Final answer:
The gravitational acceleration on the ISS at 408 km altitude is calculated using Newton's law of universal gravitation and is less than on Earth's surface, due to the inverse square relationship between gravitational acceleration and radius from Earth's center. The astronauts experience this gravity but feel weightless due to being in continuous free fall.
Step-by-step explanation:
To calculate the gravitational acceleration on the International Space Station (ISS) at an altitude of 408 km, we can use Newton's law of universal gravitation and the formula for gravitational force, which is 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 of mass. Since we want to find gravitational acceleration, we look at the force experienced by a mass of 1 kg, which means the gravitational force equals the gravitational acceleration at that location.
According to the given example, at 400 km above Earth's surface, the value of g is approximately 8.67 m/s². Given that the altitude of the ISS is 408 km, we will calculate it using the similar concept where the radius (r) will be the sum of Earth's radius and the ISS altitude, r = 6371 km + 408 km. Plugging the values into the equation for gravitational force, and considering the mass of Earth (ME) and the gravitational constant (G), we can solve for the gravitational acceleration (g).
Using the values provided, the approximate gravitational acceleration at the ISS's altitude can be calculated. This acceleration is less than the gravitational acceleration on Earth's surface (9.80 m/s²) because it is inversely proportional to the square of the radius from the center of the Earth. The astronauts on the ISS experience this gravity, but they are in a continuous free fall, giving the sensation of weightlessness.