Explanation:
Centripetal acceleration = acceleration due to gravity
v² / r = GM / r²
Solving for velocity:
v = √(GM / r)
Given:
G = 6.67×10⁻¹¹ m³/kg/s²
M = 5.97×10²⁴ kg
r = 6.38×10⁸ m + 1.44×10⁹ m = 2.078×10⁹ m
v = √(6.67×10⁻¹¹ × 5.97×10²⁴ / 2.078×10⁹)
v = 438 m/s
Period is the time to travel one circumference:
T = 2πr / v
T = 2π (2.078×10⁹) / 438
T = 2.98×10⁷ s
T = 8290 hr
T = 345 days
