Bathroom-Tissue Universe

Next time you look at a roll of bathroom tissue, you, too, may be inspired to think about the universe.

toilet rollOne day not long ago, I found myself lost in thought, contemplating the universe, when my gaze fixed on the roll of bathroom tissue on the shelf beside me. “More than 400 sheets,” the label proclaimed.

Four hundred is a popular number in astronomy. The distance to the Sun is 400 times the distance to the Moon. Thus if you were to unroll the entire roll of bathroom tissue, the length of one tissue would represent the distance from Earth to the Moon, and the whole roll would be the span from Earth to the Sun. Along the way, we would pass Venus around tissue number 135 and Mercury about tissue number 260.

Inspired, I unrolled the complete roll. At 424 sheets, I realized that this was also a perfect interstellar measuring tape. In 1994, the European Space Agency’s Hipparcos satellite precisely measured the distance to Proxima Centauri, the nearest star to the Sun. At 4.22 light-years, Proxima is two tenths of a light-year closer than Alpha Centauri, a famous bright star visible from the southern hemisphere. (Despite being the nearest star beyond the Sun, Proxima is too faint to be visible from Earth without a telescope.)

If we assign a distance of one one-hundredth of a light-year to the length of a single sheet of tissue, the whole roll is almost exactly the correct length to reach Proxima. If the Sun is a dot marked at the beginning edge of the first sheet, then Pluto, the most distant planet, is about 5 millimetres away. Voyager 2, launched way back in 1977 and the most remote spacecraft from Earth, is less than 12 millimetres from the Sun. It will reach the other side of the first tissue in the year 2181.

Suppose we increase the scale by 100. Now one sheet equals one light-year. Proxima Centauri is on tissue number 4. At the end of the roll is Polaris, the North Star, slightly more than 400 light-years from the Sun (and Earth).

Andromeda wide

The Andromeda Galaxy, M31. Courtesy Gary Seronik.

Increasing the scale by 10 this time, one sheet now equals 10 light-years. Proxima Centauri is less than halfway along the first sheet of tissue. At the end of the roll, 4,000 light-years distant, is the next spiral arm of the Milky Way, our home galaxy. You can see this spiral arm every summer as the glowing band of the Milky Way.

We’re not through yet. Let’s make the length of each tissue 100,000 light-years. Now the entire 90,000-light-year-wide Milky Way fits on one tissue. The Andromeda Galaxy, the nearest large galaxy similar to the Milky Way, is on tissue number 24. At the end of the roll is M87, the central giant galaxy in the Virgo supercluster of galaxies. At 45 million light-years from us, it is the nearest supercluster and is so big that the Milky Way and Andromeda Galaxies are not considered part of it.

One final expansion: Each tissue sheet is now 30 million light-years long, big enough to hold most of the Virgo supercluster—10,000 galaxies in total. At the end of the roll are the most distant galaxies known, 12 billion to 13 billion light-years from our solar system. We can’t go much farther, because we encounter the energy wall emitted long, long ago by the Big Bang creation of the universe. But that’s for another contemplative moment.

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