Final answer:
The center of the Moon is approximately 0.00257 AU from the Earth. An Astronomical Unit is the average Earth-Sun distance, and by converting the Earth-Moon distance into AU, we find that the Moon is about 0.00256 AU away from Earth's center.
Step-by-step explanation:
The center of the Moon is approximately 0.00257 AU from the center of the Earth. One Astronomical Unit (AU) is the average distance between Earth and the Sun, which is about 1.5 × 10⁸ kilometers (roughly 93 million miles). Considering that the average distance from the Earth to the Moon is about 384,400 kilometers, we can calculate the distance in astronomical units by dividing the Earth-Moon distance by the Earth-Sun distance.
To convert the Earth-Moon distance into AU, we use the following calculation:
- Determine the distance from Earth to the Moon: approximately 384,400 kilometers.
- Determine the distance represented by 1 AU: approximately 1.5 × 10⁸ kilometers.
- Divide the Earth-Moon distance by the distance of 1 AU:
384,400 km / 1.5 × 10⁸ km = 0.00256 AU (rounded to five decimal places).
Therefore, the center of the Moon is 0.00256 AU away from the center of the Earth. This calculation also takes into consideration the fact that the Earth-Moon distance is an average, as it can vary due to the elliptical shape of the Moon's orbit around the Earth.