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The problem involves calculating the gravitational force between two masses using Newton's law of universal gravitation. The formula provided is:

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

Where:
- \( F \) is the gravitational force,
- \( G = 6.67 \times 10^{-11} \, \text{N} \cdot \text{m}^2 / \text{kg}^2 \) is the gravitational constant,
- \( m_1 = 912 \, \text{kg} \),
- \( m_2 = 878 \, \text{kg} \),
- \( r = 25.4 \, \text{m} \) is the distance between the two masses.

### Step-by-step calculation:

1. **Substitute the values into the formula:**

\[
F = \left( 6.67 \times 10^{-11} \right) \frac{(912)(878)}{(25.4)^2}
\]

2. **Calculate the product of the masses:**

\[
912 \times 878 = 800,736 \, \text{kg}^2
\]

3. **Square the distance:**

\[
(25.4)^2 = 645.16 \, \text{m}^2
\]

4. **Now calculate the fraction:**

\[
\frac{800,736}{645.16} \approx 1,241.18 \, \text{kg}^2/\text{m}^2
\]

5. **Multiply by the gravitational constant:**

\[
F = \left( 6.67 \times 10^{-11} \right) \times 1,241.18 \approx 8.28 \times 10^{-8} \, \text{N}
\]

Thus, the gravitational force between the two masses is approximately:

\[
F = 8.28 \times 10^{-8} \, \text{N}
\]

### Answer format:
- The coefficient (green box) is \( 8.28 \).
- The exponent (yellow box) is \( -8 \).

Would you like more details on the calculations or have any questions?

### Relative questions:
1. How does the gravitational constant \( G \) influence the force between two objects?
2. How would the force change if the masses were doubled?
3. What happens to the gravitational force if the distance between the masses is halved?
4. How is gravitational force related to mass and distance in space?
5. Can gravitational force ever be zero between two objects?

### Tip:
Gravitational force decreases with the square of the distance between two objects, making small changes in distance have a large impact on the force magnitude.

Two masses are 25.4 m apart. Mass 1 is 912 kg and mass 2 is 878 kg. What is the gravitational force between the two masses?

Learn how to calculate the gravitational force between two masses, 912 kg and 878 kg, separated by 25.4 meters. This detailed solution involves Newton's law of universal gravitation, showcasing how mass and distance influence gravitational attraction. Perfect for high school physics students in Grades 10-12.

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