THE SOUTHWORTH PLANETARIUM
207-780-4249       www.usm.maine.edu/planet
70 Falmouth Street  Portland, Maine 04103
43.6667° N                   70.2667° W
Founded January 1970
        "Onwards and upwards!"



THE DAILY ASTRONOMER
Monday, July 18, 2016
Tanning in Arizona and Falling through Earth


Today's trip to Pandora keeps us planted firmly on Terra Firma.     Though
we often describe astronomy as the science concerning all things beyond
Earth's atmosphere, it truly involves everything and anything in the
Universe which, incidentally, is everything and anything.

The first question is asked by someone who often spends time in Arizona,
where life is beautiful all the time.  The second was asked by a freshman
physics student.    Both questions were placed in Pandora's Jar and now are
extracted.

*"If I spent 20 minutes out in the sun in Maine and 20 minutes in the sun
in Arizona, would I tan at the same rate?  Also, how do time zones affect
this. For instance, 10 am in AZ compared to 1 pm in Portland?"*
C. Jean,  Portland, ME

First, we should explain why some people tan (as opposed to some of us of
Northern European stock who sizzle even under fluorescent lights.)
Tanning -and burning- is caused by UV (Ultra-violet) radiation, a type of
electromagnetic radiation that is of higher energy than visible light.*
UV rays can inflict damage on DNA and RNA within cells, so the body has
developed an effective defense mechanism.    The UV photons can both
stimulate melanin in your skin and can generate more melanin.   Melanin
darkens the epidermis, thereby reducing the UV rays' penetrative
power.      So, is not the Sun's heat that causes the burn, but its UV
radiation.   The sunlight that strikes the top of the atmosphere consists
of about 8% UV light, with larger amounts of visible and infrared
radiation.     Fortunately, the atmosphere absorbs the majority of this UV
radiation.   At maximum -when the Sun is at the zenith- about 3% of the
ground-striking solar radiation consists of UV radiation. **   The lower
the Solar angle, however, the greater the UV absorption.

Let's examine the difference between Portland, Me and Phoenix, Az,. Well,
as far as sun angles are concerned.  In every other respect they are so
similar as to be interchangeable.
Portland's approximate latitude is 43 degrees, whereas Phoenix's latitude
is about 33 degrees.      The Sun will always appear higher in Phoenix's
sky than it does in Portland's because it is closer to the equator.    For
instance, on the summer solstice, the Sun is 70.5 degrees above the
southern horizon in Portland, but will be 80.5 degrees above the southern
horizon in Phoenix.     Therefore, the UV absorption rate will be greater
in Portland than in Phoenix and the rate at which a sun bather tans will be
greater in Phoenix, AZ than Portland, Maine.

In regard to the time zone issue, well, that relates to the Sun's
elevation, which is the important factor in determining the tanning
rate/      For instance, at 10:00 a.m. on June 21st in  Phoenix, the Sun's
elevation is 55.7 degrees.  At the same moment, the Sun's elevation in
Portland is 69.5 degrees.    Even though Phoenix is closer to the equator,
the Sun is closer to the meridian in Portland at 1:00 p.m. than it is in
Phoenix at the same time 10:00 a.m.    As the UV absorption rate is solar
elevation dependent, one will want to go out for a tan around noon, the
approximate -though generally not exact- time when the Sun crosses the
meridian and attains its highest elevation for the

Granted, one can tan -and burn- in both regions so we advise caution when
basking in Sol's radiance.

*"I read a physics 'thought' problem that mentioned someone falling through
Earth.   It said that if a hole were dug from the north pole to the south
pole and then someone jumped into that hole, he would just oscillate back
and forth between poles.  Why is this?  Also, what is the deepest hole ever
dug on Earth?"*
L Waters, Windham, ME

We'll address the last question first as it is the easier of the two.
The deepest artificial point on Earth remains the SG-3 borehole that was
part of the Soviet Union's "Kola Superbore Hole" project initiated in
1970.   The SG-3 borehole extended down a depth of 12,345 meters (an easy
number to remember), which is equal to 40,502 feet.  This depth is, alas,
only about 0.09% of the planet's polar diameter*** of 12,713 km.    It will
be quite awhile before we consider drilling through the planet.

As for your first question.  The scenario of someone jumping into a hole
extending between both poles is a common one used to illustrate the
physical principle of gravity.   If we did have such a hole and if we did
make it stable, as well as regulated its pressures, temperatures and oxygen
levels. (All big "ifs') a person would oscillate.     To explain how it
works, let's imagine someone at the north pole standing at this hole.  We
push him in and watch as he rapidly falls into the hole as he would in any
other hole.   When he first falls, a lot of material is below him pulling
him down.  However, as he descends, more material will become positioned
above his head.   The person's acceleration slowly decreases during the
descent as the ratio of matter above his head to that below his feet
increases.     When reaching Earth's core, this ratio is equal to one.
Though he is not experiencing any acceleration at that moment, his momentum
still pushes him toward the south pole.  As he approaches the other end of
the hole, the matter above his head exerts a breaking force that becomes
increasingly stronger.  By the time he reaches the South Pole, he will have
slowed down to rest and then will "fall" back toward the north pole as
though he had dived into it.  The same process will continue.

Of course, the acceleration is maximum at the hole's opening and then
gradually decreases as he approaches the core.  Then, the acceleration
toward the other direction slowly increases as he approaches the hole's
opening.

Like many of the other physics thought problems, it uses an absurd scenario
to illustrate a physical principle.


*The UV band consists of many sub-sets.  It extends from the comparatively
low energy UV that is adjacent to the visible spectrum (around 400
nanometers) to the extreme ultraviolet (around 10 nanometers) which is
adjacent to the x-ray band.

**We admit that we are not delving too deeply into details.   Absorption is
wave-length dependent: meaning that some wavelengths of UV light are
absorbed more than others.    Some UV light never reaches the ground at all
as it is wholly absorbed, for instance, by ozone (a chemical consisting of
three oxygen atoms.)

***Earth's polar diameter (the distance separating the poles) is not equal
to its equatorial diameter, the distance separating opposite points along
the equator.   The equatorial diameter is  12,756.27 km.  The equatorial
diameter is greater than the polar diameter because Earth is an "oblate
spheroid." It "bulges" as a consequence of its rotation.