Understanding the Concepts
* Newton's Law of Universal Gravitation: The force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
* Gravitational Acceleration: The acceleration experienced by an object due to the gravitational force of a larger body.
Calculations
1. Earth's Radius: The Earth's average radius is approximately 6,371 kilometers.
2. Distance from Earth's Center: At 200 km altitude, the distance from the Earth's center is: 6371 km + 200 km = 6571 km
3. Gravitational Acceleration Formula:
* g = (G * M) / r²
* g = gravitational acceleration
* G = gravitational constant (6.674 × 10⁻¹¹ N⋅m²/kg²)
* M = mass of Earth (5.972 × 10²⁴ kg)
* r = distance from the Earth's center (6571 km = 6.571 × 10⁶ m)
4. Substitute and Calculate:
* g = (6.674 × 10⁻¹¹ N⋅m²/kg² * 5.972 × 10²⁴ kg) / (6.571 × 10⁶ m)²
* g ≈ 9.08 m/s²
Result: The gravitational acceleration at an altitude of 200 km is approximately 9.08 m/s², slightly less than the standard value of 9.81 m/s² at the Earth's surface.
Important Note: This calculation assumes a spherical Earth and doesn't consider the Earth's non-uniform mass distribution or other factors like the rotation of the Earth.
