* Newton's Law of Universal Gravitation: The force of gravity between two objects is proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
* Distance from Earth's Center: As an object moves further away from the Earth's surface, the distance between its center and the Earth's center increases.
* Decreased Force: This increase in distance results in a weaker gravitational force, leading to a decrease in acceleration due to gravity.
Mathematical Expression:
The acceleration due to gravity at a height 'h' above the Earth's surface is given by:
```
g' = g * (R / (R + h))^2
```
where:
* g' is the acceleration due to gravity at height 'h'
* g is the acceleration due to gravity at the Earth's surface (approximately 9.81 m/s²)
* R is the radius of the Earth (approximately 6,371 km)
* h is the height above the Earth's surface
Key Points:
* The decrease in 'g' is nonlinear, meaning it doesn't decrease at a constant rate.
* At heights much smaller than the Earth's radius, the change in 'g' is negligible. However, for significant heights like those of satellites or spacecraft, the decrease becomes noticeable.
* The formula above assumes a spherical Earth with uniform density, which is a simplification. In reality, the Earth's density varies, and the actual value of 'g' can be slightly different.
Example:
At a height of 100 km above the Earth's surface, the acceleration due to gravity would be approximately 9.53 m/s², about 3% less than the value at the Earth's surface.
