Cosmic Calendar Exercise
Find out first the time when the following events have occurred. Then use the
accompanied mathematical formula to calculate each event’s corresponding time in a
yearly calendar, as if the whole history of the universe happened in one year. Two
events, “the Big Bang” and “dinosaurs appeared,” have been done for you as
examples.
(Carl Sagan, the Cornell University astronomer, was the first person to explain the
history of the universe in one year--as a "Cosmic Calendar"--in his book The Dragons
of Eden, published in 1977.)
Examples:
January 1 Time 00.00.01 - The Big Bang (13.73 billion years ago)
December 26 - Dinosaurs appeared (225 million years ago)
-----------------------------------------------------Events:
the earliest mega stars
the earliest galaxies
formation of the Sun and the Solar System
formation of the Earth
first life on Earth
first animal fossils--simple organisms in ocean
dinosaurs disappeared
first hominids
first Homo sapiens-modern humans
invention of agriculture and the beginning of civilization
birth of Buddha
birth of Confucius
birth of Christ
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Cosmic Calendar Math
You can use fractions to scale events in the history of the universe to one year.
Presently scientists estimate the age of the universe to be 13.73 billion years. So one
way to calculate this more carefully, is to set up the following ratio:
years ago the event happened
------------------------------------------years ago the Big Bang occurred
=
x days
-----------365 days
Solving for x, you can calculate the number of days counting backward from the end
of the cosmic year. Then count back the days on the calendar beginning with
December 31 to find the date that corresponds to x days.
Notice that the units of time (years, days, etc.) are the same on the top and bottom of
each ratio. That is, some number of years divided by the total number of years equals
some number of days divided by the total number of days. Unfortunately, many
people seem to think that the unit of time (or the dimension of any number) is
incidental or unimportant. Not true! Use the units as a check to see that your equation
is set up correctly. If the dimensions of the numbers are the same on the top and
bottom, then the dimensions actually cancel out - just like numbers do! So the
dimensions years/years cancels out on the left and the dimensions days/days cancels
out on the right. That leaves you with the sensible result that a certain (dimensionless)
fraction on the left equals the (dimensionless) fraction on the right. If you master this
trick (called dimensional analysis) you can even use it to eliminate incorrect answers
on multiple choice tests!
Example:
Astronomers estimate that galaxies formed 13 billion years ago. Setting up the ratio
and assuming an age for the galaxy of 13.73 billion years:
13 billion years
----------------------13.73 billion years
x
= ------------365 days
2
13
x
= ------- * 365 days, or x
13.73
= 345.59 days.
So the formation of galaxies in the cosmic calendar year happened about 345.59 days
before the present moment (midnight, Dec. 31), or about 19.41 days after midnight,
January 1 (January 19).
The ratio above works well for periods of time that are significant fractions of the age
of the universe. But when you get to events closer to our time (such as the birth of
Buddha), days are too large a subdivision and you need to develop a scale of hours, or
even minutes, on December 31 of the cosmic year.
To do this, subdivide the last day into 24 parts and divide the last of those 24 parts
into 60 subdivisions. Can you see how the following formula was derived?
number of years ago the event happened
-------------------------------------------------13,730,000,000 years
=
x minutes
--------------------525,600 minutes
525,600 is the number of minutes in a year. So now your answer, x, will be the
number of minutes before midnight on December 31 of the cosmic calendar.
(Adapted from http://www.astrosociety.org/education/astro/act2/cosmic3.html.)
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