According to Wikipedia’s list of nearest stars, there are 66 stars within 5 parsecs of planet Earth.  Some of these stars, like Epsilon Andromedae, have been confirmed as having planets, but it has not been established that any of them have planets in the supposed habitable zone.  Gliese 581, a star that was discussed in earlier articles posted on Useless-Knowledge.com, lies outside this region.

What is a parsec exactly anyway?  A parsec is the distance to a point in space that has a parallax of one second.  The parallax of a point is the angle between two lines emanating from the star, one of which passes through the Sun and the other through the Earth at a time when a line from the Earth to the Sun is perpendicular to a line from the point in question to the Sun.  In other words, for a point at a distance of one parsec, we have a triangle with one angle of 0º0’1”, one angle of 89º59’59” and one angle of 90º.  Opposite the small angle, we have the mean distance of the Sun from the Earth, called an AU (astronomical unit), which, according to NASA, is 149,597,879.691 kilometers (92,955,812.8 miles).  To calculate the length of a parsec, therefore, we must multiply 1 AU by the cotangent of 1 second.  One second is equal to 1/3600 of a degree.  So we merely get the reciprocal of tan (1/3600), which is equal to 206,264.8062.  This means that 1 parsec = 206,264.8062 AU = 3.085677765 x 10¹³ kilometers = 1.917351272 x 10¹³ miles.  Multiplying this by 5, since we are speaking of 5 parsecs, we get 3.085677765 x 10¹³ kilometers = 1.542838883 x 10¹⁴ kilometers (9.586756359 x 10¹³ miles). 

Such distances are beyond direct human comprehension.  Who can form an accurate mental picture of 96 trillion miles?  The only thing we can do to get some idea is reduce these distances to a scale model.

We have begun by creating an imaginary sphere in space with a radius of five parsecs.  This sphere, with the Earth at its center, contains 66 stars.  If we reduced this sphere to the size of the planet Earth, reducing the planet Earth proportionally, how big would the Earth become? 

The Earth has a mean polar radius of 6356.750 kilometers (3949.900 miles).  So if we reduce 5 parsecs to the mean polar radius, we calculate the following quotient: 1.542838883 x 10¹⁴ kilometers / 6356.750 kilometers = 24,270,875,570.  We have reduced by a factor of around 24 billion.  If we divide the radius of earth by the same factor, we get this calculation: 6356.750 kilometers / 24270875570 = .000000261 kilometers.  Multiplying this by 1000, we see that the radius of the reduced Earth is .000261 meters.  Multiplying again by a thousand, we see that the radius of the reduced Earth is .2619 millimeters, about 1/100 of an inch, 10 mils, 5 times the thickness of a vinyl garbage bag.

It’s hard for me to imagine that people living on a such a microscopic particle in a space the size of the Earth could take it for granted that they have the run of the space. 

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