simplified and unified the understanding of forces in nature and was central to revolutionary developments in physics.
Step-by-step explanation:
Sir Isaac Newton knew an unbalanced force was acting on both the moon and a falling apple because he recognized that the forces causing both situations were of a similar nature. Newton observed that if gravitational force caused an apple to fall from a tree, it must also extend farther than previously thought, possibly even reaching astronomical objects like the moon. This led to his understanding that the same universal law of gravitation that causes objects to fall on Earth also holds the moon in orbit. Newton's calculations showed that the acceleration due to gravity on Earth was consistent with the centripetal acceleration needed to keep the moon in orbit around the Earth. In his time, gravity was considered to be a force that only applied to objects on Earth. However, Newton's hypothesis suggested that gravity extended much further, influencing the movement of celestial bodies like the moon and the planets. This concept was groundbreaking and provided clarity to the nature of forces acting on the moon and falling objects on Earth. The gravitational force is always attractive, and it depends only on the masses involved and the distance between them, which helps to support the idea of underlying simplicity and unity in nature.