What happens to the force of gravity between two objects when they grow closer?
The correct answer and explanation is:
The force of gravity between two objects increases as they grow closer to each other.
This relationship is described by Newton’s Law of Universal Gravitation, which states that the gravitational force between two masses is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. Mathematically, the formula is: F=Gm1m2r2F = G \frac{m_1 m_2}{r^2}
Where:
- FF is the gravitational force
- GG is the gravitational constant
- m1m_1 and m2m_2 are the masses of the two objects
- rr is the distance between the centers of the two objects
As the distance rr between the objects decreases, the denominator in the equation r2r^2 becomes smaller. Since the force is inversely proportional to the square of the distance, a smaller distance results in a larger gravitational force. This means that as the objects approach each other, the gravitational attraction between them increases.
For example, if two objects are initially 10 meters apart and then move to 5 meters apart, the gravitational force between them increases by a factor of 4 (since (1/52)/(1/102)=4(1/5^2) / (1/10^2) = 4).
This principle is crucial in understanding various natural phenomena. For instance, when two planets or moons approach each other, the gravitational attraction becomes stronger, which can lead to tidal forces or even collisions if they get too close. Similarly, this effect is what causes objects to fall toward the Earth when dropped, as the gravitational force increases as they get closer to the surface.
In summary, the closer two objects get to each other, the stronger the gravitational force between them, as the force is inversely proportional to the square of the distance.