# Solar Tattoos

• This piece was written over a year ago. It may no longer accurately reflect my views now, or may be factually outdated.

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.

## The Numbers

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 $[0,1]$ produces (to 2 d.p. 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 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 d.p.)

• Sol, 0.0
• Mercury, 1.9
• Venus, 3.6
• Terra, 5.0
• Mars, 7.6
• Jupiter, 26.0
• Saturn, 47.7
• Uranus, 96
• Neptune, 150

## 1. Forearm

An average forearm is around 30 cm long. This gives us distances of 4 mm (for Mercury) up to 30 cm (for Neptune). Let’s include the Asteroid Belt too:

## 2. The whole arm

An average human arm is around 63.5 cm long. This gives us 8 mm (for Mercury) and 63.5 cm (for Neptune).

## 3. The whole body

Finally, we’re back to our 150 cm. This gives us 19 mm (for Mercury) and 150 cm (for Neptune).

## Conclusion

I think it would look quite neat, particularly the whole body one. If you ever changed your mind, you could always just pass them off as birthmarks.

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