Earthrise / Christmas


Earthrise, taken aboard Apollo 8 by Bill Anders on 24 December 1968 (NASA photo).

With Christmas coming up, it seems appropriate to post this iconic photograph, taken by Lunar Module Pilot Bill Anders on 24 December 1968, while orbiting the moon in Apollo 8. The team also did a live television broadcast, in which Anders read from Genesis:

For all the people on Earth the crew of Apollo 8 has a message we would like to send you: In the beginning God created the heaven and the earth. And the earth was without form, and void; and darkness was upon the face of the deep. And the Spirit of God moved upon the face of the waters. And God said, Let there be light: and there was light. And God saw the light, that it was good: and God divided the light from the darkness.

Command Module Pilot Jim Lovell continued: “And God called the light Day, and the darkness he called Night. And the evening and the morning were the first day. And God said, Let there be a firmament in the midst of the waters, and let it divide the waters from the waters. And God made the firmament, and divided the waters which were under the firmament from the waters which were above the firmament: and it was so. And God called the firmament Heaven. And the evening and the morning were the second day.

Commander Frank Borman closed: “And God said, Let the waters under the heavens be gathered together unto one place, and let the dry land appear: and it was so. And God called the dry land Earth; and the gathering together of the waters called he Seas: and God saw that it was good. And from the crew of Apollo 8, we close with good night, good luck, a Merry Christmas, and God bless all of you – all of you on the good Earth.

And the same from me.


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Looking back: 1982

In 1982 (35 years ago!) I finished my basic undergraduate degree, majoring in Mathematics and Computer Science (after sniffing around the job market, I continued my studies for an honours year). This was the year that the compact disc and the Commodore 64 computer came out:

Also that year, Stephen Cook won the Turing award for his work on computational complexity theory. The then Soviet Union landed two spacecraft in the hellish inferno that is Venus, and took photographs:

It was also a year of conflict – Argentina started a war with the UK over the Falklands Islands, and Israel invaded Lebanon. On a more positive note, there were several movies which became cult classics, such as Tron, E.T., and Conan the Barbarian. The superb science fiction movie Blade Runner stood out from the crowd (even with the flaws in the original cinema release):

In literature, Isabel Allende published her debut novel, as did Kazuo Ishiguro. In music, The Alan Parsons Project released their album Eye in the Sky and Australian band Icehouse (originally Flowers) released their classic single “Great Southern Land”:

Overall, it was a great year (apart from the wars).


Her pale fire she snatches from the sun

Shakespeare writes “the moon’s an arrant thief, and her pale fire she snatches from the sun” (Timon of Athens, Act 4, Scene 3). He is, of course correct. The moon merely reflects sunlight, and produces no light of its own. One way of telling this is that moonlight actually displays the same telltale absorption spectrum as sunlight:

Our eyes tend to perceive moonlight as “blueish” or “silvery,” but that is because of the way our eyes work at low light levels. Long-exposure photographs under moonlight, like this one, look much like daytime shots:

Anaxagoras (499–428 BC) seems to have been the first to discover that the moon shines only by reflected light:

Anaxagoras also explained that solar eclipses occur when the moon moves between the earth and the sun. Total solar eclipses are dark precisely because the moon produces no light of its own:


Measuring the Earth this (Southern) Christmas

In around 240 BC, Eratosthenes calculated the circumference of the Earth. The diagram above (from NOAA) shows how he did it. This Christmas, people in the Southern Hemisphere can repeat his work!

Eratosthenes knew that, at the summer solstice, the sun would be directly overhead at Syene (on the Tropic of Cancer) and would shine vertically down a well there. He also knew the distance to Syene.

On 21 December, the sun will be directly overhead on the Tropic of Capricorn at local noon. This table show the time of local noon on 21 December 2017, and the distance to the Tropic of Capricorn, for some Southern Hemisphere cities:

City Local Noon Distance to Tropic (km)
Adelaide 13:14 1270
Auckland 13:19 1490
Brisbane 11:46 450
Buenos Aires 12:52 1240
Darwin 12:45 1220
Hobart 13:09 2160
Johannesburg 12:06 310
Melbourne 13:18 1590
Perth 12:15 940
Santiago 13:41 1110
Sydney 12:53 1160

At exactly local noon, Eratosthenes measured the length (s) of the shadow of a tall column in his home town of Alexandria. He knew the height (h) of the column. He could then calculate the angle between the column and the sun’s rays using (in modern terms) the formula θ = arctan(s / h).

You can repeat Eratosthenes’ calculation by measuring the length of the shadow of a vertical stick (or anything else you know the height of), and using the arctan button on a calculator. Alternatively, the table below show the angles for various shadow lengths of a 1-metre stick. You could also attach a protractor to the top of the stick, run a thread from the to of the stick to the end of the shadow, and measure the angle directly.

The angle (θ) between the stick and the sun’s rays will also be the angle at the centre of the Earth (see the diagram at top). You can then calculate the circumference of the Earth using the distance to the Tropic of Capricorn and the fact that a full circle is 360° (the circumference of the Earth will be d × 360 / θ, where d is the distance to the Tropic of Capricorn).

Height (h) Shadow (s) Angle (θ)
1 0.02
1 0.03
1 0.05
1 0.07
1 0.09
1 0.11
1 0.12
1 0.14
1 0.16
1 0.18 10°
1 0.19 11°
1 0.21 12°
1 0.23 13°
1 0.25 14°
1 0.27 15°
1 0.29 16°
1 0.31 17°
1 0.32 18°
1 0.34 19°
1 0.36 20°
1 0.38 21°
1 0.4 22°
1 0.42 23°
1 0.45 24°
1 0.47 25°
1 0.49 26°
1 0.51 27°
1 0.53 28°
1 0.55 29°
1 0.58 30°
1 0.6 31°
1 0.62 32°
1 0.65 33°
1 0.67 34°
1 0.7 35°
1 0.73 36°
1 0.75 37°
1 0.78 38°
1 0.81 39°
1 0.84 40°
1 0.87 41°
1 0.9 42°
1 0.93 43°
1 0.97 44°
1 1 45°

Origins of the alphabet

This chart shows the origins of the Phoenician, Hebrew, Greek, and Latin alphabets. The Phoenician alphabet is adapted from Egyptian hieroglyphs, but the exact pictorial origins are rather uncertain. The specific Phoenician alphabet used is from here. The chart was produced using R.


The R100 and the R101

An instructive saga in the history of engineering is the story of the British airships R100 and R101. As part of a grand social experiment, the R100 was built by private industry (it was designed by Barnes Wallis), while the R101 was built by the British government (specifically, by the Air Ministry, under Lord Thomson). The R100 worked fine, and made a test flight to Canada in August 1930 (the trip took 78 hours). Here is the R100 over a Toronto building:

The R100 was huge. Here is a size comparison of the R100 (219 m long) and an Airbus A380 (73 m long):

While the government-built R101 used servo motors to control its gigantic rudder, the R100 team had worked out that the rudder could actually be operated quite easily by hand, using a steering wheel and cables. The government-built R101 was beset by poor choices, in fact. It contained overly heavy engines, a steel frame, and too much dead weight overall. After construction, the R101 had to be lengthened by inserting a new 14-metre section in the centre, in order to increase lift. This alteration caused a number of problems. Its design also allowed the internal hydrogen-filled gasbags to chafe against the frame, there were serious problems with the outer covering, and several “innovative” design ideas were never properly tested.

There was enormous political pressure for the R101 to fly before it was ready to do so. On the evening of 4 October 1930, it departed for India with a crowd of VIPs on board. It never arrived, crashing in bad weather over France, and bursting into flames. The disaster led to the R100 also being grounded, and the British government abandoned any thoughts of flying airships (as the rest of the world was to do after the Hindenburg disaster).

There are all kinds of lessons to be drawn from the saga of the R100 and the R101. One of them is that optimism is not a viable strategy for safety-critical engineering. Another is that engineers test things. As Kipling says, “They do not preach that their God will rouse them a little before the nuts work loose.” A third is that risky designs and fixed deadlines simply do not mix.