In Newton's time, calculating the distance of the moon involved using Kepler's third law of planetary motion. This law states that the square of a planet's orbital period is directly proportional to the cube of its semi-major axis. By measuring the moon's orbital period and using this law, Newton was able to determine its distance from the Earth.
Newton used a combination of mathematical equations and observations to calculate the distance of the moon. He relied on Johannes Kepler's laws of planetary motion and also used data from previous astronomers, such as Tycho Brahe.
Newton's calculation of the distance of the moon was remarkably accurate considering the limitations of the tools and data available to him at the time. He estimated the moon's distance to be around 60 Earth radii, which is only about 1% off from the actual value of 60.3 Earth radii.
Newton's calculation of the distance of the moon was a crucial step in understanding the structure and dynamics of our solar system. By accurately determining the moon's distance, he was able to confirm and refine Kepler's laws of planetary motion, which laid the foundation for his theory of universal gravitation.
Since Newton's time, advancements in technology and space exploration have allowed for more precise measurements of the moon's distance. We now know that the moon's distance from the Earth varies due to its elliptical orbit, and its average distance is about 238,855 miles. Additionally, we have more accurate and comprehensive models of the moon's orbit and its interactions with other celestial bodies in our solar system.