The International Space Station is in orbit around Earth at a distance r from the center of Earth. A recent addition increased the Station’s mass by a factor of 3. Did Earth’s gravitational force on the Station increase, decrease, or stay the same? If it changes, by how much?

Earth's gravitational force on an object is given by Newton's law of gravitation:

\[
F = \frac{G M_{\text{Earth}} m_{\text{Station}}}{r^2}
\]

Where:
- \( G \) is the gravitational constant,
- \( M_{\text{Earth}} \) is the mass of Earth,
- \( m_{\text{Station}} \) is the mass of the International Space Station (ISS),
- \( r \) is the distance between the center of Earth and the ISS.

Now, when the mass of the ISS is increased by a factor of 3, the new mass \( m_{\text{new}} \) becomes:

\[
m_{\text{new}} = 3 \times m_{\text{Station}}
\]

Since the gravitational force is directly proportional to the mass of the ISS, the force will also increase by a factor of 3. Therefore, Earth's gravitational force on the Station **increases by a factor of 3**.

To summarize:
- The gravitational force increases,
- It increases **by a factor of 3**.

Would you like further details or have any questions?

### Follow-up Questions:
1. What is the formula for gravitational force when two masses are involved?
2. How does the gravitational force depend on the distance between two objects?
3. What would happen to the gravitational force if the ISS moved farther away from Earth?
4. How does mass affect gravitational force compared to distance?
5. What happens to Earth's gravitational force on an object if Earth's mass changes?

**Tip**: In gravitational force problems, small changes in distance have a more dramatic effect than changes in mass because force decreases with the square of the distance.

Understand how Earth's gravitational force on the International Space Station changes when the mass of the ISS increases by a factor of 3. Explore Newton's law of gravitation, with a detailed explanation suitable for high school students. Learn the effect of mass and distance on gravitational forces.

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