The gravitational force on the satellite in orbit can be calculated using the formula:
F = G * (m1 * m2) / r^2
where G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between their centers.
Since the satellite is in orbit, we can assume that its weight is equal to the gravitational force acting on it. Therefore, the weight of the satellite on Earth is equal to the gravitational force acting on it in orbit.
The weight of the satellite on Earth is 100 kilonewtons, which is equal to its mass multiplied by the acceleration due to gravity on Earth (9.81 m/s^2). Therefore, the mass of the satellite is:
m = weight / acceleration due to gravity = 100,000 N / 9.81 m/s^2 = 10,182.07 kg
The distance between the center of the Earth and the satellite is 12,800 km - 6,400 km = 6,400 km.
Using these values and the gravitational constant G = 6.6743 × 10^-11 N m^2 / kg^2, we can calculate the gravitational force on the satellite in orbit:
F = G * (m1 * m2) / r^2
F = (6.6743 × 10^-11 N m^2 / kg^2) * (10,182.07 kg * 5.97 × 10^24 kg) / (6,400,000 m)^2
F = 3.5303 × 10^22 N
Therefore, the gravitational force on the satellite in orbit is 3.5303 × 10^22 N.