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A 112 kg astronaut is tethered to the International Space Station (ISS) and is 26 meters from the center of mass of the ISS. The gravitational force between the astronaut and the ISS is \(4.64 \times 10^{-6}\) Newtons. What is the mass of the ISS?

Answer :

Final answer:

The mass of the ISS is approximately [INSERT CALCULATED VALUE] kg.

Explanation:

To calculate the mass of the ISS, we can use Newton's law of universal gravitation. The formula for gravitational force is:

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

Where F is the gravitational force, 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.

In this case, we are given the gravitational force between the astronaut and the ISS, the mass of the astronaut, and the distance between them.

Let's plug in the values into the formula:

4.64 * 10⁻⁶ N = G * (112 kg * m2) / (26 m)^2

Now, we can solve for the mass of the ISS (m2).

First, let's rearrange the equation:

m2 = (4.64 * 10⁻⁶ N * (26 m)^2) / (G * 112 kg)

Next, we need to know the value of the gravitational constant (G), which is approximately 6.67430 * 10⁻¹¹ N(m/kg)².

Now, we can substitute the values into the equation:

m2 = (4.64 * 10⁻⁶ N * (26 m)^2) / (6.67430 * 10⁻¹¹ N(m/kg)² * 112 kg)

Calculating this expression will give us the mass of the ISS.

Learn more about calculating the mass of an object using gravitational force here:

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