Final answer:
The force of Earth's gravity acting on a spacecraft orbiting at an altitude of 2.5 Earth radii above the surface can be calculated using Newton's universal law of gravitation. The force is approximately 1.30 × 10^4 N.
Step-by-step explanation:
To calculate the force of Earth's gravity acting on a spacecraft orbiting at an altitude of 2.5 Earth radii above the surface, we can use Newton's universal law of gravitation. The formula for gravitational force is given by:
F = (G * m1 * m2) / r^2
Where F is the force of gravity, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between the two objects.
In this case, the mass of the spacecraft is not given, but we can assume it to be 1500 kg. The mass of the Earth is 5.97 × 10^24 kg, and the radius of the Earth is 6.38 × 10^6 m. The distance between the spacecraft and the Earth's surface is 2.5 times the radius of the Earth, which is 2.5 * 6.38 × 10^6 m.
Plugging in the values into the formula, we have:
F = (6.67 × 10^-11 N m^2/kg^2) * (1500 kg) * (5.97 × 10^24 kg) / (2.5 * 6.38 × 10^6 m)^2
Calculating the result, we get:
F = 1.30 × 10^4 N