The Antimatter Calculator
In the original series Star Trek episode Obsession, Captain Kirk
tells an ensign that one pound of antimatter can destroy a solar system. The truth
is considerably less dramatic. One pound of antimatter equates to 19.5 megatons, which
is comprable to a modern day H-bomb. In order to help prevent such mistakes from
occurring in the future, I present the anti-matter caculator. Just plug in the amount of
antimatter you're thinking of using and the calculator will return just how much destructive
force it contains.
A megaton is a unit of energy approximately equivalent to the energy released
in the detonation of 1,000,000 tons of TNT. Used to specify the energy output, and hence
destructive power, of nuclear weapons.
A kiloton is one-thousandth of a megaton.
To put things in perspective, here are some famous explosions from history and theory
along with their yields:
Seymour Narrows, British Columbia 1958. 1,375 tons of chemical explosives. |
1.375 kilotons |
Little Boy, the atomic bomb dropped on Hiroshima, Japan on August 6, 1945. |
13 kilotons. |
Fat man, the atomic bomb dropped on Nagasaki, Japan on August 9, 1945. |
20 kilotons. |
The Tanguska Event, suspected comet impact in Tanguska, Russia on June 30, 1908. |
10 megatons |
The Bravo test, one of the Bikini Atoll bomb tests. February 1954, was, at 15 megatons, the most
powerful bomb ever detonated by the United States--far bigger than expected. |
15 megatons |
One pound of antimatter |
19.5 megatons |
Mount St. Helen May 18, 1980. |
24 megatons |
Tsar Bomba, the largest nuclear weapon ever detonated 11:32 AM 30 October 1961 (Moscow Time) Such a device could be souped up to deliver a 100 megaton blast. |
50 megatons |
The third 1883 eruption of Krakatoa |
150 megatons |
Hurricane Katrina hitting the Gulf Coast. At full power, a hurricane like Katrina releases
10 megatons every 20 minutes. |
300 megatons |
World War III, computed as the simultaneous explosion of all known nuclear devices (about 15,000 today). |
10,000 megatons |
"Dinosaur Killer" Impact of 10-15 km asteroid traveling at 20 kilometers per second. |
100,000,000 megatons or 10^8 megatons |
A supernova, an explosion powerful enough to destroy a solar system. |
10 billion billion billion megatons or 10^27 megatons |
The Math
Several people have asked to see the math behind the calculations above.
We start with Einstein's famous equation E = M*C^2
(The energy contained within a given amount of mass = That mass times the speed of
light squared)
E is expressed in joules, which is kilograms times (meters/second)^2,
so the first thing is to convert 1 pound into it's equivalent in kg.
(A few people who wrote me on this had problems because they used grams instead of
kilograms. If your answer is 1,000 times greater than mine, that's your problem)
1 ounce equates to 0.0283495231 kilograms
Aside:
Be careful here. Pounds are a measure of weight and kilograms
are a measure of mass. An objects weight can vary while its mass
remains constant. I presume here that we're talking one pound of mass at
sea level on earth halfway between the equator and one of the poles. I never saw
Captain Kirk on a planet that didn't have 9.8 m/s^2 for some reason.
Aside
English to metric conversion was the real killer on this project.
16 ounces in a pound * 0.0283495231 = 0.453592368 kg.
Also, we have to annihilate the antimatter with an equal amount of matter, so
2 * 0.453592368 kg = 0.907184736 kg.
Aside:
Anti-matter annihilation expresses its energy as a burst of high-frequency gamma
radiation and high-speed neutrinos. Drop a pound of antimatter on the floor and you'll
see a bright flash of light and then nothing else for the remainder of your very short
life! The difficulty in getting antimatter to "blow up" is one reason why the
US never developed an antimatter bomb.
(0.907184736 kg) * (2.9979e8 m/s ^ 2) = 8.15E+16 joules
There are 4.18e15 joules in a megaton, so 8.15E+16 joules equates to 19.51 megatons.
By their own admission, most of the writers on Star Trek had no idea what
antimatter was, which is why we got wildly inaccurate statements like "One pound
can destroy a solar system" or if two identical pieces of matter and
antimatter meet, it's total annihilation of you, me, everybody!
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Antimatter Calculator
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