## 1. Temperature

Not everybody in the world uses the same temperature scale. One degree of temperature difference is not the same in the various temperature scales, and which temperature is called zero degrees also varies. The two most widely used temperature scales for everyday use are the Fahrenheit and Celsius scales. A temperature scale that is used a lot in science (and in astronomy in particular) is the Kelvin scale. These scales are described below.

Celsius

The Celsius scale was invented by the Swedish astronomer Anders Celsius (1701 - 1744, Sweden). "Degrees Celsius" or "Centigrade" can be written as . The Celsius scale is fixed by two temperatures: 0 ℃ is the freezing temperature of water (at a standard sea-level air pressure), and 100 ℃ is the boiling temperature of water at the same pressure.

The zero point of the Celsius scale is practical, because below zero degrees Celsius you have to watch for ice on the roads and for frozen water pipes.

Zero degrees Celsius corresponds to 32 degrees Fahrenheit and 273.15 kelvin. A hundred degrees Celsius corresponds to 212 degrees Fahrenheit and to 373.15 kelvin. To go from degrees Fahrenheit to degrees Celsius, use

$$C = (F - 32)×5/9 = (5×F - 160)/9$$

and to go from kelvin to degrees Celsius, use

$$C = K - 273.15$$

Fahrenheit

The Fahrenheit scale was invented by the German scientist Daniel Gabriel Fahrenheit (1686 Poland - 1736 Dutch Republic). "Degrees Fahrenheit" can be written as . The Fahrenheit scale is fixed by two temperatures: zero degrees Fahrenheit was the temperature of a mix of water, ice, and salt. Ninety degrees Fahrenheit was what people in those days thought was the normal temperature of the human body.

These two fixed points on the Fahrenheit scale were perhaps not the most practical choices, because most people do not spend a lot of time trying to keep water fluid by adding salt to it, and we now know that the normal core temperature of the human body is a few degrees higher than what people then thought.

0 degrees Fahrenheit corresponds to about −17.8 degrees Celsius and about 255.4 kelvin. 100 degrees Fahrenheit corresponds to about 37.8 degrees Celsius and to about 310.9 kelvin. To go from degrees Celsius to degrees Fahrenheit, use

$$F = (C×9/5) + 32 = (9×C + 160)/5$$

To go from kelvin to degrees Fahrenheit, use

$$F = (K×9/5) - 459.67$$

Kelvin

The Kelvin scale is named after the Scottish scientist William Thomson, Baron Kelvin of Largs (1824 Ireland - 1907 Scotland). The kelvin as unit of temperature is part of the international system of units (SI) and is written in lower-case letters, just like all other units in that system. The abbreviation for kelvin is the capital letter K (without "°" in front of it!). The temperature scale of Kelvin is fixed by one temperature and a temperature difference: 0 kelvin is the lowest possible temperature, at which everything is as motionless as it can be. A difference of 1 kelvin corresponds to a difference of 1 degree Celsius. This scale was invented by scientists for use in science, because some scientific formulas become easier if you use the Kelvin scale (such as formulas relating the pressure of a gas to its temperature, or brightness to temperature, for instance).

0 kelvin corresponds to −273.15 degrees Celsius and to −459.67 degrees Fahrenheit. A temperature difference of 1 kelvin corresponds to a temperature difference of 1 degree Celsius, and to 9/5 = 1.8 degree Fahrenheit. To go from degrees Celsius to kelvin, use

$$K = C + 273.15$$

and to go from degrees Fahrenheit to kelvin, use

$$K = F×5/9 + 255 \frac{67}{180} = (100×F + 45967)/180$$

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The temperature scales of Fahrenheit and Celsius intersect at −40°: −40 is equal to −40. The temperature scales of Celsius and Kelvin do not intersect, because there is a fixed difference between them. The temperature scales of Fahrenheit and Kelvin intersect at −654.5875°: −654.5875℉ is equal to −654.5875 K, but that temperature is below the absolute zero point and therefore cannot actually be reached.

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## 2. What Determines How Warm Something Is?

The temperature of an object such as a glass of water shows how things are in the fight between things that take heat away from the glass and things that put heat into the glass of water. If more heat goes out than comes in, then the glass of water gets colder. If more heat comes in than goes out, then the glass gets hotter.

One way in which the glass can lose heat is through thermal radiation. All things emit thermal radiation, but hot things emit much more thermal radiation than cold things. You can see thermal radiation of things with an infrared camera.

Heat tries to distribute itself as equally as possible, so if the glass of water is colder than the things around it, then heat from the surroundings will go into the glass and heat it up, until the glass of water has the same temperature as the things around it. If the glass of water is hotter than the things around it, then some heat will leave the glass and go to the surroundings, again until the glass has the same temperature as the things around it.

This holds for all things, so it holds also for a desert. During the day, a desert receives much heat from the Sun, which is very hot, so then the temperature in the desert goes up. But at night, the desert looks out into ice cold space, which is very much colder than the desert, so then heat goes out of the desert into space, and then the desert cools down. There usually isn't anything between the desert and space to make it hard for the heat to escape, so a desert cools down rather quickly at night, and it can get pretty cold there just before dawn.

In areas that are not deserts the land or sea also loses heat to space at night, but if there are many clouds then they make it harder for the heat to escape, so then the temperature drops much less fast than in a desert.

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## 3. The Lowest Temperature

Temperature is a measure for how fast atoms move. If all atoms are as motionless as possible, then the temperature is the lowest that it can get. You can't go even lower in temperature, because you cannot be more motionless than motionless. That lowest possible temperature is called the "absolute zero" of temperature and corresponds to −273.15 or −459,67 . Nothing can be colder than that temperature, so a temperature of −1000 degrees on either the Celsius or Fahrenheit scales cannot occur anywhere in the Universe.

On the temperature scale of Kelvin, the absolute zero of temperature is equal to 0 kelvin, so temperatures on the scale of Kelvin cannot be negative.

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## 4. Climate Zones

The five climate zones of the world each cover a certain range of latitudes. They are separated from one another by the two polar circles (the Arctic Circle at about 67 degrees north latitude and the Antarctic Circle at about 67 degrees south latitude) and the two tropics (the Tropic of Cancer at about 23 degrees north latitude and the Tropic of Capricorn at about 23 degrees south latitude).

From north to south, the five zones are:

1. Northern polar zone: between the North Pole and the Arctic Circle.
2. Northern temperate zone: between the Arctic Circle and the Tropic of Cancer.
3. Tropical zone: between the Tropic of Cancer and the Tropic of Capricorn.
4. Southern temperate zone: between the Tropic of Capricorn and the Antarctic Circle.
5. Southern polar zone: between the Antarctic Circle and the South Pole.

The polar zones are the zones where the Sun does not rise at least one day (date) of the year. The tropical zone is the zone where the Sun is straight overhead at least once every year.

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## 5. How Much Sunlight?

The answer to the question "which country gets the most sunlight annually?" depends on how you measure "the most sunlight". If you want to take the weather (cloud cover) into account, then you should ask a meteorologist, because I don't have detailed cloud cover information for the whole world. So, I'll assume clear skies all year long. In a mountainous area the Sun may be blocked by a mountain for part of the day, so a flat area or sea is generally better than a mountainous area. I'll assume a flat area.

If you mean "the most heating by direct sunlight of a black sphere with a clear view of the whole sky", then the answer is "at the equator", where (assuming an optical thickness of the atmosphere of 0.1) such a sphere captures about 0.10 units, which is 0.10 times as much sunlight as a flat piece of land of the same surface area would do with the Sun continuously overhead. If we ignore the atmosphere completely, then the sphere captures pretty much the same amount of sunlight everywhere on Earth, namely 0.13 units.

If you mean "the most heating by direct sunlight of a black piece of flat land", then the equator is best, at 0.26 units, and the heating drops to about 0.09 units at the poles. Without an atmosphere, these numbers would increase by about 0.04 units.

If you mean "the most heating by direct sunlight of the surface of a thick, black, south-facing wall", then the best spot is around 53 degrees north latitude (0.16 units). Without absorption by the atmosphere, the poles would be best (at 0.31 units), but because the Sun never gets higher than 23 degrees above the horizon at the poles, the sunlight there always travels through a lot of air and has a large fraction absorbed by the atmosphere. For a north-facing wall the results are the same, except that north and south are exchanged.

For an east or west-facing wall you're best off at the equator (0.11 units) but the worst-off place then still gets 0.09 units, so the variation is small. Without an atmosphere, the results would be the same everywhere on Earth, at 0.31 units.

It seems from these numbers that the equator is generally the place with the most sunshine, unless you measure it by the heating of a vertical wall that isn't facing east or west. Also, I'd expect the least cloud cover in desert areas, which tend to lie at about 30 degrees from the equator, and perhaps the reduced cloudcover in such areas compensates for its distance from the equator. So my answer would be: either the equator, or else one of the big deserts, such as the Sahara.

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## 6. Temperature from Pole to Equator

Generally speaking, the average temperature goes down as you move away from the tropics, because the greatest height of the Sun in the sky goes down so the same amount of sunlight is divided over ever more land. However, the temperature is determined not just by how the Sun moves across the sky (an astronomical thing) but also by the distribution of land and mountains and vegetation and sea across the Earth, and by your altitude (higher is colder). Some atlases show the distribution of temperatures across the Earth.

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## 7. The Temperature at the Equator

The temperature is not the same everywhere at the equator. Sunlight heats things up where it is day, and things cool down where it is night. At the same time, it is day on half of the equator and night on the other half, so there are places where it is heating up and places where at the same time it is cooling down.

Even if you just look at the greatest temperature for the day (which is reached at different moments for places that are far away from each other) then that temperature is not the same everywhere on the equator. The amount of sunlight that is received per 24 hours is the same everywhere on the equator (ignoring very small differences because the distance between the Earth and the Sun is not always the same), but how easily that energy is lost again (which makes the temperature go down) depends on the local circumstances such as plant cover and clouds, and there is a great variety of those along the equator, for example between land and sea.

Great ocean currents also influence the temperature at the equator, because they can bring extra heat or extra cooling. They naturally influence the temperature of the ocean but also the temperature along the coasts of the continents that the flow along.

And even at a given spot on the equator the temperature depends on the altitude. It will be cooler at night above the canopy of trees of the tropical forest than below it, and it is cooler on top of a tall mountain (even at the equator) than in the lowlands around it.

All in all there does not appear to be a very great variation in the average temperatures around the equator. In most places they seem to be between about 25 and 30 degrees Celsius, except high in the mountains (such as the Andes).

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## 8. Maximum Temperature

The greatest temperature that an object can reach depends on its location and on its shape, orientation, and albedo. (The albedo is a measure for how much energy the object reflects immediately ― that energy therefore does not heat up the object).

If you position mirrors in the right way then you can reflect sunlight from a large area to a small object and thereby heat up the object tremendously. The solar oven of the CNRS near Odeillo in France is currently (2003) the largest on Earth and can heat an object in its focus to 3800 degrees Celsius.

In the same way it can be hotter at the bottom of a dune valley than on a sandy plain without dunes, because the surrounding dunes reflect some extra sunlight to the bottom of the valley.

There is therefore no well-defined maximum temperature that can be reached on Earth.

However, if we limit ourselves to a plain on which each point receives the same amount of sunlight, then there is a greatest attainable temperature. That temperature is reached if (1) the Sun is in the ideal location (e.g., straight overhead if we're talking about the temperature of a horizontal plate), (2) the object is pitch black so it absorbs all radiation from the Sun that reaches it, (3) the Earth is closest to the Sun in its annual orbit, (4) the influence of the atmosphere is ignored, (5) there is sufficient time for the temperature to reach a balance, and (6) the object can cool down only by radiating heat. In that case, the maximum attainable temperature on Earth (and the Moon) is equal to 396 K = 123 degrees Celsius. Temperatures of around 120 degrees Celsius have been observed on the Moon.

How hot an object really gets depends on the albedo of the object: on how much of the arriving radiation is reflected immediately. Such reflected radiation does not heat up the object. For example, if the object immediately reflects 50% of the incoming radiation, then its greatest attainable temperature will be 332 K = 59 degrees Celsius.

The temperature also depends on the shape and orientation of the object. A horizontal plate can (with the Sun overhead) reach 123 degrees Celsius, but a vertical plate at most 100 degrees Celsius. A cube gets to 108 degrees Celsius, and a sphere to 95 degrees.

Such temperatures of around 100 degrees Celsius are not actually encountered in the air on Earth, mostly because the Earth rotates too fast for that. The Sun is straight overhead for far too short a time to allow the temperature to reach 100 degrees. The Moon rotates much more slowly than the Earth, so temperatures can get that high there.

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## 9. Transport of Heat

Heat and energy can travel in three ways:

1. as thermal radiation or heat radiation or infrared radiation through the air. You cannot see these rays, but you can feel them on your face, coming from a fire or from a heat lamp. If you hold your hand between your face and the fire or the lamp, then you don't feel the heat on your face anymore so the heat travels in a straight line from the fire or lamp.
2. through things at rest. This is called conduction of heat, and this is how soup in a pan gets heated. The heat travels through the metal of the pan and gets into the soup. When the soup isn't very hot yet, then the soup itself is heated by conduction, too.
3. by movement of hot fluids or gases. This is called convection of heat, and this is how the air quite far above a burning candle gets to be hot. The air close to the candle is heated by radiation or conduction and then rises up to your hand quite far above the candle. When soup in a pan gets hot enough, then you can see bubbles of hot soup rising to the surface, and that is convection, too.

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## 10. Equilibrium Temperatures and Planets

Objects in space that do not have their own heat source or cooling will heat up or cool off until their temperature is such that they emit exactly as much thermal energy as they receive from the Sun. This temperature is called the equilibrium temperature. A planet that is at $$d$$ AU from the Sun and that is pitch black so that it absorbs all the sunlight that falls on it has an equilibrium temperature

$$T_\text{eq} = \frac{279}{\sqrt{d}} \text{ K} = \frac{279}{\sqrt{d - 273}} \text{℃} = \frac{502}{\sqrt{d - 460}} \text{ ℉}$$

If the planet is not pitch black but reflects part of the sunlight away, then its equilibrium temperature will be lower because the reflected sunlight does not heat up the planet. If the planet has an atmosphere, then the temperature at the surface of the planet can be much higher than the equilibrium temperature, because an atmosphere works like a blanket.

If a pitch-black planet without an atmosphere always shows the same side to the Sun and if the planet is a poor conductor of heat, then the point at which the Sun is in the zenith gets a temperature of

$$T_\text{hot} = \frac{394}{\sqrt{d}} \text{ K} = \frac{394}{\sqrt{d - 273}} \text{ ℃} = \frac{710}{\sqrt{d - 460}} \text{ ℉}$$

$$T_\text{eq}$$ is a reasonable estimate for the temperature at the outside of the atmosphere or at the surfece (if there is no atmosphere) of planets that rotate fast or that have a thick atmosphere that rotates fast, which means all planets except Mercury and Pluto, and excludes the Moon.

$$T_\text{hot}$$ is a reasonable estimate for the hottest temperatures on planets that rotate slowly and that have no fast atmosphere, such as Mercury and Pluto and the Moon.

How cold the dark side of a planet or moon can get depends mostly on how fast that planet or moon rotates around its axis. Slow rotators cool off more than fast rotators. The below table lists $$T_\text{eq}$$ and $$T_\text{hot}$$ for the average distances $$d$$ (in AU) of the planets from the Sun, and also for an imaginary object just above the solar surface. The last column $$T_\text{obs}$$ of the table lists the observed surface temperature on the planets and the Moon. All temperatures are measured in degrees Celsius.

Table 1: Equilibrium Temperatures

Planet $${d}$$$${T_\text{eq}}$$$${T_\text{hot}}$$$${T_\text{obs}}$$
Sun 0.00465 3807 5497 5497
Mercury 0.39 173 365 −170 … +350
Venus 0.72 55 191 480
Earth 1.00 5 121 22
Moon 1.00 5 121 −163 … +117
Mars 1.52 −47 46 −23
Jupiter 5.20 −151 −100 −150
Saturn 9.54 −183 −146 −180
Uranus 18.20 −208 −181 −210
Neptune 30.06 −222 −201 −220
Pluto 39 −228 −210

Venus has a large greenhouse effect in its atmosphere, so that the temperature at the surface of Venus is much higher than both $$T_\text{eq}$$ and $$T_\text{hot}$$. The Earth has a greenhouse effect, too, but it is much smaller than that of Venus. Mercury and the Moon have no atmosphere and they rotate slowly, so the temperature at their equator gets close to $$T_\text{hot}$$. Mars and the Jovian planets rotate relatively quickly, so their average temperature is near $$T_\text{eq}$$.

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## 11. Temperature at Sunrise

The ground and air continuously lose heat, in the form of infrared radiation which escapes into space. If there is no source of heat to make up for the loss, then it cannot but keep getting colder. So, one expects that the longer it is since the Sun last provided heat to the area (i.e., since sunset), the colder it gets.

At sunrise the Sun starts heating up the area again, so at (or just before) sunrise it is longest since the Sun last heated up the area, so it tends to be the coldest at sunrise.

Compare it to a bathtub from which the water (which stands for the heat) is slowly draining. Once in a while you turn on the tap so that more water enters the tub -- that corresponds to daytime. After a while you turn the tap off again -- that corresponds to nighttime. When is the water level lowest? Right before you turn on the tap, because after that the level starts rising again. If you hold off turning on the tap for some more time, then the water level keeps dropping, so there is no special draining effect associated with the turning on of the tap.

Likewise, sunrise does not have a special cooling effect.

If sunrise could be delayed, then it would get colder still. The Moon is about as far from the Sun as the Earth is, yet the temperature on the Moon gets as low as −160 (−250 ), which is far colder than it gets on Earth, mostly because night lasts about two weeks on the Moon so there is far more time there for it to cool down.

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## 12. Global Warming

That the average temperature on Earth has been increasing during the last couple of decades seems now to be beyond a reasonable doubt, but opinion is still divided about the causes of this increase, and specifically about whether we ourselves are the main cause of the increase.

That opinion is divided because (1) it is difficult to prove the causes of global warming, and (2) a lot of money is riding on the results, which biases policy makers towards favoring whatever opinion suits their personal needs.

The weather is an enormously complex system with many buffers and feedback loops and dependencies on the oceans and the continents (as well as the Sun). This makes it difficult to tell which parts of weather changes are natural (however you define that, which is yet another problem) and which are man-made.

Additionally, correlation does not prove causation. In other words: if you see quantity A rise or fall with quantity B, then that is not in itself proof that A must be causing B, or that B must be causing A. If two quantities A and B are not related at all, then they will still occasionally rise or fall together. If you happen to observe them at such a time, then you may draw the wrong conclusion that they must be related. Proving causation is difficult.

Temperatures and other aspects of the weather on Earth have been monitored crudely for several centuries, and in ever greater detail during the last couple of decades, and yet it is proving to be very difficult to settle the questions regarding global warming. If we measured that the Moon and the other planets were also getting warmer just like the Earth, then that would be a good clue that the cause of the warming is not on Earth. However, the number of observations of temperatures on other objects in the Solar System is enormously smaller than the number of such observations on Earth is, and cover a much shorter period of time, so I don't think that the available observations of the weather on other planets can already be decisive in settling the questions regarding global warming on Earth.

I still think that science offers the best way to settle these questions, imperfect though it is. Science has self-correction built in, so any bad science does tend to get exposed eventually.

I myself am not engaged in research of global warming, so I must rely on the results of others to make up my mind about it, just like most other people.

I expect that in the coming 10 or 20 years we'll get much better understanding of the causes and nature of the global warming, if only because we'll have a lot more observations by then to base our conclusions on.

Perhaps a more important question about global warming than "where does it come from?" is "what are we going to do about it?". Regardless of whether we are the main cause of global warming, we have to deal with its immediate effects.

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