what would it weigh if it were 3970 miles from the center of the earth?

Question

the weight of an object above the surface of the earth varies in veries with the square of its distance from the center of the earth. if a body weighs 50 pounds when it is 3960 miles from the center of the earth, what would it weigh if it were 3970 miles from the center of the earth?

Answer 1

The weight is in inverse relation with the square of its distance from the center of the earth, so the product of weight (W) and square of its distance from the center of the earth (r²) is constant.

W₁r₁² = W₂r₂²

W₂ = (r₁ / r₂)² W₁.= (3960 / 3970)² (50) pounds = 49.75 pounds