How We Deal with Larger Scales
To make a model of the Universe on larger scales, we have to start over since Dallas is already pretty far away. Let's make the sun the size of a grain of salt. Now the next star is only about 5 miles away, and the center of the Milky Way galaxy in which we live is -- 40,000 miles. If we shrink the entire Milky Way - about 100,000 miles in diameter on this scale - to only ten feet, then the more distant galaxies we study are 100 miles away. The Universe is huge, so large its size is hard to describe.
Our usual units of feet, miles, meters, and kilometers seem inadequate to measure something so gigantic, so we use units of "light years" and "parsecs". A light year is the distance light travels in a year. Light goes a distance equivalent to traveling all the way around the earth in just over a tenth of a second. It takes about 8 minutes for light from the sun to traverse the 93 million miles to the earth.
Let's try to compute how far a light year is. We use the formula distance = speed X time (where X means "times" or multiplication). The speed of light is 3 X 1010 cm/sec, 30 billion centimeters per second. A year has 3.2 X 107 sec (test this by multiplying 60 seconds per minute times 60 minutes per hour times 24 hours per day times 365.25 days per year). Light therefore travels
3 X 1010 cm/sec X 3.2 X 107 sec = 9.6 X 1017 cm in a year.This is about 6 X 1012 miles, 6 trillion miles.
Just for practice, how many light years is it from here (Tucson) to Dallas, assuming the distance is 1000 miles?
1000 miles is 1000/.62 kilometers, or 1600 km = 1.6 X 103 km.
1 km is 105 cm
So the distance to Dallas is 1.6 X 103 km X 1 X 105 cm/km = 1.6 X 108 cm.
Light travels that distance in 1.6 X 108 cm/3 X 1010 cm/sec = 5.33 X 10-3 sec = 0.00533 sec
In years, this converts to 5.33 X 10-3 sec/3.2 X 107 sec/year = 1.67 X 10-10 years
Therefore, the distance from Tucson to Dallas is about 1.67 X 10-10 light years.The distance to the nearest star is 4 light years.
Try some examples of your own at http://janus.astro.umd.edu/astro/distance/ and http://janus.astro.umd.edu/astro/sizes.html.