Final answer:
The gravitational acceleration at a height of 1600 km above the Earth's surface for a spacecraft is calculated using the formula for gravitational acceleration and is approximately 6.28 m/s^2.
Step-by-step explanation:
To calculate the gravitational acceleration of the spacecraft at a height of 1600 km above the Earth's surface, we will use the formula for gravitational acceleration g = G M / r^2, where G is the gravitational constant (~6.674 × 10^-11 N m^2/kg^2), M is the mass of the Earth (~5.972 × 10^24 kg), and r is the distance from the center of the Earth to the spacecraft. Since the Earth's radius is 6400 km, at a height of 1600 km, the distance r would be the sum of the Earth's radius and the spacecraft's altitude above the surface, which is 6400 km + 1600 km = 8000 km or 8 × 10^6 meters.
By substituting these values into the equation, we can find the gravitational acceleration experienced by the spacecraft:
g = (6.674 × 10^-11 N m^2/kg^2) × (5.972 × 10^24 kg) / (8 × 10^6 m)^2
g = 9.81 m/s^2 × (6400 / 8000)^2
g = 9.81 m/s^2 × 0.64
g = 6.28 m/s^2
The gravitational acceleration at a height of 1600 km above the Earth's surface for a spacecraft is approximately 6.28 m/s^2.