Based on Newton’s law of universal gravitation, complete the following table.distance increasesmass increasesdistance decreasesmass decreases

To analyze the relationship between distance, mass, and gravitational force according to Newton's law of universal gravitation, we first need to understand the law itself, which is stated mathematically as:

$F = G \frac{m_1 m_2}{r^2}$

where:

• $F$ is the gravitational force between two masses,
• $G$ is the gravitational constant,
• $m_1$ and $m_2$ are the masses of the objects, and
• $r$ is the distance between the centers of the two masses.

Analysis Based on the Given Conditions

1. Distance Increases:

   • As the distance $r$ between two masses increases, the value of $r^2$ (the denominator) increases as well, resulting in a decrease in the gravitational force $F$. Therefore, the gravitational force weakens as distance increases.

2. Mass Increases:

   • Increasing either mass $m_1$ or $m_2$ will linearly increase the gravitational force $F$ since mass appears in the numerator of the formula. Thus, a greater mass results in a stronger gravitational pull.

3. Distance Decreases:

   • Conversely, if the distance $r$ decreases, the value of $r^2$ decreases, leading to an increase in gravitational force $F$. Hence, the gravitational attraction becomes stronger.

4. Mass Decreases:

   • A decrease in either mass $m_1$ or $m_2$ reduces the gravitational force $F$. The weaker the mass, the weaker the gravitational pull.

Conclusion

Based on this analysis, the table can be completed as follows:

Thus, this demonstrates the inverse square relationship of gravitational force with distance, and the direct relationship with mass.