How does gravity decreases with increase in altitude?

Answer:

Gravitational forces are central forces, which implies that the gravitational force between any two particles is along the line connecting their mass centres. Also, since the sphere’s surface increases with r².

Where r is the radius.

The Gravitational field must be uniformly distributed over the sphere’s surface. We can assume that the gravitational field is proportional to 1/R².

Example

Consider the radius of the earth at the equator to be 6400 km. If an aeroplane flies at a distance of 40 km above the earth’s surface then the gravity, g₂ is calculated by equating the ratio of acceleration due to gravity, g₁ and g₂ to square of ratio of the radius. This gives g₂ as 9.67 m/s².
Therefore, it can be said that the gravitational force decreases by 1.2% for an aeroplane which is flying at 40 km distance.