To find the new weight of the object, we'll use the Law of Gravitation. This equation states that the force of gravity (F) between two objects is equal to the gravitational constant (G) times the mass of the first object (m1) and the mass of the second object (m2), divided by the distance between the centers of the two objects (r) squared. In mathematical terms:
F = G * (m1 * m2) / r^2
However, we're interested in the weight of the object. Weight is the force an object experiences due to gravity. Therefore, if we know the weight of the object at the Earth's surface, we can relate this to the object's weight at a new height.
Let's denote the weight of the object at the Earth's surface as W. Then the weight at a height h above the Earth's surface is W_new. So:
W / W_new = (R / (R + h))^2
The radius of the Earth (R) is 6.371 * 10^6 m, the weight at Earth's surface (W) is 535 N, and the height above the Earth's surface (h) is 3.20 * R. Substituting these values into the equation gives us:
W_new = W * (R / (R + h))^2
By plugging the known values into the equation, we find that the weight of the object at a height of 3.20R above the Earth's surface is approximately 30.33 N.