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Quantitative Assignment 1
The availability of new astronomical instruments, called spectrographs, have allow us to
measure galaxies’ speeds using Doppler shifts, or visible changes in wavelengths commonly
called “redshifts”. The distance could then be calculated using reference points of specific
variable stars called Cepheids. Using Hubble’s law (V = H0 ∙ D, where V = velocity1, H0 = the
Hubble Constant or 70 km/s/Mpc, and D = distance) and the time formula (T = 1 / H0 in units of
(km/s) / Mpc, where T = time and Mpc or megaparsecs = 3.086 ∙ 1022 m) as an inverse of
velocity, one can find the age of the universe.2 In this instance, H0 = 70 km/s/Mpc and 1 Mpc =
3.086 ∙ 1022 m.
T = 1 / H0
T or time is equal to the inverse of H0. Therefore, to solve for T, one must divide 1 by H0. The
formula can be rearrange to include the Hubble Constant, 70 km/s/Mpc, and the conversion of
units for megaparsecs, in which 1 Mpc = 3.086 ∙ 1022 m.
T = 1 / [(70 km/s) / 3.086 ∙ 1022 m)]
Since 1 kilometer equals 1,000 meters, the Hubble constant can be changed for meters for easier
conversion between distance and time.
T = 1 / [(70 ∙ 1000 m/s) / 3.086 ∙ 1022 m)]
70 kilometers is 70,000 meters, so 7 ∙ 104 meters can be substituted. This will allow both units of
distance, or meters, in H0 and the megaparsecs conversion to cancel out, thus leaving an
expression of seconds.
T = 1 / [(7 ∙ 104 m/s) / 3.086 ∙ 1022 m)]
The equation’s numerical values are separated from its units of measurement for easier division.
Numbers, powers of ten, and units are isolated.
T = 1 / [(7 / 3.086) ∙ (104 / 1022) ∙ (m / s ∙ m)]
1. Velocity1: In layman’s terms, velocity is a measurement of speed in a certain direction.
Direction is not a necessary component because the number calculated will eventually be
converted into time.
2. According to the metric system, seconds is abbreviated as “s” rather than “sec”.
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To relieve the equation of extra mathematical operators, the last part of the equation that consists
of units can be simplified through negative exponents. Numbers and units in the denominator of
a fraction can be expressed as the same base with negative exponents. For example, 100 m/s can
be expressed as 100 m s-1.
T = 1 / [(7 / 3.086) ∙ (104 / 1022) ∙ (m ∙ s-1 ∙ m-1)]
The equation can simplified to cancel out the duplicated meters, thus leaving only units of time
left. Meters multiplied by its inverse, or m-1, equals 1. The expression omits the number “1”
because any number multiplied by 1 is equivalent to the previous value as seen in the expression
“5 ∙ 1 = 5”.
T = 1 / [(7 / 3.086) ∙ (104 / 1022) ∙ (s-1)]
The expression’s mathematical operators can be carried out, so that it may later be divided by 1
for H0’s inverse. The numbers are not simplified until the end for accuracy.
T = 1 / 2.26830849 ∙ 10-18 s-1
The denominator is divided by 1 for preparation when multiplying by larger units of time.
T = 0.4408571492 ∙ 1018 s, or 4.408571492 ∙ 1017 s
To find the age of the universe in years, seconds must be multiplied by its conversion according
to minutes, hours, days, and years.
1 year = 365 days/year ∙ 24 hours/day ∙ 60 minutes/hour ∙ 60 seconds/minute
When the previous conversions are multiplied out, the direct conversion from 1 year to seconds
remains.
1 year = 31,536,000 seconds, or 3.1536 ∙ 107 s
The new value can be integrated into a simple division equation to reduce the powers of 10 to
include years.
T = 4.408571492 ∙ 1017 s / 3.1536 ∙ 107 s
The equation’s numerical values are separated from its units of measurement for easier division.
Numbers, powers of ten, and units are isolated again.
T = (4.408571492 / 3.1536) (1017 / 107) (s / s)
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The expression’s mathematical operators can be carried out, so that it seconds canceled out and
is replaced by years for the unit of measurement. “7” is subtracted from 17 to reduce the powers
of 10 and normal division follows for the numerical values at the front of the equation.
T = 1.39794885 ∙ 1010 years, or 13,979,488,500 years
Therefore, the value can be simplified (according to sudo-significant figures) to billions of years.
T = 13.979 billion years
As Carl Sagan said, “it is far better to grasp the Universe as it really is than to persist in
delusion, however satisfying and reassuring” (Sagan 12). While the meaning of the universe may
never be completely obtainable, its pursuit allows us a sense of humility as we are engulfed by
the sheer magnitude of information. Among all knowledge is the age of the universe itself, which
happens to be almost 14 billion years old and begs the question: How can an origin for the
universe exist? Without a starting point, everything would commence ad infinitum; before point
A, there lies another point, and point beyond that…In reality, the origin of the universe—or
anything for that matter—is man-made for simplicity as Ockham’s razor postulates.
Naturally, the theory that the universe undergoes a period of expansion until collapsing
on itself and later “bouncing” back is—more often than not—rejected. A cyclical universe does
not provide one with the same concrete evidence that the Bible has provided through Genesis
and the Popol Vuh3 through “The Creation of Earth.” However, many people fail to realize all
processes are looped and intertwined, such as with respiration and photosynthesis. Instead, most
people view processes with a terminal as from life to death (without the decomposition phase). If
this is the case, can we truly place the origin of the universe at the Big Bang? The answer is no,
but how the universe formed remains open to interpretation.
Some scientists hope that the age of the universe will aid our understanding of its
formation (Randall). Others figure that the age of universe will help bridge the gap between the
scientific notion of the age of the universe and the idea from the Bible that the universe was
created in six days. As humans, we find little solace in the unknown and seek shelter under an
umbrella of theories and ideas, such as the Big Bang and religion as the Maya had found with the
Popol Vuh. This blissful ignorance eventually led to the Maya’s collapse as leaders were no
longer able to bring rain (Moyes). The Maya were not the only people to organize under a
common principle as the Bible much of Western Europe. While tying the origin of the universe
to a certain date could help predict future cosmological patterns, such as solar flares, and bring
society together under a unified fact, the origin and age of the universe merely humors us with
trivial knowledge (for now).
3. Works of religious text, such as the Bible and the Koran, are not italicized.
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Works Cited
Moyes, Holley. “Maya Culture and the Popol Vuh.” CORE. COB 102, Merced. 8 Sept. 2011.
Lecture.
Randall, Lisa. Warped Passages: Unraveling the Mysteries of the Universe’s Hidden
Dimensions. New York: Harper Perennial, 2006. Print.
Sagan, Carl. “The Most Precious Thing.” The Demon-Haunted World: Science as a Candle in
the Dark. New York: Random House, 1996. 12. Print.