A CHILD IS BORN ON EARTH IN 2000. yOU ARE 94.6 TRILLION KILOMETERS AWAY FROM EARTH AND YOU SEE THE CHILD'S 3RD BIRTHDAY. HOW OLD IS THE CHILD AT THE TIME OF THE CHILD'S 3RD BIRTHDAY?
To determine the child's age at their 3rd birthday, we need to consider the concept of time dilation due to the vast distance between you and Earth.
Time dilation occurs when there is a significant difference in speed or gravitational forces between two objects. In this case, the large distance of 94.6 trillion kilometers means you are observing the child from a great distance away, which results in a time dilation effect.
The equation to calculate time dilation is:
t' = t / √(1 - v^2/c^2)
Where:
t' = time experienced by the observer (you)
t = time experienced by the child on Earth
v = relative velocity between the observer and the child
c = speed of light (approximately 299,792 kilometers per second)
In this scenario, let's assume that you and the child are not moving relative to each other, so the velocity (v) is zero in the equation. Thus, the equation simplifies to:
t' = t / √(1 - 0) = t / √1 = t
Since there is no relative speed between you and the child, time dilation does not occur. Therefore, the child's age at their 3rd birthday would be the same as it would be on Earth – 3 years old.