The Distance to Pluto

This 1270th Buffalo Sunday News column was first published on July 26, 2015.

Recently the media has had much to say about the New Horizons spacecraft passing the dwarf planet Pluto on July 14. In this column I suggest some ways that we can make some mathematics and physics related to this adventure more meaningful.

Not me, I can hear you say, math turns me off. And, my wife tells me, physics are what she takes when she has digestive problems. Well, at least read on. I will try to make the case that most of the math I will discuss is easily accessed and relates to very simple ideas. The only difference is that the numbers are big and that suggests the use of a calculator. (Anyway, approximations are all we need.)

What led me to write this column was the statement on a recent news program that it took computer messages over four hours to reach Earth from New Horizons. Shortly after I heard that, on July 4, all communications from the spacecraft suddenly stopped requiring "immediate" action by the mission team. Wow! Given that time delay, they already knew that the spacecraft computer went down over four hours earlier. Then corrective signals wouldn't reach the spacecraft for another four hours and they wouldn't know if they worked for still another four.

Now back up a bit to see where that four plus hour delay came from? As a starter, consider the following inquiry: When lightning strikes, which reaches you first, the sight of the event or the sound?

Of course, the answer from our experience is that the sight appears first. This is so because sound travels only about 1/5 mile per second while light (what you see) travels a bit faster: in fact about 186,000 miles per second.  As far as we are concerned, we see the event instantaneously.

But that speed is not really instantaneous, it is just very fast. One way to think of it is to compare it with the circumference of the earth, which is about 24,000 miles. Light would race around the earth (if it could bend) 186000/24000 = 7 3/4 times in one second.

That is indeed very fast, but it becomes far from instantaneous as is shown by how long light takes to travel from the sun to us on Earth. That distance, called by astronomers the astronomical unit (AU), is about 92 million miles. Another simple calculator division: 92,000,000/186,000 = 495, so it takes about 495 seconds for the sun's light to reach us. Divide by 60, the number of seconds in a minute and that tells further that it is about 8 1/4 minutes. Suddenly what appears to be instantaneous turns out to take a significant amount of time. What we see when we look at the sun is the way it appeared more than eight minutes ago.

Now what about Pluto? Here we can use that AU to tell us. It is every bit as useful as a unit as feet and miles are; it is simply larger. Instead of saying that Pluto is about three billion miles from Earth today, NASA astronomers tell us that it is about 32 AUs from Earth.

That means that light (and computer signals that go just as fast) will take 32 times as long as does light from the sun: 32 times 8 1/4 = 265 minutes. That is 4 hours and 25 minutes.

Pluto is still in our solar system. Think about how far it is to the nearest star. The nearest star, Proxima Centauri, is 271,000 AUs from Earth. You can check my math: it leads to about 4 1/4 years for light to reach us from that nearest star.

Notice how the number of AUs is getting large. Astronomers use still another unit, the light year. As the name indicates, it represents the length of time it takes light to travel in one year. Proxima Centauri is then about 4 1/4 light years from Earth.

Briefly, how big is Pluto? Not very, it's smaller than our moon. Its radius is 700 miles; our Earth radius is 8000 miles. Without doing the math, I'll tell you that what you see in each of those wonderful hemispheric photographs is less than the area of the United States.

Pluto really is a dwarf planet.-- Gerry Rising