Understanding the Concepts
* Newton's Law of Universal Gravitation: This law states that every particle in the Universe attracts every other particle with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
* Acceleration due to Gravity: The acceleration experienced by an object due to the gravitational pull of a planet. It's denoted by 'g'.
Formula
The acceleration due to gravity (g) at a height 'h' above the Earth's surface is given by:
```
g' = g * (R / (R + h))^2
```
Where:
* g' = acceleration due to gravity at height h
* g = acceleration due to gravity at the Earth's surface (approximately 9.8 m/s²)
* R = radius of the Earth (approximately 6400 km)
* h = height above the Earth's surface
Calculations
1. Convert height to meters: h = 6400 km = 6400000 m
2. Plug in the values:
g' = 9.8 * (6400000 / (6400000 + 6400000))^2
g' = 9.8 * (1/2)^2
g' = 9.8 * 0.25
g' = 2.45 m/s²
Therefore, the acceleration due to gravity at a height of 6400 km above the Earth's surface is approximately 2.45 m/s².
Important Note: This calculation assumes a uniform spherical Earth. In reality, the Earth's gravitational field is not perfectly uniform, and the actual acceleration due to gravity can vary slightly depending on location.
