How exactly is the speed of light measured? What process was taken to measure it?

Answer 1

The first reasonably effective method of measuring the speed of light was to measure the eclipses of the satellites of Jupiter against their predicted times. The orbits of Jupiter and its four largest ("Galilean") satellites were worked out with reasonable precision not long after they were discovered, including the regular pattern by which they were eclipsed as they entered the shadow of Jupiter.

It was soon noticed that sometimes the eclipses were observed about 10 minutes ahead of the predicted time, and other times about 10 minutes behind the predicted time. A Danish astronomer named Ole Romer worked this out in 1676 and figured that light took about 22 minutes to cross the earth's orbit. (He was off by a bit; actually it takes about 16-2/3 minutes.) This meant that he figured the speed to be about 2/3 of its actual speed, but that was better than had been done before.

The next improvement took place about 50 years later, when James Bradley reasoned that light should behave the same way as rain. If you're walking into rain, it appears to slant toward you; if you're walking backward, it appears to slant away from you. The amount of slant depends on how fast you're walking and how fast the rain is falling. He said that light falling on the earth is like rain falling on walking people, because the earth is moving, and the light should thus appear to fall at slightly different angles depending on whether it was being observed near sunrise (the leading edge of the earth as it orbits the sun, akin to walking forward) or near sunset (the trailing edge, akin to walking backward). His instruments were good enough to measure the change in the observed angle of the light (or the positions of the stars) and he calculated the speed of light to be 185,000 mi/sec, less than 1% below the value accepted today.

Answer 2

Read about Michelson-Morley Experiments either in a good Physics text book or through a google search.