A body of mass 1 kg is 1 lightyear far from another body of the same mass in the universe. If both came into existance at the same time then after howmuch time will they start to exert gravitational force b/w them.

To understand when two bodies in the universe will start to exert gravitational force on each other, we need to consider the nature of gravity and the speed of light. In this scenario, we have two bodies, each with a mass of 1 kg, located 1 light-year apart. The key point here is that gravitational force is a function of mass and distance, but it also depends on the propagation of gravitational effects, which travel at the speed of light.

The Nature of Gravitational Interaction

Gravitational force is described by Newton's law of universal gravitation, which states that every mass attracts every other mass with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them. However, this force is not felt instantaneously. Changes in the gravitational field propagate at the speed of light.

Understanding the Distance and Time Factor

In your scenario, the two bodies are 1 light-year apart. This means that if one body were to suddenly appear or change its mass, the gravitational influence of that change would take 1 year to reach the other body. Therefore, even though both bodies exist simultaneously, they will not start to exert gravitational force on each other until the effects of their masses can communicate across the distance separating them.

Calculating the Time Delay

Since gravitational effects travel at the speed of light, we can conclude that:

• The distance between the two bodies is 1 light-year.
• Light (and gravitational effects) takes 1 year to travel that distance.

Thus, if both bodies came into existence at the same time, they will start to exert gravitational force on each other after a time delay of 1 year. This is because it takes that long for the gravitational influence of one body to reach the other.

Real-World Analogy

Think of it like a conversation between two people standing far apart. If one person shouts a message, the other person won't hear it until the sound travels the distance between them. Similarly, the gravitational effects act like that sound, taking time to travel across the vastness of space.

Final Thoughts

In summary, while the two 1 kg masses exist simultaneously, they will not start to exert gravitational force on each other until 1 year has passed, due to the finite speed at which gravitational effects propagate. This concept is fundamental in understanding how forces work over astronomical distances.