Understanding the Relationship
Newton's Law of Universal Gravitation states:
* F = G * (m1 * m2) / r²
Where:
* F is the gravitational force
* G is the gravitational constant
* m1 and m2 are the masses of the objects
* r is the distance between their centers
Key Points
* Inverse Square Law: The force of gravity is inversely proportional to the square of the distance between the objects. This means if you decrease the distance, the force increases.
* Direct Proportionality: The force is directly proportional to the product of the masses. This means if you increase the mass, the force increases.
Calculating the Change
1. Original Distance: Let's call the original distance "r".
2. New Distance: Decreasing the distance by two-thirds means the new distance is (1/3)r.
3. Ratio of Forces: The ratio of the new force (F') to the original force (F) can be found by considering the change in distance:
* F' / F = (r² / ((1/3)r)²) = 9
Conclusion
The gravitational force between the two masses will increase by a factor of 9 when the separation distance is decreased by two-thirds.
