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Answer :
The total force on the spacecraft can be determined using Newton's law of universal gravitation. The formula for the gravitational force between two objects is F = G * (m1 * m2) / r^2, where F is the force, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between their centers.
In this case, the mass of the spacecraft (including occupants) is 1000 kg and the mass of the black hole is 100 times that of the Sun, which is approximately 1.989 x 10^30 kg. The distance between the nose of the spacecraft and the center of the black hole is 10.0 km, which is equal to 10,000 m. Plugging these values into the formula, we get F = (6.67430 x 10^-11 N * m^2 / kg^2) * (1000 kg) * (1.989 x 10^30 kg) / (10,000 m)^2.
Simplifying this equation, we get F = 1.325 x 10^20 N. Therefore, the total force on the spacecraft is approximately 1.325 x 10^20 Newtons. The total force on the spacecraft can be determined using Newton's law of universal gravitation, which states that the force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. In this case, the mass of the spacecraft (including occupants) is given as 1000 kg, while the mass of the black hole is 100 times that of the Sun.
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