Calculating Weight at a Height Above Earth's Surface

To calculate the weight of a body at a height above Earth's surface, we need to consider the gravitational force acting on the body. The gravitational force is given by the formula:

F = G * (m1 * m2) / r^2

Where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the two bodies, and r is the distance between the centers of the two bodies.

Calculating Gravitational Force at Earth's Surface

Given that the weight of the body at the surface of Earth is 20 N, we can calculate the gravitational force acting on the body due to Earth's gravitational pull. Since the body is at the surface of Earth, the distance between the centers of the two bodies is equal to the radius of the Earth, which is 6400 km.

Using the formula above, we can calculate the gravitational force as follows:

F = G * (m1 * m2) / r^2
20 N = G * (m1 * m2) / (6400 km)^2

Since the mass of the body is not given, we cannot calculate it directly. However, we can make use of the fact that the weight of the body is equal to its mass multiplied by the acceleration due to gravity (g).

Therefore, we can write:

20 N = m * g

Where g is the acceleration due to gravity at the surface of Earth, which is approximately 9.81 m/s^2.

Solving for m, we get:

m = 20 N / 9.81 m/s^2 = 2.04 kg

Calculating Gravitational Force at a Height Above Earth's Surface

Now that we know the mass of the body, we can calculate the gravitational force acting on it at a height of 6400 km above Earth's surface. At this height, the distance between the centers of the two bodies is equal to the sum of the radius of the Earth and the height of the body above the surface, which is 12800 km.

Using the formula above, we can calculate the gravitational force as follows:

F = G * (m1 * m2) / r^2
F = G * (m * M) / (12800 km)^2

Where M is the mass of the Earth.

Substituting the values of G, m, M, and r, we get:

F = (6.67 x 10^-11 N m^2/kg^2) * (2.04 kg * 5.97 x 10^24 kg) / (12800 km)^2
F = 16.6 N

Therefore, the weight of the body at a height of 6400 km above Earth's surface is 16.6 N.