Yes, Newton conjectured that the same type of force, which is gravitational in nature, acts between the Earth and both the apple and the moon.

The fall of an apple near Newton made him contemplate whether the same force responsible for attracting the apple towards the Earth also influenced the motion of the moon.

Gravitational force causes celestial bodies to attract one another, resulting in phenomena such as planets orbiting around stars (like the Sun) and moons orbiting around planets.

The observation that objects dropped from a height fall towards the Earth and that planets orbit around the Sun indicated the presence of a force acting upon them.

Isaac Newton recognized that the same force, known as the gravitational force, is responsible for the motion of objects on Earth as well as the orbits of planets and moons.