The chart above shows approximate radiation releases (in becquerels) for some major nuclear disasters. It should be interpreted with caution, since some radioisotopes are more dangerous than others. For example, the releases from Three Mile Island were largely noble gases (mostly xenon), and that incident appears to have had few detectable environmental or health effects. Ticks on the vertical axis of the chart go up logarithmically, in steps of ×1000. For comparison, radium and bananas are also listed.
Following up on my “origins of the alphabet” chart, here is one for numerals. The chart was produced using R, and the pictures are purely illustrative – unlike the pictures in the alphabet chart, they do not relate to the origins of the symbols.
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.”
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:
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):
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:
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:
Distance to Tropic (km)
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).