I.  Introduction

A.  Man's Quest to Understand Mars

    Man has long felt that the best place to look for life
in our solar system is the planet Mars.  In fact, at the
turn of the century [1], near the period of the Lowell
frenzy of canals a decade later, a publication offered a
reward for anyone coming forth with proof of life on another
planet or anywhere in space excepting Mars.  They felt that
Mars would soon be proven to possess life, even including
intelligent life.
    Just about every major observatory, at the beginning of
this century, had released hand paintings of Mars and some
were even releasing photographs as astrophotography was
up and coming.  If you examine these drawings and compare
different observers' sketches you see quickly that no two
could agree on the formations on the planet's surface.  What
is of importance to this study is the fact that even these
showed a Mars with a varied surface possessing darker and
lighter areas, as well as those polar caps.
    The first successful Mars flyby mission was Mariner 4
[2], whose closest approach came on July 15, 1965. The
pictures from this mission were most disappointing for all
those Lowellians.  There were no canals and the surface was
disappointingly looking like that of the moon, and quite
lifeless.
    In 1969 the United States launched two successful craft
to Mars.  Mariner 6 was launched in February and Mariner 7
in March.  In the summer, July for Mariner 6 and August for
Mariner 7, both craft made their closest approach to Mars at
a distance of approximately 3400 kilometers.  Each craft
contained not only narrow and wide angle cameras, but also
an infra-red radiometer, infra-red spectrometer and an
ultra-violet spectrometer.  The temperature, pressure and
atmospheric constituents were analyzed [2].  The pictures
were still anything but spectacular, and Mars was very
disappointing to many.
    The year 1969 also saw two unsuccessful attempts by the
Russians to rendevous with Mars.  These failures were
repeated nearly two decades later, when probes sent to
rendevous with the Martian moon Phobos failed to complete
their mission.  In 1971, both the Americans and Russians had
an unsuccessful missions to Mars.  But 1971 was also a
successful year for both nations.  The Russians had Mars 2
and Mars 3, both equipped with lander modules but neither
successful in their attempts.  The Americans had Mariner 9
[3] which had the unfortunate circumstance to reach Mars
during a global dust storm.  However, the storm did
eventually subside and the mission was enough of a success
so as to provide pictures for the choosing of a site for
landing the upcoming Viking missions [3].
    The Viking missions were first approved in December of
1968 for a 1973 launch [4].  In May of 1969, Martin
Marietta received a contract for $250 million to build the
landers while the mother craft was put together by the
Caltech Jet Propulsion Laboratory using the same technology
as that used on Mariners 8 and 9.
    As is typical, the launch date was postponed due to
Congressional funding cutbacks.  Someone then came up with
the great idea to launch the craft in 1975 for a landing to
take place on Independence Day in 1976.  Viking 1 was to be
launched on August 11, 1975 but was postponed due to a
malfunction.  While fashioning repairs for the spacecraft,
the twin unit was substituted and so Viking 2 became Viking
1 and vice versa.
    Finally, on August 20,1975 the first Viking craft was
successfully launched, to be followed by the second on
September 9, 1975 [5].  Each Viking orbiter consisted of a
television camera system, a atmospheric water detector and
an infra-red thermal mapper [4,5].  Each Viking lander was
imbued with a television camera system, gas chromatograph
mas spectrometer, x-ray fluorescence spectrometer,
seismometer, biology lab, weather station and the vital
sampler arm. Each spacecraft also conveyed with their
aeroshell a retarding potential analyzer and an
upper-atmosphere mass spectrometer [4,5].
    Although Viking 1 did arrive at its Martian destination
by June 19,1976 the attempt to gain beneficial pictures to
aid in the choice of a landing site for the lander caused a
delay in the landing beyond its Independence Day rendevous
[5].  Using the latest pictures, the western slopes of
Chryse Planitia were selected for the landing [6].
    On July 20, six years after man had taken his first
steps on the moon, the Viking lander successfully descended
upon the soil of Mars [5].  Immediately after successful
touchdown, the lander had instructions for taking pictures
with its camera (there was actually a concern that the
lander might sink into the soil, and so at least a picture
was desired before it conceivably had sunken).
    The Viking cameras were not cameras in the conventional
sense [7,8].  Each consisted of a nodding mirror and a
rotating turret which caused the images to be reflected down
to the photodiode, which built up a picture as a series of
pixels from each scan of the mirror and rotation of the
turret [7,8].  Such a technique had been criticized for its
inability to detect any moving objects, as some still felt
it possible that there might be macroscopic creatures on the
planet [9].  It wasn't until July 22 that the sampler arm
was to be deployed.  However, due to difficulties, overcome
by ingenious engineers, the arm was deployed on July 28.
    The first instrument to give results on its sample was
the x-ray fluorescence spectrometer, which was on board in
order to determine the inorganic composition of the soil
sample [10].  Its results determined that the Martian
material was composed of between 15-30 percent silicon,
12-16 percent iron, 3-8 percent calcium and 2-7 percent
aluminum [10,11].
    The gas chromatograph mass spectrometer gave an
indication of carbon dioxide and a little water but no
organic compounds [12]. This marked the beginning of a
controversy which continues today, because this negative
result conflicted with results from the biology experiments
which were indicative, to some, of the existence of
microbial life [13-16].
    The biology laboratory, packed into approximately a
single cubic foot of volume on the Lander, consisted of a
pyrolytic release experiment, a labeled release experiment
and a gas exchange experiment.
    The labeled release experiment was headed by Dr.
Gilbert Levin [14,17,18].  The basis for his experiment was
that property of microorganisms to metabolize organic
compounds made available to them in a nutrient broth.  The
organics in the broth were tagged with carbon 14.  The soil
sample was initially wetted with the nutrient.  If there
were organisms in the sample which were metabolizing the
nutrient, the carbon-14 would appear in the chamber's gas by
the appearance of tagged carbon monoxide or carbon dioxide
[14,17].
    The pyrolytic release experiment was headed by Dr.
Norman Horowitz [13,19].  His experiment was also based on
the ability of an organism to metabolize, but in this case
he was looking for the ability of an organism to take
carbon dioxide and produce some product for its own use, a
reversal of the process sought by Levin's experiment.  The
soil sample was place in the test chamber for five days and
incubated with or without the presence of light.  If the
soil had somehow fixed or metabolized the carbon dioxide
which was tagged with carbon-14, then once the chamber had
been evacuated, the sample would be pyrolyzed and carbon
would be detected within it from the labeled gas [13,19].
    The gas exchange experiment was headed by Dr. Vance
Oyama [15].  It also was looking for evidence of metabolism
by noting changes in the gaseous environment of the sample.
First the sample would be introduced into the chamber and
the chamber's atmospered sampled and analyzed.  Then after a
period of incubation, the gas would be re-examined and any
differences between it's analysis as compared to the initial
analysis would by noted and viewed as a sign of activity.
    The initial results of all three biology experiments
registered results which were indicative of some very active
samples [13-16,18]. If these results were obtained here on
earth there would be no doubt that organisms were
responsible, but was that the case for the Martian samples?
There was immediate doubt of the biological results once the
GCMS had failed to detect any organics within the soil
sample [12].
    Theories dealing with superoxides, peroxides and
superperoxides all attempted to explain away the results of
the biological experiments [16].  Soon, there was only one
stubborn hold out for the possibility that these still might
indicate the existence of life on Mars, and that was Dr.
Gilbert Levin [14,18].

B.  The Physics Behind Thermal Conditions on Mars

    Planck's Equation relates the rate of emission of
radiation at a particular wavelength to the temperature and
the wavelength [20,21].  You can derive from this two of the
basic laws of radiation, the Stefan-Boltzmann Law and Wien's
Law [20,21].
    The Stefan-Boltzmann Law relates the total rate of
radiation of a black body (all wavelengths combined) to the
fourth power of the absolute temperature.  Wien's Law
relates the wavelength of the point of maximum intensity in
the continuous spectrum of a black body inversely
proportional to the body's absolute temperature.
    There is another physical relationship which was first
proposed by Lambert in 1760 and Beer in 1852 [22].  They
proposed that the amount of monochromatic radiant energy
absorbed or transmitted by a media is an exponential
function of the concentration of the absorbing substance
present in the path of the radiant energy.
    Another concept key to understanding the effective
radiative temperature on the planet Mars deals with the
reflectivity of the planet's surface and atmosphere.
Reflectivity is the fraction of incident light reflected
(an effective reversal in the photon velocity vector) from a
surface.  Normal reflectivity is that property whereby light
is caused to be reflected 180 degrees from a beam incident
normally (perpendicular) to the reflecting surface.
    When dealing with the reflective properties of a planet,
astronomers have developed the concept of Bond albedo [20].
The Bond albedo is the ratio of total incident light to
total reflected light.  It is a measure of global reflection
and absorption of sunlight and is often numerically smaller
than the normal reflectivity.
    The Bond albedo tells us the amount of solar energy
which is reflected and thus the amount of solar energy
absorbed.  Therefore, the albedo of a planet should, to a
first approximation, be able to tell us the effective
temperature for a planetby using the Stefan-Boltzmann law
which expresses the radiation emitted by a "perfect
radiator" at a specific temperature.
    If you've ever looked at a planet through a telescope,
or just glanced at the full moon some night, it is apparent
that the surface of a planet is not anything close to
uniform and thus it's surface temperature would be expected
to vary in a non-uniform manner.  Astronomers have defined
the effective temperature as that temperature which
satisfies the energy balance of the planet when the absorbed
sunlight is equated to the emitted thermal power.
    In examining the albedo to temperature relationship, it
is noted that the area of the planet is a required
parameter.  Now the area of a flat surface is pi times the
radius squared but that of a surface of a sphere is four
times the flat surface area.  Astronomers assume that the
planet radiates energy from the entire surface but only
absorbs the energy on one face of the planet, thus leading
to the equation provided [20,21].
    There is another type of albedo used by astronomers,
referred to as the geometric albedo [20].  The geometric
albedo is the ratio of the blobal brightness, viewed in the
direction of the sun, to that of a hypothetical surface
which is white, diffusely reflecting, and possesses the same
surface area at the same distance from the sun.
    Numerically, the geometric albedo is just about the same
as the standard reflectivity, as defined previously.  Also,
because of how the geometric albedo is defined, it is
possible to have a geometric albedo greater than one, that
is the boday reflects more light than the reference white
body sphere.  One body in the solar system with a geometric
albedo greater than one is the moon of Saturn known as
Enceladus (geometric albedo 1.1) [20].
    Astronomers have also defined a simple relationship
between the Bond albedo and the geometric albedo which is
known as the phase integral.  In many cases the Bond albedo
and the geometric albedo have a ratio of 2 to 3, i.e. the
Bond albedo is two-thirds the geometric albedo [20].
    In addition to the radiation laws of physics that one
must take into consideration when dealing with the energy
balance of the planet Mars, there is the matter of the
orbital dynamics of the planet.
    Johannes Kepler was the first to derive the laws of
planetary motion.  Simply put, Kepler derived a fundamental
description of the motion of the planets, without
understanding the force of gravity that guides the planets.
Classically, his findings are divided into three laws
[20,21].
    Kepler's first law states that all planets follow
ellipses about the sun, where the sun is at one of the foci
of the ellipse.  Kepler's second law states that the line
joining the centers of mass of the sun and a planet covers
an area that increases at a constant rate as the planet
moves in its orbit.  This second law is often stated in
other terms, i.e. the radius vector sweeps over equal  areas
in equal periods of time, regardless of where the planet is
in its orbit.
    Finally, Kepler's third law states that the square of
the sidereal period divided by the cube of the planet's mean
distance from the sun forms a ratio that is the same for all
of the planets, i.e. a constant.

II. The Planet Mars

A.  Physical Characteristics

    Here I present some of the physical characteristics of
the planet Mars and a comparison to the same characteristics
of the our own planet Earth.
    When it comes to comparisons, size is the first that
many consider.  Mars is of course smaller than the Earth,
with a diameter of 6794 kilometers compared to Earth's 12756
kilometers.  This little fact can be used to calculate the
ratio of the surface areas of the two planets which is a key
consideration in the heat balance of a planet.  The surface
area of Mars is only 28 percent of the Earth's.
    After size, another key characteristic is mass which is
linked to the density of the planets under consideration.
Mars has a density of 3.9 grams per square centimeter while
Earth possesses a density of 5.5 grams per square
centimeter.  The total mass of Mars turns out to be only
10.7 percent of the mass of Earth.
    Another key parameter in the study of heat balance of a
planet is the distance from the source of all the energy,
namely the sun.  Mars is approximately 228 million
kilometers from the sun, about 1.52 AU, or more than 50
percent further from the sun than our own Earth which, being
at 1 AU, is about 150 million kilometers from the sun.
    When considering the radiation both absorbed by the sun
facing side of a planet and the amount radiated into space
by the darkside, one parameter that helps in the
understanding of the heat balance of the planet is the
rotation rate, i.e. the length of a day.  The Earth day is
some 86,400 seconds in length, and as it turns out the
length of a typical Martian day is approximately 88,640
seconds long, only about 2 percent different.
    Another factor influencing the thermal balance of a
planet is of course the obliquity of the planet which causes
the seasons in the northern and southern hemispheres to be
opposite of one another.  The Earth's obliquity is about
23.5 degrees, while Mars possesses an obilquity of about 25
degrees.  Again, fate has decreed some very similar numbers
in this realm.
    Following Kepler's laws the solar orbital period for
Mars can be calculated in Earth days and one finds that the
Martian year is about 687 Earth days long.
    Another important physical characteristic of Mars that
is relevant to any study of the heat balance of the planet
is the fact that the Martian orbit is more elliptical than
Earth's.  The eccentricity of the Earth's orbit is 0.017
while Mars comes with an eccentricity of orbit of 0.093,
over 5 times that of Earth's.
    The eccentricity causes the planet Mars to be as near to
the sun as 1.38 AU at perihelion and as far from it as 1.66
AU at aphelion.  The amount of radiation received near
perihelion is about 40 percent larger than the amount of
radiation received from the Sun at aphelion.  This combined
with the obliquity of the planet produces a relatively long,
cool northern summer and a short, hot southern summer.  I
hope to elaborate on the fact that the precession of
perihelions through this cycle produces important climatic
changes on Mars.

B.  The Martian Atmosphere

    The first close-ups of the Martian atmosphere were
provided by the Mariner series of spacecraft.  When Mariner
9 began orbiting the planet, the atmospheric scientists
effectively had the cameras to themselves because of the
presence of a global dust storm which prevented viewing the
Martian surface.
    Images from Mariner 9 illustrated the progress of a
feature that looked very much like a terrestrial cold front
[24].  The front was visible as a bright band extending
across many of the images.  There was evidence of an intense
dust storm associated with strong northerly winds.  On the
third day of imaging, a large crater rim was seen to produce
wave clouds, believed to be compose of water ice, which
resembled a "sonic boom shock wave."  Apparently, the clouds
were being produced by extremely strong low level winds
passing over the crater, and the day-to-day variations were
indicative of day-to-day weather changes and frontal
systems.
    The Viking Lander itself was equipped with a package of
meteorological instruments at the end of a boom that
deployed after landing.  The package contained thermocouple
units to measure the atmospheric temperature and wind
speed.  There was also an atmospheric pressure sensor which
was not on the boom so as to be shielded from winds.
    Wind speed was actually measured by using two
orthogonally oriented, heated sensors, together with an
unheated reference temperature sensor.  The power required
to maintain a constant overheat of the two orthogonal
sensors relative to the reference was measured and the
cooling due to the wind was determined.  From this the wind
speed could be determined but the velocity vector
determination required an additional thermocouple array.  It
worked like the proverbial wet finger, heat it, expose it to
the wind, and then measure which side is cooler [24].
    Seymour Hess produced the first Martian weather report:
"Light winds from the east in the late afternoon, changing
to light winds from the southwest after midnight. Maximum
winds were 15 miles per hour.  Temperature ranged from minus
122 degrees Fahrenheit just after dawn to minus 22 degrees
Fahrenheit.  Pressure steady at 7.7 millibars." [24]
    With long term data available from Viking Lander 1
through Novermber 5, 1982 and from Viking Lander 2 through
April 11, 1980, atmospheric scientists were able to learn
much about the Martian atmosphere.  They discovered the
nature of surface pressure variations over the Martian
seasons and the cycling of the atmosphere between the polar
caps.  The minimum in the pressure cycle occurs during the
southern winter when the carbon dioxide mass condensing onto
the south polar cap was at its maximum.  As the seasonal
carbon dioxide sublimes out of the south polar cap, the
pressure rises until the north polar cap starts to form.
The process reverses as the season changes and the carbon
dioxide begins to reform at the south polar cap as winter
ends in the norther hemisphere.  This cycling was observed
repeatedly by the pressure measurements made by the two
Viking Landers [24].
    There were other characteristics of the Martian
atmosphere deduced by the pressure measurements.  The
difference in pressures between the two landers could be
attributed to the difference in elevations between the two
sites.  However, there was also much apparent noise on the
pressure curves.  The spikiness, in the end, was determined
to not be attributable to noise, but associated with
traveling cyclones of the kind that had been speculated on
based on images from Mariner of the dust storms.  They
occurred only during the winter season and were detected at
both sites [24].
    Pressure variations were linked to optical depth
computations and demonstrated the presence of what
meteorologists call atmospheric tides.  Atmospheric tides
are not to be confused with gravitational tides.
Atmospheric tides are those wind and pressure variations
that are produced by the daily cycle of heating over the
whole atmosphere.  What results from the daily loading
cycle, among other things, are traveling waves that follow
the sun and have both diurnal and semidiurnal periods [24].
    The Viking Landers were also able to help produce charts
of meridional circulation on Mars.  On Earth we have the
familiar pattern of rising motion in the tropics and a
descending motion in the subtropics with a connecting
meridional flow pattern.  On Mars, there is a strongly
seasonally varying circulation rather than one centered
about the equator.  In the summer the air rises near the
subsolar point in the southern hemispherer subtropics and
crosses the equator to a point where it can descend.  It is
more like a one-cell circulation with a strong descending
motion in the winter hemisphere, rather than the two cell
motion that we have on Earth [24].

C.  The Martian Geology

    One may wonder why I choose to discuss the geology of
Mars in a paper which is to concentrate on the heat balance
of the planet.  Simply put, one of the key considerations in
developing a heat balance model of a planet is the amount of
solar energy reflected by that planet.  So an understanding
of the planets geology is crucial in developing a model of
the albedo, which is used in the model of the thermal
profile of the planet.
    Like all planets and moons in the solar system, Mars is
far from a uniform surface.  Mars is blessed with the
largest volcano in the solar system and a canyon so large as
to make the Grand Canyon on this planet seem small.
    Viking Orbiter imaging as well as the Mariner images
have provided us with a view of Mars whose global appearance
is roughly organized latitudinally.  The equatorial belt is
somewhat darker than the mean albedo and very changeable
over time.  The northern and southern mid-latitude regions
are brighter, due probably to the deposits of very fine,
bright material.  There is a dark collar around the north
polar region.  Then of course there is the polar regions
themselves with the very bright polar caps [25].
    Viking Orbiters acquired some high resolution images
which contributed to better understanding of the surface.
There was indication that the darker materials may be in
areas where the silicates are somewhat more reduced and
richer in ferrous rather than ferric silicates [25].
    The Viking mission itself was postponed by the selection
of a landing site.  The areas that were originally
considered for landing were found to be too hilly and more
suitable sites were selected.  However, it was certainly a
surprise to mission managers when the Lander actually found
itself in a field strewn with rocks, one of which called
Little Joe, was large enough that if the Lander had landed
in its vicinity, would have ended the mission disasterously.


III.Radiation Effects on Mars

A.  Solar Heating

    The sun is the source of energy for all planets in our
solar system.  Its radiation provides the heating of the
planet and the energy necessary for the formation of the
food chain of our Earth.  Mars suffers from its location
being further from the Sun.  It also suffers from a
eccentricity of orbit that causes variations that life here
on Earth would have difficulty in adjusting.
    The heating of a planet is, as has been alluded to in
previous sections here, related to the albedo of the planet,
i.e. the reflectance of that energy back into space.  Mars
has a varied surface as mentioned, and albedoes that range
from 0.34 for the brightlands and 0.17 for the darklands. 
The polar caps present an albedo of approximately 0.45 [26].
    The sun has been monitored by our most state-of-the-art
instrumentation and its radiation (integrated over the
spectrum) is well known.  Also well known is the fact that
the solar radiation is by no means a true constant.
    The solar radiation not only varies over its 11 year
sunspot cycle, but also presents variations even to a daily
cycle and yearly cycle.  Values for this are presented for
reference.  Of key note is that we really are unsure how
much solar radiation has varied over the period of the
existence of the planets.

B.  Thermal Radiation

    Mars, like the Earth, re-radiates some of the solar
energy it sees as thermal radiation out to space.  The
thermal radiation from Mars arises mostly from its surface,
since its atmosphere is so much finer than our own planet's
atmosphere, which does have a more significant role in the
re-radiation of the solar energy [26].
    The Martian atmosphere emits weakly under unobscured
surface conditions.  When dust stjorms are present, the
atmosphere absorbs sunlight directly and also radiates more
effectively.  The effect of increasing dust in the
atmosphere is to reduce diurnal temperature variation at
the surface.  On the other hand, the dust enhances
atmospheric thermal variation [26].
    Other components causing thermal radiation from the
surface of Mars is the dissipation of mechanical energy of
winds, of wind waves, atmospheric tides and the energy
transferred by the precipitation of carbon dioxide and
possibly water, at least at the poles.