Final answer:
The force of Earth's gravity on a spacecraft 2.00 Earth radii above the Earth's surface with a mass of 1550 kg is calculated using Newton's law of universal gravitation. The spacecraft experiences a gravitational force of approximately 1.722 x 10^3 Newtons.
Step-by-step explanation:
To calculate the force of Earth's gravity on a spacecraft 2.00 Earth radii above the Earth's surface, we can use Newton's law of universal gravitation, which states that the force (F) between two masses (m1 and m2) is proportional to the product of the masses and inversely proportional to the square of the distance (r) between their centers:
F = G * (m1 * m2) / r2
Where G is the gravitational constant (6.674×10-11 N·m2/kg2). For the given problem, m1 is the mass of the Earth (5.972×1024 kg), m2 is the mass of the spacecraft (1550 kg), and r is the distance from the center of the Earth, which is 3 Earth radii (the radius of the Earth plus the 2 Earth radii above the surface).
Therefore, r = 3 * 6.38×106 m = 1.914×107 m. Plugging the values into the equation, we get:
F = 6.674×10-11 N·m2/kg2 * (5.972×1024 kg * 1550 kg) / (1.914×107 m)2
F = (6.674×10-11 * 5.972×1024 * 1550) / (1.914×107)2
F = 1.722×103 N
The gravitational force on the spacecraft is thus approximately 1.722×103 Newtons.