To isolate \( r \) in the equation \( F = \frac{G m_1 m_2}{r^2} \), you can follow these steps:

1. **Start with the given equation:**
   \[
   F = \frac{G m_1 m_2}{r^2}
   \]

2. **Multiply both sides by \( r^2 \) to get rid of the fraction:**
   \[
   F \cdot r^2 = G m_1 m_2
   \]

3. **Divide both sides by \( F \) to solve for \( r^2 \):**
   \[
   r^2 = \frac{G m_1 m_2}{F}
   \]

4. **Take the square root of both sides to isolate \( r \):**
   \[
   r = \sqrt{\frac{G m_1 m_2}{F}}
   \]

This is the formula for \( r \) in terms of \( F \), \( G \), \( m_1 \), and \( m_2 \).

Would you like further details or have any questions?

### Related Questions

1. What is the physical meaning of the gravitational constant \( G \)?
2. How does the force \( F \) change if the distance \( r \) between two masses is doubled?
3. Can the gravitational force equation be used for very small objects, like electrons?
4. How does the gravitational force between two objects change if one of the masses is tripled?
5. What units are used for \( G \), \( m_1 \), \( m_2 \), \( r \), and \( F \)?

### Tip

When dealing with equations involving powers, such as squares or square roots, remember that taking the square root of a squared term can yield both positive and negative values. However, in physical contexts like this one, we typically consider only the positive root when dealing with distances or magnitudes.

Learn how to isolate r in the gravitational force formula F = (G * m1 * m2) / r^2 with a detailed step-by-step solution. This problem covers key physics concepts, including gravitation and the application of algebraic manipulation to solve for a variable. Suitable for advanced high school students in Grades 10-12.

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