Notes

What kind of bond gives water increased stability, compared to other liquids?
hydrogen bond
USING SIM
That's correct! Solid and liquid are the only stable phases of water on Earth. Although we see vapor, there are no places on Earth where large amounts of water vapor remain stable indefinitely. It all eventualy rains or snows out.
On the Moon, solid and vapor are the only stable phases. Stable ice deposits exist in the perpetually shadowed craters of the Moon's poles. In illuminated (hotter) regions of the Moon, any water would be present as a vapor (that is, of course, if it doesn't escape the Moon's low gravity).
Does liquid water appear during a transition from vapor to solid (or solid to vapor)?
EARTH=yes
Moon= no
the difference is atmosphere


That is correct! Temperature is not the only important variable for determining the phase of water ... pressure is too. The Moon has a much lower surface pressure than Earth, and as a result, liquid water is never a stable phase ... not even when changing from solid to vapor or vapor to solid. Phase transitions that bypass the liquid state are called sublimation (solid to vapor) and deposition (vapor to solid).

An example of sublimation you may be familiar with is dry ice. Dry ice is frozen carbon dioxide. At Earth surface pressure, it sublimates, resulting in ice that vanishes directly to a vapor. Only at high pressures, as you can see here, can you observe liquid carbon dioxide. Here, the pressure is reported in kilopascals (kPa). Note how the solid carbon dioxide becomes liquid as the pressure is raised. At lower pressure, only solid and vapor states are stable.

Create a solid-to-vapor or vapor-to-solid transition on each body. Identify on which ones liquid water appears during the transition
VENUS Earth mars
Good job! Recall that pressure is important for the stability of liquid water. On Venus, Earth, and Mars, which have relatively high surface pressures, liquid water appears between solid and vapor as one transitions to the other.
On the Moon and Mercury, where surface pressures are very low, this does not happen. At these pressures, liquid appears to never be stable, not even during transitions.

How is the stability of liquid water related to air pressure? More stable at high pressures
What is the name of the pressure and temperature at which all three phases of water can stably coexist? triple point

Good job. Atmsopheric pressure plays a critical role in the stability of liquid water. At low pressures, liquid water will be less stable than at high pressures. Below the triple point of water, a temperature and pressure at which all three phases of water can coexist, liquid water is never stable.

Having the right temperature is not enough. Although the Earth and Moon lie the same distance away from the Sun and can have similar temperatures (depending on location), liquid water is never stable on the Moon. Atmospheric pressure is just as important for the stability of liquid water as temperature.
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ENERGY BALLENCE MOD
Water is a critical component for life as we know it, and as we've previously discovered, liquid water is only stable at certain temperatures and pressures.

Previously, we used the Sun's flux at Earth's location (1360 W/m2) as our definition of a "habitable" world. We will now begin to expand this definition until we've built the habitable zone, the zone around a star where a planet can be Earth-like.
We can use basic physics to calculate what a planet's surface temperature should be. We call this predicted temperature the effective temperature.
If we want to be able to calculate the effective temperature of any given planet, we need to first determine which properties of the system will affect the temperature
We already know luminosity varys
You are also aware that you can vary the distance (or orbital radius) of a planet from its host star.
As you are aware, planets can also have many different sizes.
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Now we introduce a new concept, albedo. Albedo is the reflectivity of a substance. You can also think of it as a measure of how dark an object is. It can take values between 0 (black) and 1 (white).

Water is rather dark and has a very low albedo (0.07 - 0.10).
Snow and ice are very bright and have a very high albedo (0.8 - 0.9)

A planet's albedo is an average of all the albedos of all its surfaces (ocean, continents, ice, clouds)
RADIUS HAS NO RELATIONSHIP TO TEMPURATUURE
NOTEBOOK
In order for a planet to be in "energy balance", what percentage of absorbed sunlight must be emitted by the planet? 100%
Good job. In order for a planet to be in energy balance, all (100%) of the energy that it absorbs must be re-emitted to space.

If the planet emits less energy than it absorbs from its star, what will happen to the planet's temperature? it warms up
That's correct! If a planet emits less energy than it receives, then the planet must warm up. Recall that at higher temperatures, an object will emit more energy. So the planet warms up until it can emit the same exact amount of energy it absorbs.

If the planet emits more energy than it absorbs from its star, what will happen to the planet's temperature? cools down
That's correct! If a planet is emitting more energy than it absorbs from its star, it will be losing energy and must cool down. It will cool down until it reaches a temperature where it emits exactly the same amount of energy it receives.

A planet's effective temperature will depend on the flux it receives, which itself is a function of the star's luminosity, the planet's distance from the star, and the planet's albedo (or how much energy it reflects back into space without absorbing it). The planet's temperature will always adjust to this energy input until it is emitting 100% of it back into space (energy balance). That's why the effective temperature is often also called the equilibrium temperature.


So if we want to know the effective temperature of any planet

(and hence whether it will support liquid water), we need to know how to calculate

the flux it receives at any distance around any kind of star.

Recall that a star's luminosity (total flux) is related to its temperature (color) and its size. The temperature determines how much energy is emitted by a square meter. The size determines how many square meters there are.

Recall that for the Sun (surface temperature of about 5800 K), about 64,000,000 watts are emitted per square meter. The radius of the Sun is about 695,500,000 meters. We can use some simple arithmetic to calculate how much total energy the Sun emits per second:


Luminosity = surface area of Sun (in square meters) x amount of energy emitted per square meter


Luminosity = 4 x pi x radius2 x energy emitted


Luminosity = 4 x pi x (695,500,000 m)2 x 64,000,000 W/m2


Luminosity ~ 3.9 x 1026 W


The actual measured value of our Sun (1 LS) is 3.839 x 1026 W,

very close to what we calculated from basic physics!

to know the flux at Earth's distance, we simply need to take the Sun's surface energy and spread it over the surface of a larger sphere that is as wide as Earth's orbit.


What was the relationship between brightness and distance again ... ?
brightness = 1/distance^2
That's correct ... the brightness decreases with the square of the distance. Recall that this is because the surface area of a sphere has a radius^2 term in it and the brightness of a star must be spread across the surface of a larger and larger sphere.



Now we simply take the luminosity of the Sun (1 LS = 3.839 x 10^26 W) and spread it across the surface of a sphere as large as Earth's orbital radius (1 AU = 1.496 x 1011 m).


Flux at a planet = (Luminosity of star) / (4 x pi x (orbital radius)2)


Flux at Earth = (1 LS x 3.839 x 1026 W) / (4 x pi x (1 AU x 1.496 x 1011 m)2)


Flux at Earth = 1365 W/m2




For different luminosities, simply replace "1 LS" with the luminosity of your star. For different distances, replace "1 AU" with the distance of your planet

AU Conversion
r = distance x 1.496 x 10^11 m
Luminosity Conversion
L = Lstar x 3.839 x 10^26 W
Energy Flux Calculation
Fs = L/(4r^2)

SAMPLE______----------
What is the flux for a planet orbiting at 4.5 AUs around a 8.4 LS star?
Convert 4.5 AUs to meters:

4.5 AU x 1.496 x 1011 m = 6.73 x 1011 m

Convert 8.4 LS to watts:

8.4 LS x 3.839 x 1026 W = 3.225 x 1027 W
Flux:
3.225 x 1027 W / (4 x x (6.73 x 1011 m)2) = 566.6 W/m2
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157.3*3.839*10^26
luminosity is the first number and the only thing that changes is this cal
29.44*1.496*10^11 
distance is the first number and the only thing that changes is this cal
6.0387470000000015e+28/(4*pi*(4404224000000)^2)
PLACE LUMINOSITY ANSWER FIRST THE DISTANCE ONE GOES SECOND


Energy (Fs): 1000 W/m^2

Albedo: 0.32

Stefan-Boltzmann constant (special character that looks like o) = 5.67 x 10^-8 W/m^2/K^4


Temperature = ( Energy x (1 - albedo) / (4 x ) )^0.25


T = ( 1000 W/m2 x (1 - 0.32) / (4 x 5.67 x 10-8 W/m2/K4) )0.25 = 234 K


*The fourth root is the same as raising something to the 1/4 or 0.25 power.
easy just type it in to cal like this
(2000*(1-0.999)/(4*5.67*10^-8))^0.25 

(2000 is energy or w/m2) (0.999 is the albedo)
That's correct! You have already had a lot of experience with how flux affects temperatures. In general, it's the same relationship you have used many times already ... planets around more luminous stars or closer to their stars are hotter than planets far away or around dimmer stars.
Note how much a difference albedo can make in planetary surface temperatures. By raising the albedo from 0 to 0.999 (a completely absorbing surface to one that's a near-perfect reflector), we could easily plunge the temperature of our planet from ~300 K (~27°C or ~80°F) to ~50 K (-223°C or -370°F). That's a huge difference in terms of habitability! And it leads to some very interesting phenomena, as you will see in a future exercise ...

We have focused on calculating fluxes and effective temperatures because they can allow us to predict whether liquid water can be found on the surface of exoplanets.

Remember that atmospheric pressure plays a role in liquid water stability as well.


Are the boundaries of the water zone bigger when atmospheric pressure is high or low? High pressure
That's correct! Recall from our phase diagram that liquid water is stable over a larger range of temperatures at higher pressures than at lower pressures. When the surface pressure is too low, liquid water cannot exist at all!

That's correct! Our effective temperature calculation does not account for a planet's atmosphere. You can consider the effective temperature as the "basic" temperature of your planet ... it can't be any colder than this based on the physics. But the atmosphere can and does raise this basic temperature. When we account for this effect, we can figure out the true surface temperature of the planet.
Equations____________

Tools

Stellar Flux at Planet Orbit:

Flux = Star Luminosity / (4 x x distance2)


Effective Temperature:

Temperature = (Flux x (1 - albedo) / (4 x ) )0.25

Conversions and Constants:

1 LS = 3.839 x 1026 Watts

1 AU = 1.496 x 1011 meters

= 5.67 x 10-8 W m-2 K-4
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codes
water-86668
energy balence-39199
HABITABLE ZONE*********
Our models of solar system formation suggest that Venus, Earth, and Mars may have all been Earth-like early in their history! So why are they so different now? Their different histories help us define the boundaries of the habitable zone.