Question

How far from the surface of Earth is the magnitude of Earth's gravitational field equal to 7.86 N/kg?

The mass of Earth is 5.97 x 1024 kg and the mean radius of Earth is 6.37 x 106 m.

Answer 1

7.48 x 10⁵ m

Step-by-step explanation:

g = 7.86 N/kg

M = 5.97 x 10²⁴ kg, R = 6.37 x 10⁶ m.

Find height h

g = GM/(R + h)²

(R + h)² = GM/g = 6.67 x 10⁺¹¹ x 5.97 x 10²⁴ /7.86 = 5.066 x 10¹³

R + h = 7.12 x 10⁶ m

so

h = 7.12 x 10⁶ - 6.37 x 10⁶ = 7.48 x 10⁵ m