Suppose the moon were closer to Earth. How would the force of gravity between Earth and the moon be different?
It would be greater on both bodies as gravity is inversely proportional to distance.
If the moon were closer to Earth, the force of gravity between them would be stronger. To understand this, let's recall Newton's law of universal gravitation, which states that the force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
Mathematically, the gravitational force (F) between two objects can be represented as:
F = (G * m1 * m2) / r^2
Where:
F is the force of gravity
G is the gravitational constant
m1 and m2 are the masses of the two objects
r is the distance between their centers
If the moon were closer to Earth, r would decrease. Since the distance is in the denominator and squared, a smaller distance would lead to a larger force:
F' = (G * m1 * m2) / (r')^2
As a result, F' would be greater than F. Hence, if the moon were closer to Earth, the force of gravity between them would be stronger.