Final answer:
The variation of the intensity of the gravitational field of the Moon follows an inverse square law with distance from the center of the Moon. The formula representing this variation is given as 1/r² (option a), which is a fundamental concept derived from Newton's Law of Universal Gravitation.
Step-by-step explanation:
The question concerns the variation of the intensity of the gravitational field of the Moon as a function of distance from its center. To address this, we reflect on Newton's Law of Universal Gravitation, which implies that the gravitational force (and thus the field intensity) between two masses diminishes with the square of the distance between their centers. Therefore, the intensity of the gravitational field varies inversely with the square of the distance from the center of the mass creating the field.
In the case of the Moon, which has a distinct radius (R), if we consider a point at a distance r from the center of the Moon (where r could be within or outside the Moon's radius), the formula for the gravitational field intensity would follow an inverse square law, particularly represented by 1/r² (option a) when we're considering points outside the lunar surface. This is due to the geometric nature of how the gravitational force spreads over a sphere's surface, leading to the conclusion that the correct option answer is option (a) 1/r².
It is essential to note that this relationship assumes a point mass or a spherical mass distribution, as is the case with celestial bodies like the Moon. The formula conflates to the well-known expression for gravitational field strength (g = G*M/r²), where G is the gravitational constant, and M is the mass of the object generating the field, which in this case would be the Moon.