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\begin{flushleft}
So we must realize that there are other worlds in other parts of the universe, 
with races of different men and different animals.\\
      --- Titus Lucretius Carus (99-55 B.C.)
\end{flushleft}

\section{Introduction}

For centuries human beings have wondered if their existed other forms of life 
on one of the other planets in our solar system, or on planets orbiting other
stars. While life might exist on the planet Mars, or in the subsurface oceans
of Jupiter's moon Europa, it is much more likely that life exists on planets
in orbit around other stars in the Milky Way galaxy. How can we discover 
this life, and where is the best place to look? In today's lab we will find out
how astronomers are finding planets around other stars, show how
hard it is to find these planets, determine which planets are the best hosts
for life, and how we might ultimately discover signs of life on these planets.

\section{What Does Life Need?}

Life appears to have been present for more than 3 billion years on Earth---given
that the Earth is 4.5 billion years old, life arose very quickly here. What
is it about Earth that is different from the other planets in our solar system
that made it the only known planet that harbors life? For one thing, the
Earth has a solid surface. Jupiter, and the other ``Jovian'' planets
(Saturn, Uranus, and Neptune), have enormous atmospheres that surround a
small rocky/metallic core. The pressure at the surface of this core is so
intense that large molecules cannot exist, and thus no life can evolve. If
life were to evolve on the Jovian planets, it would have to be some strange
form of life that could float around in the atmospheres of the gas giants. The 
{\it terrestrial} planets (Earth, Venus, Mercury and Mars) all have rocky 
surfaces. What else is important for life? We compare the surface conditions 
of the four terrestrial planets in Table 1.

\begin{center}
Table 1: The Properties of the Terrestrial Planets\\
~  \\
\begin{tabular}{|l|c|c|c|c|c|}
\hline
Planet & Mass & Distance & Atmospheric& Ave. Surface &Albedo\\
   & (Earth=1)& from Sun & Pressure   & Temperature &\\
\hline
Earth  & 1.00 & 1.0 AU & 1 Atm & 288 K (= 59$^{o}$F) &0.39\\
Mercury& 0.06 & 0.387  & 0     & 452 K (= 354$^{o}$F) & 0.10\\
Venus  & 0.82 & 0.723  & 92    & 755 K (= 899$^{o}$F)& 0.65\\
Mars   & 0.11 & 1.88   & 0.007 & 210 K (= $-$82$^{o}$F)&0.15 \\
\hline
\end{tabular}
\end{center}

From this table, it is clear that the surface temperatures of Mercury and 
Venus are much higher than that of Earth. Given that the boiling point of water
is 373 K (= 212$^{o}$F), liquid water could not exist on the surfaces of
Venus and Mercury. The reverse is true about Mars: the temperature at the
surface of Mars is usually so low, that water would generally stay frozen
all year long (though temperatures well above freezing on Mars do occur
depending on the martian season, and the elevation of the local terrain).
Most biologists believe that liquid water is required for life to evolve. Thus,
only Mars and the Earth seem capable of supporting life as we know it.

Why is Mecury hotter than the Earth? Because it is much closer to the Sun
than the Earth! The amount of heating of a planet by the Sun goes as
1/distance$^{\rm 2}$. This is one of the ``inverse square'' laws frequently
found in physics and astronomy--if you double the distance, the heating
goes down by a factor of four. We can use this relationship to understand
why the temperatures of Earth and Mercury are so different. Mercury has a 
distance to the Sun of 0.387 Astronomical Units (AU), while the Earth is at 
1 AU. The Earth is 2.58 times further away
from the Sun than Mercury. If we use the inverse square law, we find that
1/(2.58)$^{\rm 2}$ = 1/6.67 = 0.15. The Earth receives 0.15 times as much
energy from the Sun as Mercury does, thus the surface temperature of the Earth
is much lower than Mercury. To predict the actual temperature requires a
deeper understanding of physics, but the result is a simple equation:
T$_{\rm planet}$ = 395/R$^{\rm 1/2}$ K (that is 397 divided by the square root
of the planet's distance from the Sun measured in AU). This would
be the temperature of a planet if it absorbed all of the energy that
fell upon it. But all planets reflect some light, and a better prediction
for a planet's temperature comes from the equation: T$_{\rm planet}$ = 
277/R$^{\rm 1/2}$ K. Given that the Earth's distance from the Sun is 1 AU, the 
square root of 1 = 1, thus the equation predicts a temperature for the Earth 
of 277 K.

{\bf Exercise \#1:} Use the equation T$_{\rm planet}$ = 277/R$^{\rm 1/2}$ K 
predict the surface temperatures of Mercury, Venus, Earth and Mars. Compare 
them to the temperatures listed in Table 1. For which planets does this 
equation predict fairly accurate temperatures? Which planet does not seem to 
follow this law?

\vspace{2.7in}

If you compare your results from exercise \#1 to Table 1, we find that all
of the planets are found to be warmer than we would predict. Why is this? 
There are two answers---one for Mercury, and one for the other three planets. 
Mercury has a very elongated orbit (``highly eccentric''), and at closest
approach (``perihelion'') it comes as close to the Sun as 46 million 
kilometers, while at its furthest point (``aphelion''), it is 70 million 
kilometers distant! Thus,
while the average distance from the Sun for Mercury is 0.387 AU, the best
distance used to predict its temperature is harder to decide upon since the 
heating rate changes rapidly throughout its orbit. 

The reason that Venus, Earth and Mars are wamer than predicted can be seen
in Table 1: they have atmospheres. Atmospheres act like blankets in that
they let the Sun's energy in, but do not let it all back out. This is the
``greenhouse effect'', as diagrammed in Figure 1. The Sun emits most of
its energy in the visible portion of the electromagnetic spectrum (the 
light that our eyes can see). This visible light heats up the ground which
tries to re-radiate it back into space through infrared (``heat'') radiation. 
But greenhouse gases, such as water vapor and carbon dioxide, absorb this 
radiation and heat up the atmosphere, and this keeps the Earth, Mars, and Venus
warmer than they would be if they had no atmosphere. 

\begin{figure}[h]
\centering
\leavevmode
\epsfysize=0.3\textheight
%\epsfbox{EXOPLANETS/greenhouse.ps}
\epsfbox{greenhouse.ps}
\caption{The greenhouse effect. The atmosphere of a planet acts the same
way the glass in a greenhouse does: it lets in the visible light from the 
Sun, heats up the ground and air in the greenhouse, and when this heat tries
to escape it cannot, so the building is warmer than its surroundings. The
atmosphere of a planet works the same way in that it lets through most of
the visible light from the Sun, this is absorbed by the solid surface (or in the
oceans on Earth). The surface of the planet heats-up and tries to re-radiate
this energy back into space as infrared (``heat'' radiation). Infrared light is 
efficiently absorbed by molecules such as water vapor and cabon dioxide. }
\end{figure}

On Earth the dominant greenhouse gas is water vapor. On Venus and Mars it
is carbon dioxide--these two planets have atmospheres that are more than 95\%
carbon dioxide, compared to the Earth where carbon dioxide makes up only 
0.035\% of our atmosphere.
Carbon dioxide is highly effective in heating-up a planet. The reason Venus
is so much hotter than it should be is due to the incredibly thick carbon
dioxide atmosphere, causing the famous ``runaway greenhouse effect''. Mars
on the other hand has a very thin atmosphere, and thus the heating due to
the greenhouse effect is much smaller.

{\bf Exercise \#2:} In exercise \#1 you calculated what the temperature of 
Venus 
would be if it is wasn't for the runaway greenhouse effect. If Venus had an 
atmosphere similar to that of Earth, do you think you could live there? [To
convert the predicted temperature in Kelvin to Farenheit use the 
following equation: $^{\rm o}$F = 1.8*(K $-$ 255)]

\vspace{1.0in}

If you had all of the money, material and power to do anything you wished, how 
might you make Mars a more livable place (without moving it closer to the
Sun!!!)?

\vspace{1.2in}


Given that recent evidence suggests that Mars was warmer and wetter in its
youth, Mars may have once had a thicker atmosphere that it has now, and lost it
either because its mass, and hence gravity, was not large enough to retain
that atmosphere, or some other event caused the atmosphere to be lost.
Given that initial conditions in the early solar system could have been
different with a slightly altered history, Mars might have ended up as a 
bigger planet than it turned out to be, and thus could have had a denser 
atmosphere, a larger greenhouse effect, and might have been a nice place to 
live. Of course, the opposite is also true--if the Earth had ended up with an 
atmosphere like Venus, we would not be here! Understanding exactly why
the atmospheres of Venus, Earth and Mars ended up so differently is one of the 
unsolved mysteries in planetary science.

\section{The Habitable Zone}

With slightly different initial conditions, we can envision a solar system
with three ``habitable'' planets, planets where life, or even humans might
find a home. In our solar system, the ``habitable zone'' extends from about
the orbit of Venus out to the orbit of Mars. If an Earth-like planet is
inside the habitable zone, it is possible (with the right conditions) to be
a host for life. If we are going to identify which stars might be good places
to host solar systems with planets harbouring life requires us to examine
the habitable zones of other types of stars. In your lecture sections (or if
you have already completed the HR Diagram lab) you found out that astronomers
have seven main categories of stars that have dramatically different
temperatures: O, B, A, F, G, K, and M. Table 2 summarizes the various 
properties of these stars.

\begin{center}
Table 2: The Properties of Main Sequence Stars\\
~ \\
\begin{tabular}{|c|c|c|c|c|c|}
\hline
Star &Lifetime& Surface &Mass & Radius &Luminosity \\
Type & (years) & Temperature & (Sun=1)& (Sun=1)& (Sun=1)\\
\hline
O  &$\leq$ 3 million  & over 25,000 K  & 60  & 15 &1,400,000\\
B  & 80 million & 11,000 - 25,000 K &18 &7 &20,000\\
A  & 1.5 billion &7,500 - 11,000 K &3.2 &2.5 &80\\
F &5 billion &6,000 - 7,500 K &1.7 &1.3 &6 \\
G &10 billion &5,000 - 6,000 K &1.1 &1.1 &1.2\\
K &35 billion &3,500 - 5,000 K &0.8 &0.9 &0.4\\
M &$>$ 100 billion &under 3,500 K &0.3 &0.4 &0.04\\
\hline
\end{tabular}
\end{center}

It is obvious from this table, that if the Earth was orbiting at 1 AU from
an O-type star, it would receive more than a million times the energy that 
currently falls on its surface. This would probably be enough energy to entirely
vaporize the Earth---thus, such planets cannot form close-in to O stars.
For an M-type star, which only emits 4\% of the Sun's luminosity, a planet
orbiting at 1 AU would be a very cold place! Thus, the habitable zone is
very close to an M-type star (actually inside the orbit of Mercury).
A plot of the habitable zones for stars with spectral types between A and
M is shown in the next figure.

\begin{figure}[!ht]
\centering
\leavevmode
\epsfysize=0.3\textheight
%\epsfbox{EXOPLANETS/habzone.ps}
\epsfbox{habzone.ps}
\caption{The habitable zones for stars with spectral types of A, F, G, K, and
M (dotted horizontal lines on left side of diagram). The habitable zone is
the gray shaded region. The locations of the planets in our solar system, from 
Mercury to Pluto, are indicated as dots. You can see that for the Sun, a
G-type star, the habitable zone runs from Venus (dot \#2 from the left), to
Mars (fourth dot).}
\end{figure}

If we carefully examine this plot, we see that if a planet like Jupiter
was orbiting around an A-type star at 5 AU, it would be inside the habitable
zone. If the Earth was orbiting an M-type star, it would have to have a
much smaller orbit, 0.1 AU, to be inside the habitable zone. This is ten times 
closer than its current orbit. You can also see that if Mercury was orbiting
around a K-type star, it would be in the habitable zone. Thus all types of
stars, no matter their temperatures or luminosities, have a habitable zone,
and could be hosts for planets with life as we know it.

\end{document}
