THE SOUTHWORTH PLANETARIUM 207-780-4249 www.usm.maine.edu/planet
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70 Falmouth Street Portland, Maine 04103 43.6667° N
70.2667° W Altitude: 10 feet below sea level Founded January 1970 Julian
Date: 2459354.18
2020-2021: CXXXIII
THE DAILY ASTRONOMER
Thursday, May 20, 2021
Amazing Astronomy Questions
_______________________
Welcome back, daughter! Today's DA is lovingly
dedicated to my older daughter Jacqueline who returned from
an overseas adventure and brought her adoring father
an Icelandic air-sick bag as a present. There is nothing
worse than a sarcastic sense of humor
_______________________
A while ago, we posted "Amazing Astronomy Facts" in four parts. These
articles elicited a few amazing astronomy questions that we shall happily
answer today. (We have also included a question based on one of this
week's articles.)
*What is Zeno's paradox?*
*-C.W.*
Zeno's paradox simply states that motion should be impossible. Imagine a
race between the swift-footed Achilles and a lethargic tortoise.
[image: im-318904.gif]
*Do you want Achilles to catch the tortoise? Stare at any point midway
between them*
*and wait a few moments. *
Achiles, being a nice fellow, gives the tortoise a head start.
Consequently, according to Zeno's paradox, Achilles should never be able to
overtake his opponent despite the former's superior running ability. Why?
Well, in order to reach the tortoise, Achilles must first cover half their
separation distance and then must next cover half of the remaining distance
and then half of that distance and so forth. (For instance, if they are
separated by a mile, Achilles must run half a mile. He then must run a
quarter of a mile, then an eighth of a mile, then a sixteenth of a mile, et
cetera,) Meanwhile, the tortoise continues to move and since Achilles has
to continue traveling at half distances, he shouldn't be able to pass the
tortoise at all.
[image: Zeno_Dichotomy_Paradox-696x331.png]'
Of course, in the physical world, Achilles will be able to easily overtake
the tortoise. We ascribe to Zeno of Elea (490-430 BCE) who likely devised
it to expose the absurdity of Parmenides' assertion that motion is
illusory.
*What does it mean when one says a "star is born?"*
*-S.B. *
Stars form after a gaseous nebula collapses in on itself. Gravitational
attraction draws the material into different clumps that experience
compression and internal heating. Eventually, the internal temperature is
sufficient to ignite thermonuclear fusion reactions inside the object's
core. A star is considered active (i.e. a star is born) when the core
thermonuclear fusion reactions begin.
*[image: in-a-nuclear-fusion-reaction.jpg]*
*A star is born when thermonuclear fusion reactions begin in its core.
According to recent estimates, at least 3,000 stars are born every second
in the Universe.*
*Could you explain again how astronomers know the distances to nearby
stars? I can't believe that light needs more than 4 years to travel from
the nearest star to the Sun.*
*-Nancy K. *
We would be happy to explain parallax again. Stellar parallax illustrates
how a branch of mathematics as terrestrial as 'geometry,' can be used in
the service of celestial science. We'll begin with a famous
illustration. Find an object in your background, such as a tree or a
stop sign. Close one eye and extend an index finger out in front of
your face. Align the finger with the chosen background object. While
keeping the finger steady, close the open eye and open the closed eye.
You might notice that the finger's position relative to the background
object shifted. If you extend the finger out to its maximum extent and
repeat the demonstration,* you'll observe the shift is small. If you hold
the index finger just in front of your face and repeat the demonstration,
the shift will be quite large.
[image: smile-000-000-002-513.jpg]
The apparent shift of an observed object's position resulting from a change
of perspective is called "parallax." With the previous demonstration,
we've established an inverse relationship. The closer the object, the
greater the parallax angle.
We can apply the same principle to the stars.
Astronomers can measure the position of a star relative to the background
stars at one moment and then, in six months -when Earth is as far from its
original orbital position as possible- the astronomers measure the star's
location again. Provided the star is sufficiently close,** its parallax
angle will yield its distance.
[image:
500px-Stellar_parallax_parallel_lines_from_observation_base_to_distant_background.png]
Without delving into all the delicious details pertaining to right angle
trigonometry, we can share a simple equation relating the parallax angle
and the distance. If the distance is expressed in parsecs -one parsec
equals 3.26 light years- and the parallax angle is expressed in
arc-seconds,*** the star's distance is 1 divided by the parallax angle.
In 1838, Friedrich Wilhelm Bessel estimated the distance to the star 61
Cygni based on the observed parallax angle. Though his calculation of 10.3
light years was about ten percent less than the currently accepted value of
11.4 light years, Bessel was the first to successfully employ stellar
parallax to measure a star's distance.
*We could have referred to this exercise as a 'experiment,' except that it
was nothing of the sort. Any exercise that will yield a known result is a
demonstration. An exercise that will lead to a result that, though
predicted, isn't certain, is an experiment.
**For ground based observations, the range has been about 500 parsecs. (A
parsec equals about 3.26 light years.)
***One degree can be equally sub-divided into 60 arc-minutes. One
arc-minute can be equally sub-divided into 60 arc-seconds. An arc-second
is a particularly small angle.
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