Isaac Newton observed the fall of an apple in 1666 and deduced that the same force pulling the apple to Earth was the same that kept the moon in orbit. He did not publish his theory until 1687.
Newton was primarily a mathematician, and he used calculations to determine if his prediction was correct. Correspondences with leading scientists of his day led him to calculate the shape of planetary orbits. However, Isaac Newton was a very private man, and he lived almost as a recluse. He did not publish until he was urged and encouraged to by a fellow scientist named Edmond Halley, who was impressed by Newton's mathematical insights.