Question

10. The Earth's radius is about 6370 km. An object that has a mass of 20 kg is taken to a

height of 160 km above the Earth's surface. How much does the object weigh at this
height?

Answer 1

Weight:

P =m·g₁ = 20·9.55 = 191 H

Step-by-step explanation:

Given:

R = 6 370 км = 6 370·10³ m

m = 20 kg

h = 160 km = 160·10³ m

g = 9.8 m/s²

____________________

P - ?

Acceleration of free fall at the Earth's surface:

g = G*M / R² (1)

Acceleration of free fall at height h:

g₁ = G*M / (R + h) ² (2)

Divide (1) by (2):

g / g₁ = ((R + h) / R)²

g / g₁ = ( 1 + h / R)² = ( 1 + 160 / 6 370)² ≈ 1.026

g₁ = g / 1.026 = 9.8 / 1.026 ≈ 9.55 m/s²

Weight:

P =m·g₁ = 20·9.55 = 191 H