Question

A 112 kg astronaut is tethered to the International Space Station (ISS) and is 26 m from the center of mass

of the ISS. The gravitational force between the astronaut and the ISS is 4.64 × 10^-6 N.
Calculate the mass of the ISS.
Write your answer using two significant figures.

Answer 1

Using Newton's law of universal gravitation, the calculated mass of the ISS, considering the gravitational force between the astronaut and the ISS, is approximately 3.4 × 10^6 kg.

Step-by-step explanation:

The question concerns the calculation of the mass of the ISS using the gravitational force between the ISS and an astronaut. To calculate the mass, we can use Newton's law of universal gravitation:

F = G * (m1 * m2) / r^2

Where F is the gravitational force, G is the gravitational constant (6.674 × 10^-11 N·m^2/kg^2), m1 and m2 are the masses of the two objects, and r is the distance between the centers of mass of the two objects. We know the following:

• F = 4.64 × 10^-6 N (gravitational force between astronaut and ISS)
• m1 = 112 kg (mass of astronaut)
• r = 26 m (distance from astronaut to the center of mass of the ISS)

We need to find the mass of the ISS (m2). Rearranging the formula to solve for m2:

m2 = F * r^2 / (G * m1)

Plugging in the values:

m2 = (4.64 × 10^-6 N) * (26 m)^2 / (6.674 × 10^-11 N·m^2/kg^2 * 112 kg)

Performing the calculations gives us:

m2 ≈ 3.37 × 10^6 kg

Therefore, the mass of the ISS is approximately 3.37 × 10^6 kg, or 3.37 million kg, when expressed with two significant figures, this is 3.4 × 10^6 kg.

Answer 2

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.