Final answer:
The gravitational force due to the earth at a height of 3200 km is 4.9 N.
Step-by-step explanation:
To calculate the gravitational force due to the earth at a certain height, we need to use Newton's law of universal gravitation. The formula is:
F = (G * m1 * m2) / r^2
Where F is the gravitational force, G is the gravitational constant (approximately 6.67 x 10^-11 Nm^2/kg^2), m1 and m2 are the masses of the two objects (in this case, the body and the earth), and r is the distance between their centers of mass. In this scenario, the body weighs 63 N on the surface of the earth, so its mass can be calculated using the formula weight = mass * gravitational acceleration. Therefore, the mass of the body is:
m1 = 63 N / 9.8 m/s^2 = 6.43 kg
At a height of 3200 km from the earth's surface, the distance between the body and the earth's center of mass is 6400 km + 3200 km = 9600 km = 9.6 x 10^6 m. Plugging the values into the formula, we get:
F = (6.67 x 10^-11 Nm^2/kg^2 * 6.43 kg * 5.97 x 10^24 kg) / (9.6 x 10^6 m)^2
F = 4.9 N