Speed of Light

A lot of times, when sharing views of heavenly objects through a telescope, the question comes up: “How far away is it?” If I know the answer and the target is located outside of our solar system of planets, the response is usually some number in the tens, hundreds, thousands or millions, followed by “light-years.”

The light-year is simply a unit of measurement for distance equivalent to the span traveled by light in one year in a vacuum. Thus, if an object is 20 light-years away, then the light from it we are seeing left that object 20 years ago during which time it rapidly traveled through space before meeting our eyes.

There are various methods and techniques for estimating and measuring discrete astronomical distances that we won’t get into now. However, aside from the numerical answer are two other fundamental questions: (1) how fast does light travel and (2) how do we know?

The first question is easy to answer by looking it up. Light travels at about 186,000 miles (300,000 kilometers) per second. So, in a year light travels a distance of about six trillion miles, or one light-year. The next question is a little more difficult to explain. But first, there is an even more fundamental question lurking like an elephant in the room.

How do we know light travels at a finite speed in the first place? In our normal every day experience light appears to be instantaneous. Flip on a flashlight and a cone of light promptly appears. We know that sound has a finite speed. We see a flash of lighting and the thunder belatedly reaches our expecting ears. But is the arrival of the flash itself likewise delayed, albeit by a lesser amount, or not?

The discovery of the finite speed of light has its origin in a solution to the maritime problem of measuring a ship’s Longitude. Finding the Latitude of a ship is pretty straightforward. At night the pole star Polaris may be used. By day, observing the sun as it transits at local Noon is used. Even if you drop your watch overboard you can still figure out when Local Noon is by watching the sun and measuring its altitude. The highest altitude always occurs at local Noon.

But Longitude is trickier and involves more precise timekeeping. Shipboard clocks whose time was set upon leaving port could not remain accurate throughout a long voyage. Even an inaccurate clock would be useful if it could be reset precisely and periodically. And so, astronomers were tapped to come up with a solution for setting a cruising clock. The answer that they discovered involved making observations of the planet Jupiter.

Once the telescope was invented, Galileo discovered Jupiter’s four largest moons. Soon, astronomers were observing “occultations” as the moons passed across Jupiter’s face or vanished behind it and reappeared, and “eclipses” as the moons either slipped into and out of Jupiter’s shadow or their own shadows traversed Jupiter’s face. Turned out that these events can be predicted. The predictions were then published in an ephemeris, a copy of which was carried to sea on the ship along with a telescope.

The telescope was used to observe Jupiter looking for an eclipse or occultation event. The time of the observed event could be read from the ephemeris and used to set the ship’s clock once the event occurred. The ship’s clock could then be consulted while making other observations necessary for determining Longitude.

But there was a problem. It was noticed that the predicted event times were not always accurate. In fact the predictions had a tendency to be late most of the time, but not by a constant amount. This led the 17th century Danish astronomer Ole Rømer to suspect that the problem could be explained if the speed of light was finite.

The distance between the Earth and Jupiter varies as they orbit the sun. When both planets are on the same side of the sun they are at their closest, or at “opposition.” Not only is Jupiter closest to the Earth but is also up all night and convenient to observe. Therefore, the event predictions were based on this opposition configuration when the two planets were closest to one another.

But later, as the Earth wheels around to the opposite side of the sun from Jupiter the distance between the two planets increases. Therefore, light requires more time to span the gap between them and the light from Jupiter and its moons is tardy causing a given event to take place up to 22 minutes later than scheduled.

Not only did Ole Rømer conclude correctly that light travels at a finite speed, he was also able to conduct experiments leading to a rough calculation of that speed, answering our second question above (how do we know?). Additional experiments in the following centuries have refined the value of the speed of light, now known to astronomers as the constant referred to as ‘C’ — the first letter in the Latin word celeritas meaning “speed.”

— Curtis Roelle


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