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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.

Respuesta :

Answer:

7.48 x 10⁵ m

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