Friday, February 6, 2015

How far has the earth gone?

A question in my physics text led me to a fact I could hardly believe.  The question was: "How far has the earth traveled in its orbit around the sun since it first formed?  Assume the earth is 4.5 billion years old and has a circular orbit with a radius of 149,597,870km.  Ignore the solar system's movement through space."  The math is simple, but the result amazing.  Every year the earth goes 2π149,597,870km=939,953,337km.  Over its lifetime, that's (939,953,337km/y)X(4,500,000,000yrs) =4.3X1018km.  

Now that number, ending in 17 zeroes, is so large it’s almost meaningless.  Let's use the light year to put it in perspective.  Light, traveling at 300,000,000m/s, is the fastest thing in the universe.* In a year's time, light can travel 3.00X108m/sX365X24X60X60 =9.46X1012km (about 6 trillion miles).  That distance is a light year.**  A light year is unimaginably large: it would take you 10 trillion years to cover that distance at highway speed.  Yet even the nearest star to our sun is several light years away, and many of those visible in the night sky are tens or hundreds of LY away.  Our whole galaxy, the Milky Way, is about 100,000LY across.
The earth, moving much faster than highway speed, covers more than 900 million km each year, for a speed of 939,953,337km/(365X24X60X60) =29.806km/s.  (That's about 67,000 mph.  Don't challenge the earth to a race.)  That cumulative distance is equal to 455,000LY!  Over its life, the sun could have made 1½ laps around our entire galaxy!

The earth takes about 10,000 years to travel 1LY in its revolution about the sun. 

*In its broadest sense, light includes all forms of electromagnetic radiation: x-rays, radio, etc, as well as visible light.  All travel at that magical speed of 3.00X108m/s.  Oh, and of course light isn't a "thing" at all.  Actual things (matter) can't go that fast.

**Right: the LY is a measure of distance, not time.

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