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Measuring in the mid-point of the lines, the circle is about one fortieth of the width of the frame of the comic. The absolute circle size depends on the display resolution, size and mode, but it can reasonably be taken to be 1mm diameter, or 0.5mm radius, giving a total area π r<sup>2</sup> or about π/4 square millimeters. You're probably holding the phone about a half a meter away from your eye. The surface area of a sphere is 4 π r<sup>2</sup>. With a radius of one-half meter, that comes out to be π square meters. Thus, the area of the circle is about 1/4000000 of the area of the sphere, 200 billion galaxies divided by 4 million is the 50,000 average mentioned in the cartoon. A similar mathematics was used for the comic [[1276: Angular Size]], in which the projective sphere was at the Earth's own radius and cross-sectional areas of objects were compared, rather than an approximate count of objects within a given angular spread.  
 
Measuring in the mid-point of the lines, the circle is about one fortieth of the width of the frame of the comic. The absolute circle size depends on the display resolution, size and mode, but it can reasonably be taken to be 1mm diameter, or 0.5mm radius, giving a total area π r<sup>2</sup> or about π/4 square millimeters. You're probably holding the phone about a half a meter away from your eye. The surface area of a sphere is 4 π r<sup>2</sup>. With a radius of one-half meter, that comes out to be π square meters. Thus, the area of the circle is about 1/4000000 of the area of the sphere, 200 billion galaxies divided by 4 million is the 50,000 average mentioned in the cartoon. A similar mathematics was used for the comic [[1276: Angular Size]], in which the projective sphere was at the Earth's own radius and cross-sectional areas of objects were compared, rather than an approximate count of objects within a given angular spread.  
  
While galaxies usually are between 3,000 to 300,000 {{w|light-years}} across and contain between 10^8 (100 million) and 10^14 (100 trillion) stars, most are so far away from the Earth (upwards of billions of light-years) that they are invisible to the naked eye, or even through most telescopes. When magnified across such vast distances, even something as small as a pinhole expands to huge sizes, easily able to fit tens of thousands of galaxies.
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While galaxies usually are between 3,000 to 300,000 {{w|light-years}} across and contain between 10^8 (100 million) and 10^14 (100 trillion) stars, most are so far away from the Earth (upwards of millions of light-years) that they are invisible to the naked eye, or even through most telescopes. When magnified across such vast distances, even something as small as a pinhole expands to huge sizes, easily able to fit tens of thousands of galaxies.
  
 
The premise of this comic is that although galaxies are giant, space is <i>unimaginably</i> big and contains a vast number of things. Randall is apparently overwhelmed by this, as shown in the caption: ''Astronomy Fact: There are too many galaxies''.  
 
The premise of this comic is that although galaxies are giant, space is <i>unimaginably</i> big and contains a vast number of things. Randall is apparently overwhelmed by this, as shown in the caption: ''Astronomy Fact: There are too many galaxies''.  

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