Variation of g with altitude:

The value of g is inversely proportional to the square of the radius of the Earth 

$\left(g \: a\frac{1}{R^{2}}\right)$

But it does not remain constant. It decreases with altitude. Altitude is the height of an object or place above sea level. The value of g is greater at sea level than at the hills.

 

Variation of g with altitude:

Equation g = G $\: \frac{me}{R^{2}}$ shows that the value of acceleration due to gravity g depends on the radius of the Earth at its surface.The value of g is inversely proportional to the square of the radius of the Earth $\left(g \: a\frac{1}{R^{2}}\right)$. But it does not remain constant. It decreases with altitude. Altitude is the height of an object or place above sea level. The value of g is greater at sea level than at the hills.

 

Explanation:

Consider a body of mass m at an altitude h. The distance of the body from the center of the Earth becomes R+h. Therefore, using equation g = G $\: \frac{me}{R^{2}}$ ………. (i)

 

 

Note:

According to the above equation, we come to know that at a height equal to one Earth radius above the surface of the Earth. g becomes one-fourth (1/4) of its value on the Earth.

Similarly, at a distance of two Earth's radii above the Earth’s surface, the value of g becomes one-ninth (1/9) of its value on the Earth.