Final answer:
Using Newton's universal law of gravitation and the provided gravitational force, astronaut's mass, and distance from the ISS, the mass of the ISS is calculated to be approximately 3.7 × 10^5 kg, rounded to two significant figures.
Step-by-step explanation:
To calculate the mass of the International Space Station (ISS), we can use Newton's universal law of gravitation. The formula is F = G (m1 * m2) / r^2, where F is the gravitational force, G is the gravitational constant (6.674 × 10^-11 N m²/kg²), m1 and m2 are the masses of the two objects, and r is the distance between the centers of mass of the two objects.
The question states that the gravitational force between the astronaut and the ISS is 4.64 × 10^-6 N, the mass of the astronaut is 112 kg, and the distance from the astronaut to the center of mass of the ISS is 26 m. We can rearrange the formula to solve for the mass of the ISS (m2): m2 = (F * r^2) / (G * m1).
Plugging in the values we have:
m2 = (4.64 × 10^-6 N * 26 m * 26 m) / (6.674 × 10^-11 N m²/kg² * 112 kg)
m2 ≈ 370,000 kg
Thus, the calculated mass of the ISS would be approximately 370,000 kg. As the mass should be reported with two significant figures, the answer is 3.7 × 10^5 kg.