1. Understand the Concepts
* Orbital Period (T): The time it takes for a satellite to complete one full orbit around the Earth.
* Orbital Radius (r): The distance from the center of the Earth to the satellite.
* Gravitational Acceleration (g): The acceleration due to gravity at the satellite's altitude.
* Centripetal Force: The force that keeps the satellite moving in a circular path.
2. Formulas
* Orbital Period (T): T = 2π√(r³/GM)
* Where:
* G is the gravitational constant (6.674 × 10⁻¹¹ m³/kg s²)
* M is the mass of the Earth (5.972 × 10²⁴ kg)
* Orbital Velocity (v): v = √(GM/r)
3. Calculations
* Calculate the orbital radius (r):
* The radius of the Earth is approximately 6371 km.
* r = 6371 km + 400 km = 6771 km = 6.771 × 10⁶ m
* Calculate the orbital velocity (v):
* v = √(GM/r)
* v = √((6.674 × 10⁻¹¹ m³/kg s²)(5.972 × 10²⁴ kg) / (6.771 × 10⁶ m))
* v ≈ 7668 m/s
4. Convert to km/h (optional):
* v ≈ 7668 m/s * (3600 s/h) / (1000 m/km) ≈ 27605 km/h
Therefore, the speed of the satellite is approximately 7668 m/s or 27605 km/h.
