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The formula given is for the gravitational force between two objects:

\[
F_g = \frac{G M_1 M_2}{r^2}
\]

We need to solve for \( M_2 \) in terms of \( F_g \), \( G \), \( M_1 \), and \( r \). Let's rearrange the equation step by step:

1. Start with the formula:
   \[
   F_g = \frac{G M_1 M_2}{r^2}
   \]

2. Multiply both sides by \( r^2 \) to eliminate the denominator:
   \[
   F_g r^2 = G M_1 M_2
   \]

3. Divide both sides by \( G M_1 \) to isolate \( M_2 \):
   \[
   M_2 = \frac{F_g r^2}{G M_1}
   \]

Thus, the solution for \( M_2 \) is:

\[
M_2 = \frac{F_g r^2}{G M_1}
\]

Would you like further details or have any questions?

Here are five related questions to expand your understanding:
1. How does the gravitational force between two objects change as the distance between them increases?
2. What happens to the force if one of the masses is doubled?
3. How is Newton's law of universal gravitation related to the inverse-square law?
4. Can you explain how \( G \) (the gravitational constant) was experimentally determined?
5. How would this equation apply to calculating the force between Earth and an object in orbit?

**Tip:** Always pay attention to units when dealing with physical equations. For gravitational problems, the units of mass, distance, and force must be consistent (e.g., kilograms, meters, and newtons).

The formula to calculate the gravitational force between two objects is F_g = (G M_1 M_2) / r^2. Solve for M_2 in terms of F_g, G, M_1, and r.

Learn how to solve for M_2 in the gravitational force equation F_g = (G M_1 M_2) / r^2. This step-by-step solution explains the algebraic manipulation required and covers Newton's Law of Universal Gravitation. Suitable for high school students in Grades 9-12.

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