Answer:
g = 0.171 m/s²
v = 2870 m/s
Explanation:
Acceleration due to gravity is:
g = GM / R²
where G is the universal gravitational constant,
M is the mass of the Earth,
and R is the distance from the Earth's center.
Given:
G = 6.67×10⁻¹¹ Nm²/kg²
M = 5.98×10²⁴ kg
R = 4.2×10⁷ + 6.357×10⁶ = 4.84×10⁷ m
Find: g
g = (6.67×10⁻¹¹ Nm²/kg²) (5.98×10²⁴ kg) / (4.84×10⁷ m)²
g = 0.171 m/s²
The centripetal acceleration is equal to the acceleration due to gravity.
v² / R = g
v = √(gR)
v = √(0.171 m/s² × 4.84×10⁷ m)
v = 2870 m/s
