When you look at a distant galaxy through a telescope, how is it that you're looking backward in time?

Answer 1

This is because the speed of light is finite: c = 299792458 m/s

Ole Christensen Rømer in about 1670 actually found out that the speed of light was finite (and estimated its value), by observing the moons of jupiter. The distance between Earth and jupitar changes, as both the Earth and Jupiter revolve around the Sun but with different rotational periods.

The moons of jupiter have some fixed orbital period, so you can predict where they will be relative to jupiter. However, because the speed of light is finite, you will observe them with some delay that depends on the distance between the Earth and Jupitar. This delay changes over the course of a year, and from this you can compute the speed of light.

Rømer could only estimate the ratio of the lightspeed and the Earth's speed in its orbit around the Sun, because at that time the overall scale of the solar system was unknown (only the ratio of distances to Earth-Sun distance was known then)