The force of attraction between the earth and some object is called the weight of that object. The law of gravitation states, then, that the weight of an object is inversely proportional to the square of its distance from the center of the earth. If a person weighs 120 lb on the surface of the earth (assume this to be 3960 mi from the center), how much will he weigh 1300 mi above the surface of the earth?
To find out how much a person will weigh 1300 miles above the surface of the earth, we can use the law of gravitation. The law states that the weight of an object is inversely proportional to the square of its distance from the center of the earth.
Let's denote the weight on the surface of the earth as W₁ and the weight 1300 miles above the surface as W₂.
According to the law of gravitation:
W₁ ∝ 1/r₁² (where r₁ is the distance from the center of the earth, which is 3960 miles in this case)
And
W₂ ∝ 1/r₂² (where r₂ is the new distance from the center of the earth, which is 3960 + 1300 = 5260 miles in this case)
According to the problem, W₁ = 120 lb.
We can set up the equation to solve for W₂:
W₁/W₂ = (r₂/r₁)²
Plugging in the values:
120/W₂ = (5260/3960)²
Let's solve for W₂:
120 * (3960/5260)² = W₂
W₂ ≈ 70.97 lb
Therefore, a person will weigh approximately 70.97 pounds 1300 miles above the surface of the earth.