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Two spacecraft launched in 1977 are now beyond the planets, each carrying a gold-plated record meant for anyone who might find it. One of them later turned around and took a picture of Earth as a single speck of light. Carl Sagan was behind both ideas. This post covers what he did, works through the physics on the record and in the photo, and ends with what students can learn from how he worked.
Who was Carl Sagan?
Sagan was a planetary scientist at Cornell University. NASA's page on the Pale Blue Dot describes him as a NASA consultant from the 1950s who briefed Apollo astronauts and, as a visiting scientist at JPL, helped design and manage missions including Mariner 9, the Viking landers and both Voyagers. He was a member of the Voyager imaging team. The Planetary Society, which he co-founded and served as its first president, notes that he won a Pulitzer Prize and was David Duncan Professor of Astronomy and Space Sciences at Cornell when he died on 20 December 1996.
What is on the Voyager Golden Record?
NASA's Golden Record overview calls it a time capsule: a 12-inch gold-plated copper disc of sounds and images chosen to portray life and culture on Earth. According to NASA's page on the record's contents, the selection was made by a committee chaired by Sagan. It holds 115 images, natural sounds such as surf, wind, thunder, birds and whales, music from many cultures and eras, and spoken greetings in 55 languages.
India is well represented. The list of greetings includes Hindi, Bengali, Marathi, Telugu, Kannada, Gujarati, Punjabi, Rajasthani, Oriya and Urdu. The Kannada greeting sends "good wishes" on behalf of Kannada-speaking people. Among the music on the record is the raga "Jaat Kahan Ho", sung by Kesarbai Kerkar.
NASA quotes Sagan on the purpose: "The spacecraft will be encountered and the record played only if there are advanced spacefaring civilizations in interstellar space. But the launching of this bottle into the cosmic ocean says something very hopeful about life on this planet."
How does the record tell its own age?
The making-of page explains that the aluminium cover carries an ultra-pure sample of uranium-238, which has a half-life of 4.468 billion years. A finder could measure how much has decayed and work out how long the record has been travelling.
Worked example. What fraction of the uranium-238 remains after 1 billion years?
Fraction left = (1/2)^(t / T½) = (1/2)^(1 / 4.468) = (1/2)^0.2238.
Take logs: 0.2238 × log₁₀(0.5) = 0.2238 × (−0.3010) = −0.0674. So the fraction is 10^(−0.0674) ≈ 0.856.
About 85.6% of the uranium would still be there. Because the half-life is so long, this clock works over billions of years, not centuries. Our post on radioactive decay and half-life covers the method in more depth.
How was the Pale Blue Dot taken?
NASA's Pale Blue Dot page explains that Sagan had the idea in 1981 to point one Voyager's cameras back at Earth. The team knew the images might show little, and that was the point: to let people see how small and fragile Earth looks from far away. On 14 February 1990, Voyager 1, about 6 billion km from the Sun, took 60 images for a "family portrait" of the solar system. The Earth frame was taken at 04:48 GMT, 34 minutes before the cameras were switched off for good, and Earth showed up as a point of light about a pixel in size. All the image data reached Earth by 1 May 1990.
In his book Pale Blue Dot, Sagan wrote: "Look again at that dot. That's here. That's home. That's us."
Worked example: how far is 6 billion km?
Light travel time. With c = 3.00 × 10⁵ km/s (from NASA JPL's astrodynamic constants), t = 6 × 10⁹ / 3.00 × 10⁵ = 2.0 × 10⁴ s, which is about 5.6 hours. A command sent to Voyager 1 that day took over five hours to arrive.
How big did Earth look? Earth's mean radius is 6371 km on NASA's Earth fact sheet, so its diameter is about 12,742 km. Earth was roughly as far from Voyager as the Sun was (Earth is only 1 AU, about 1.5 × 10⁸ km, from the Sun), so use 6 × 10⁹ km.
Angle = 12,742 / (6 × 10⁹) = 2.1 × 10⁻⁶ rad. Converting with 1 rad = 206,265 arcseconds gives about 0.44 arcseconds.
That is about the same size as the parallax shift Friedrich Bessel measured for 61 Cygni, and it shows why Earth was only a dot.
Common mistakes: mixing km and m in c, forgetting to double the radius, and leaving the angle in radians when the question asks for arcseconds.
What can a student take from Sagan?
Ask what a result means to people. A photo with almost no scientific detail became what NASA calls an iconic image, because of the question Sagan asked.
Work with many kinds of people. The record needed astronomers, musicians, linguists and engineers.
Explain your subject. Sagan wrote for the public as seriously as he did for journals.
When the scale of space is hard to picture, the Fermi Simulation Lab has interactive simulations for ideas that are easier to see than read.
Try it tonight: work out how long light takes to reach you from the Moon, the Sun and Voyager 1's 1990 position, and compare the three.
