What is done in these coordinates is to fix the calculation to be at a specific time. The proper distance will be different at different times because the universe is expanding, meaning objects within the universe are getting further apart.Apashanka Das said:actually I want to clarify that is the proper distance a(t)*dr is the elementary length along the radial direction which is changing with respect to time and if integrating a(t)*dr and dr ,which may be considered the actual distance
A(t)*dr is an expression used in physics and mathematics to represent the instantaneous change in position, or displacement, over a small interval of time. In simpler terms, it is the rate at which an object's position is changing over time.
A(t)*dr is directly related to velocity, as it represents the change in position over a small period of time. Velocity is defined as the rate at which an object's position changes over time, and it can be calculated by dividing the change in position by the change in time.
A(t)*dr is important because it allows us to calculate the actual distance traveled by an object, taking into account any changes in velocity that may occur over time. By using this expression, we can accurately determine the total distance an object has traveled, even if its velocity is changing constantly.
A(t)*dr is used in various real-world applications, such as calculating the distance traveled by a moving vehicle, determining the displacement of an object in motion, or predicting the position of a satellite in orbit. It is also used in calculus to find the area under a curve, which has many practical applications in fields such as engineering and physics.
Yes, a(t)*dr can be negative. This would indicate that the object is moving in the opposite direction of its initial position. For example, if a car starts at position 0 and moves -5 meters in 1 second, the a(t)*dr would be -5 meters per second.