Introduction:

Gravitational force is the attractive force that exists between any two objects with mass. According to Newton's law of universal gravitation, this force is directly proportional to the product of the masses of the two objects and inversely proportional to the square of the distance between their centers.

Equal in Magnitude:

The gravitational force between two bodies is equal in magnitude because it depends on the product of their masses. Let's consider two bodies, Body A and Body B, with masses mA and mB, respectively. The gravitational force (F) between them can be calculated using the formula:

F = G * (mA * mB) / r^2

where G is the gravitational constant and r is the distance between the centers of the two bodies. Since the masses of the bodies are multiplied together, the force will be directly proportional to the product of their masses. Therefore, the magnitude of the gravitational force will be the same regardless of which body we consider.

Opposite in Direction:

The gravitational force between two bodies is also opposite in direction. According to Newton's third law of motion, for every action, there is an equal and opposite reaction. In the case of gravitational force, the force exerted by Body A on Body B is equal in magnitude but opposite in direction to the force exerted by Body B on Body A.

To understand this concept, let's consider Body A and Body B again. Body A exerts a gravitational force on Body B, pulling it towards itself. At the same time, Body B exerts an equal and opposite gravitational force on Body A, pulling it towards itself as well. This creates a pair of forces that act along the line joining the centers of the two bodies, but in opposite directions.

This opposite direction of the gravitational force ensures that the bodies attract each other rather than repel. If the forces were in the same direction, the bodies would repel each other due to the inverse square relationship between force and distance.

Conclusion:

In conclusion, the gravitational force between two bodies is equal in magnitude because it depends on the product of their masses. However, it is opposite in direction according to Newton's third law of motion. This ensures that the bodies attract each other, allowing for the formation of stable orbits and the existence of celestial bodies such as planets, stars, and galaxies.