The acceleration due to gravity (g) is a decreasing function of the distance (h) from the planet's center because it is inversely proportional to the square of the distance when the planet's mass is constant.
If the mass of a planet (m) is held constant, the acceleration due to gravity (g) is a decreasing function of the distance (h) from the center of the planet. According to Newton's law of universal gravitation, g is inversely proportional to the square of h. The formula for gravitational acceleration is g = GM/h², where G is the gravitational constant, M is the mass of the planet, and h is the distance from the planet's center. As h increases, h² increases much faster, causing g to decrease.
In conclusion, as the distance from the planet's center increases, g decreases, given that the mass of the planet remains constant. This relationship is fundamental to understanding the effects of gravity at various altitudes from a planetary body.