"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.