why is looking through a powerful telescope like looking back through time?

Because the light you are seeing was emitted a very long time ago.

If you were to see light from a star that is 1,000.000 light years away, you would see the star as it looked 1,000.000 years ago (by the time you get to see it, it might not even exist anymore.)

Looking through a powerful telescope can give us the ability to observe distant objects in space, which includes galaxies, nebulae, and other celestial bodies that are millions or even billions of light-years away. To understand why this is like looking back through time, it's important to consider the concept of the speed of light.

The speed of light is extremely fast, traveling at about 300,000 kilometers per second (or 186,000 miles per second) in a vacuum. When we look at objects in space, we rely on the light that they emit or reflect to reach our eyes or telescopes. This means that when we observe a distant object, we are seeing the light that was emitted or reflected by that object in the past.

For example, if we observe a galaxy that is located 100 million light-years away, the light we see from that galaxy today actually started its journey toward us 100 million years ago. Therefore, looking through a powerful telescope and observing such distant objects allows us to effectively "look back in time" and see what those objects looked like millions or even billions of years ago.

This concept is known as the "cosmological distance ladder," which is used by astronomers to measure distances in the universe and understand its history. By studying objects at different distances, astronomers can piece together the timeline of the universe's evolution and gain insights into its past.

So, looking through a powerful telescope is like looking back through time because the light we observe from distant objects has traveled for vast periods before reaching us, allowing us to witness the universe's past.