I don’t know if I’ll ever get a tattoo—I’m rather squeamish about needles and would almost certainly change my mind about any tattoo I did get shortly after doing so—but I do have an idea or two for them. This is one such idea.
Search for solar system tattoo online and you’ll find page after page of similar-looking designs. What they all have in common is inaccuracy. This led me to wonder, what would an accurately-scaled solar system tattoo actually look like? Obviously, this can be accurate only in terms of distance—to try and include the relative sizes of the different planets as well would leave them all invisibly small. To prove this, simply look at the diameter of the largest object—Sol, at 695,700 km across—and the distance of the furthest planet from Sol—Neptune, at 4.5 billion km. At that scale, even if you had a canvas 100 m long with Sol at one end and Neptune at the other, Sol would be 2 cm wide. Obviously, humans tend to be rather shorter than 100 m, so we shall have to ignore the size of the bodies.
I don’t know if I’ll ever get a tattoo—I’m rather squeamish about needles and would almost certainly change my mind about any tattoo I did get shortly after doing so—but I do have an idea or two for them. This is one such idea.
Search for solar system tattoo online and you’ll find page after page of similar-looking designs. What they all have in common is inaccuracy. This led me to wonder, what would an accurately-scaled solar system tattoo actually look like? Obviously, this can be accurate only in terms of distance—to try and include the relative sizes of the different planets as well would leave them all invisibly small. To prove this, simply look at the diameter of the largest object—Sol, at 695,700 km across—and the distance of the furthest planet from Sol—Neptune, at 4.5 billion km. At that scale, even if you had a canvas 100 m long with Sol at one end and Neptune at the other, Sol would be 2 cm wide. Obviously, humans tend to be rather shorter than 100 m, so we shall have to ignore the size of the bodies.
However, we can use accurate distances for our tattoo. In that case, where should we place each planet? I’ll go through a couple potential placements, helpfully illustrated using the guys from the Pioneer plaque.
Below is each solar body and their distance from Sol (in km):
Sol, 0
Mercury, 57,000,000
Venus, 108,000,000
Terra, 150,000,000
Mars, 228,000,000
Jupiter, 779,000,000
Saturn, 1,430,000,000
Uranus, 2,880,000,000
Neptune, 4,500,000,000
Normalising these values to the range \( \left[0, 1\right] \) produces (to 2 dp for readability):
Sol, 0.00
Mercury, 0.01
Venus, 0.02
Terra, 0.03
Mars, 0.05
Jupiter, 0.17
Saturn, 0.31
Uranus, 0.64
Neptune, 1.00
Let’s say that the average person is around 175 cm tall, from the balls of their feet to the top of their head. The head is about \( \frac{1}{7} \) of that, and we might want to remain employable after getting this tattoo, so discounting it leaves us 150 cm to work with. Multiplying each normalised value by 150 gives us the following distances in cm (to 1 dp)
