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 (g): This is the acceleration experienced by an object due to the gravitational pull of a massive body like the Earth.
Formula
The formula for calculating acceleration due to gravity is:
g = (G * M) / r²
Where:
* g = acceleration due to gravity (m/s²)
* G = gravitational constant (6.674 × 10⁻¹¹ N m²/kg²)
* M = mass of the Earth (5.972 × 10²⁴ kg)
* r = distance from the center of the Earth (9,000,000 meters)
Calculation
1. Plug in the values:
g = (6.674 × 10⁻¹¹ N m²/kg² * 5.972 × 10²⁴ kg) / (9,000,000 m)²
2. Calculate:
g ≈ 0.54 m/s²
Result
The acceleration due to gravity at a distance of 9,000,000 meters from the center of the Earth is approximately 0.54 m/s². This is significantly less than the acceleration due to gravity at the Earth's surface (approximately 9.81 m/s²).
