# Binary Code on the Pioneer 10 Spacecraft

The Pioneer 10 (also known as Pioneer F) spacecraft, launched in 1972 and now on a very long journey towards Taurus, has a plaque mounted on it which is designed to inform alien civilizations about the spacecraft’s origin. The plaque contains a diagram of our solar system, the trajectory of the spacecraft, a drawing of a man and woman, and groups of vertical and horizontal strokes — you guessed it, binary code — that gives information about how to find us:

Disclaimer: I’m a computer scientist, not a physicist or astronomer.

## Binary Encoding

The binary information in the diagram is encoded as groups of vertical strokes (|) and horizontal strokes (—). | means 1, and — means 0. For example, |—|— is 1010. Each group of strokes represents a binary integer, and there are binary integers associated with three entities: pulsars, planets, and people. I’ve annotated the original diagram and highlighted their encodings in gray:

## Hydrogen As a Yardstick

The hydrogen atom, indicated by the two circles at the top left of the diagram, serves as a universal reference for time and distance. Specifically, the atom’s hyperfine transition, which is about 1420 MHz, is the base of measure. A frequency of 1420 MHz gives a period of about 7.04 * 10-10 seconds, and a wavelength of about 8.3 inches. These numbers are implied as units in other parts of the diagram.

## Pulsars

There are 14 radial lines in the diagram, representing the positions of 14 pulsars relative to the sun. Pulsars emit radio waves at a different frequencies, which helps identify them. The waves emanate across much of the galaxy, so presumably an alien culture could detect them and locate our solar system. Also, since a pulsar’s frequency decreases with time, aliens could use that to determine when the spacecraft was launched.

Each pulsar line is labeled with an encoded binary integer, which is read in the direction of the gray arrows I’ve drawn. Starting at the unlabeled line (appearing at 3:00 in the diagram) and heading clockwise, those numbers and their decimal equivalents are:

Binary Encoding of Pulsar Periods
Pulsar Number In Binary In Decimal
1 1000110001111100100011011101010 1,178,486,506
2 10110010011000101011101101111 374,101,871
3 100000110110010110001001111000 551,117,432
4 111100011011011001010100111 126,726,823
5 10101011011001101100101000011 359,455,043
6 101100111011010101011110001011 753,751,947
7 10110011100000101010000010 47,057,538
8 100111101000110101000100111000100 5,320,116,676
9 111100011111100011111000010110 1,014,906,390
10 101101100101101001000010110001 764,842,161
11 101111001111001110011000001101 792,520,205
12 11110010111110001110100011110 509,549,854
13 10011001011010111010010111000 321,746,104
14 100000110100101010001110101100 550,675,372

These numbers represent the period of the pulsar’s radiation, counted in units of 7.04 * 10-10 seconds. Multiply each integer by 7.04 * 10-10 to get the period.

## Planets

The binary code for each planet indicates its average distance from the sun. (Pluto is included because it was still considered a planet in 1972.) The distances are relative to Mercury’s distance from the sun, which is given as 10 units. For example, Saturn is 24.7 times farther from the sun than Mercury. Confusingly, the wavelength derived from the hydrogen atom plays no role in these values.

Binary Encoding of Distance from Sun
Planet In Binary In Decimal
Mercury 1010 10
Venus 10011 19
Earth 11010 26
Mars 100111 39
Jupiter 10000110 134
Saturn 11110111 247
Uranus 111101111 495
Neptune 1100001100 780
Pluto 1111111100 1,020

## People

The height of the woman in the diagram is encoded by the |— — —, which is 1000, or 8 in decimal (nevermind that it’s written from the bottom up and one of the horizontal strokes has a defect in it). If you multiply this by the reference unit of length, 8.3 inches, you get the height of the woman — about 5 feet, 6 inches.

## Commentary

Will aliens know how to read binary code? Will they know that the binary code represents binary integers? Will they understand that the units of distance and time associated with those integers, in most cases, are derived from properties of the hydrogen atom? Will they make numerous other assumptions required to understand that plaque? Not likely. But the scientists wanted to make an attempt at communication, and having chosen binary is a testament to its simplicity and universality.

## Other References

1. A funny, yet informative, article about the plaque.
2. Details on the science of pulsars.
3. The Pioneer 11, also known as Pioneer G, was launched in 1973, with the same plaque.

1. Thank you. This is a great article. I really appreciate you writing it.

2. By the way, the distances at the bottom of the plaque use a different font for the “1” digits. It uses something like a Roman Numeral “I” (“seriff” with “feet” as opposed to “sans seriff”) this is so that the space aliens would just know that this font change signals the change to calculations unrelated to hydrogen. Seriously, that’s what a 1973 article about the plaque says.

3. Bruce,

Interesting, thanks. Any chance that 1973 article is online somewhere?

4. Dear Rick:

Yes, it was scanned many years ago, but it appears whoever did the scanning did not understand what to do. Instead of saving it as a text file, the article is saved as artwork, as a jpg file. You will have to save the web pages that it is on, and then use adobe photoshop or microsoft paint to open it and zoom it and read the very grainy text.

Each piece of the article is located here:

Have a good day,

Bruce Steo

5. Bruce,

Wow — great stuff. Thanks! My eyes hurt from reading it, but it was worth it. (Oddly, under Firefox, I get “403 Permission Denied”; but the images load under IE.)

I like the detailed rationale they give as to why they think it will be interpreted correctly; it still may be a stretch, but they make good arguments.

Here are some quotes I liked:

“The serifs on the binary “ones” are presented to stress that the units are different from those of pulsar length and period.” (RR: Bruce, this is the one you pointed out.)

“The large number of digits is the key that these numbers indicate time intervals, not distances or some other quantity. … There are no other
conceivable quantities that we might know to ten significant figures…”

“The problem of which end of a number is the most significant digit is expressed automatically in this formulation, since all binary numbers start with a 1 but end in a 1 or a 0.” (RR: this is how you know to read the binary numbers correctly, which is in the direction I’ve drawn the arrows).

“The binary notation, in addition to being the simplest, is selected in order to produce a message that can suffer considerable erosion and still be readable. In principle, the reader only need to determine that there were two varieties of symbols present, and the spacings alone will lead to a correct reconstruction of the number.”

6. Dear Rick:

Here is a handy chart that students might like to use:

100 centimeters = 1 meter
convert meters to centimeters by multiplying by 100
299792458 meters per second = C (speed of light)

29979245800 centimeters per second = C (speed of light)
1427583133 hertz = f (Frequency for Hydrogen)
21 centimeters = lambda (wavelength for Hydrogen)
7.004845999 X 10 -10 (period for Hydrogen) = T
0.0000000007004845999 seconds = T = period for Hydrogen

lambda is a letter of the greek alphabet used for wavelength

T is the letter used in physics to represent period
T= the time needed for just one wave (the period)

C is the letter used in physics to represent speed of light
hertz means “waves per second,” or frequency

velocity (speed of light) = frequency (hertz) X wavelength (lambda)
velocity = frequency X wavelength

T= period = 1/frequency (hertz)

wavelength (lambda) = velocity (speed of light) / frequency (hertz)

one second
1427583133
1010101000101110011000010011101
| – | – | – | – – – | – ||| – – || – – – – | – – ||| – |

one minute
85654987980
1001111110001011011110110010011001100
| – – |||||| – – – | – || – |||| – || – – | – – || – – || – –

one hour
5139299278800
1001010110010010110000110111001111111010000
| – – | – | – || – – | – – | – || – – – – || – ||| – – ||||||| – | – – – –

one day (24 hours)
123343182691200
11100000010111000010010100101101111101110000000
||| – – – – – – | – ||| – – – – | – – | – | – – | – || – ||||| – ||| – – – – – – –

7. tom says:

The map of the Solar System doesn’t show any of the satellites in orbit around any of the other worlds that are pictured. Saturn is shown with a line through it? And you had Pluto, but not Ceres or Sedna or Quaror? This is pretty much nit picking, but would the ‘aliens’ assume we thoroughly mapped our own star system before we launched an ‘Interstellar probe’? With the primitive nature of the technology designed in the craft… could it be concluded that the probe was used only as a ‘flyby’ and had no propulsive or extreme long life power to do an interstellar mission? Could the decayed RTGs be used as a way to date the ‘age’ of the probe? Since the pioneer was shown twice in the plaque, will they use its ‘scale’ to measure the ‘humans’? The male has 5 fingers spread with one hand;and the probe is shown flying inclined around the 5th planet? When the pioneer has been sitting in an alien museum for 10 million years, will the message be understood?