Sunlight and the Earth’s Temperature
Now let’s get back to science. Energy flows onto the Earth from the Sun, and energy is essential for life. Yet energy also flows out from the Earth to the cold of outer space. The inflow of energy from the Sun is actually slightly less than the outflow of energy from the Earth, because some of the outflow is heat escaping from the Earth’s interior. If the inflow were always even slightly greater than the outflow, the Earth’s temperature would rise without limit.
We may calculate the Earth’s temperature from the solar surface temperature and the amount of sky the Sun occupies. The Sun’s absolute surface temperature is about 6 000 kelvins.
The Sun’s disk as seen from the Earth has an angular diameter of about half of one degree or 30 minutes of arc. Consider a map of the sky. The equator is 360 degrees around. Therefore 720 suns would fit on the equator with the edges of one touching the edges of the suns on either side. Then it is 90 degrees from the equator to the North Pole, and another 90 degrees to the South Pole. Therefore 360 suns would fit on a longitude line in the sky. The product of 360 and 720 is 259 200. That is more than the number of suns it would take to fill up the sky, because the latitude circles get smaller as one approaches the poles. On the other hand, once the sky was full of suns with their edges touching, one would need to cut up additional suns to fill in the spaces between the circles. It takes calculus to work this out precisely. The sky would be packed full with 210 000 suns. Under such conditions the Earth would have the same temperature as the surface of the Sun, 6 000 kelvins. Even a few extra suns, let alone 210 000 of them, would make the Earth intolerably hot. Happily for us there is only one Sun.
Outer space has an absolute temperature of less than 3 kelvins. This temperature is so low it may be taken as zero for the purposes of our calculation. Radiant energy flow is proportional to the fourth power of the absolute temperature, that is, to the square of the square of the absolute temperature. The total inflow has to be averaged over the whole sky. The main inflow is from the Sun. The remaining inflow from all the stars and planets in the rest of the sky is practically zero. The average inflow is therefore 6 000 kelvins squared and squared again, divided by 210 000. The average outflow is almost equal to the average inflow. Therefore the Earth’s temperature is the square root of the square root of the average inflow. We can simplify the calculation if we use the square root of the square root of 210 000, which is equal to 21.4. Then if we divide 6 000 kelvins by 21.4, the result we get is 280 kelvins. Subtracting 273º C from this, we get the Earth’s average temperature as 7º C or 45º F. That is a bit chilly but not freezing. Since the average Earth temperature is a little higher than this, some of the Earth’s warmth must still be coming from its internal heat. Besides the inflow of heat from the Sun, radioactive materials in the Earth’s core disintegrate and produce additional internal heat, which eventually flows out into space. The Earth’s core is not as hot as the interior of a star, so the core cannot synthesize new radioactive materials. The disintegration is irreversible and contributes continually to the Earth’s increasing entropy.
The Earth absorbs sunlight a little better than it emits heat, because of the greenhouse effect of the atmosphere. That raises the Earth’s temperature slightly.
The foregoing is an equilibrium calculation. If all the incoming energy from the Sun flowed away immediately to the rest of the universe, there would be no change of entropy on the Earth. In perfect balance the net inflow of heat would be zero, so the change in entropy would also be zero. However, some of the Sun’s heat drives winds and makes turbulence in the Earth’s atmosphere. The winds sandblast the mountains and also bring rains that wear the mountains down. No one can ever exactly reverse the random irregularities of turbulent flow. These two processes are therefore irreversible.
We may calculate the Earth’s temperature from the solar surface temperature and the amount of sky the Sun occupies. The Sun’s absolute surface temperature is about 6 000 kelvins.
The Sun’s disk as seen from the Earth has an angular diameter of about half of one degree or 30 minutes of arc. Consider a map of the sky. The equator is 360 degrees around. Therefore 720 suns would fit on the equator with the edges of one touching the edges of the suns on either side. Then it is 90 degrees from the equator to the North Pole, and another 90 degrees to the South Pole. Therefore 360 suns would fit on a longitude line in the sky. The product of 360 and 720 is 259 200. That is more than the number of suns it would take to fill up the sky, because the latitude circles get smaller as one approaches the poles. On the other hand, once the sky was full of suns with their edges touching, one would need to cut up additional suns to fill in the spaces between the circles. It takes calculus to work this out precisely. The sky would be packed full with 210 000 suns. Under such conditions the Earth would have the same temperature as the surface of the Sun, 6 000 kelvins. Even a few extra suns, let alone 210 000 of them, would make the Earth intolerably hot. Happily for us there is only one Sun.
Outer space has an absolute temperature of less than 3 kelvins. This temperature is so low it may be taken as zero for the purposes of our calculation. Radiant energy flow is proportional to the fourth power of the absolute temperature, that is, to the square of the square of the absolute temperature. The total inflow has to be averaged over the whole sky. The main inflow is from the Sun. The remaining inflow from all the stars and planets in the rest of the sky is practically zero. The average inflow is therefore 6 000 kelvins squared and squared again, divided by 210 000. The average outflow is almost equal to the average inflow. Therefore the Earth’s temperature is the square root of the square root of the average inflow. We can simplify the calculation if we use the square root of the square root of 210 000, which is equal to 21.4. Then if we divide 6 000 kelvins by 21.4, the result we get is 280 kelvins. Subtracting 273º C from this, we get the Earth’s average temperature as 7º C or 45º F. That is a bit chilly but not freezing. Since the average Earth temperature is a little higher than this, some of the Earth’s warmth must still be coming from its internal heat. Besides the inflow of heat from the Sun, radioactive materials in the Earth’s core disintegrate and produce additional internal heat, which eventually flows out into space. The Earth’s core is not as hot as the interior of a star, so the core cannot synthesize new radioactive materials. The disintegration is irreversible and contributes continually to the Earth’s increasing entropy.
The Earth absorbs sunlight a little better than it emits heat, because of the greenhouse effect of the atmosphere. That raises the Earth’s temperature slightly.
The foregoing is an equilibrium calculation. If all the incoming energy from the Sun flowed away immediately to the rest of the universe, there would be no change of entropy on the Earth. In perfect balance the net inflow of heat would be zero, so the change in entropy would also be zero. However, some of the Sun’s heat drives winds and makes turbulence in the Earth’s atmosphere. The winds sandblast the mountains and also bring rains that wear the mountains down. No one can ever exactly reverse the random irregularities of turbulent flow. These two processes are therefore irreversible.
What Makes Sunlight Suitable?
Sunlight has a number of properties that make it suitable for supporting life and for providing information. Let’s start with the most obvious property, so obvious it may seem trivial, and then go on to properties that are not so well understood but just as important for life.
The Sun’s light comes to the Earth’s surface from one direction only at any given time. If sunlight came to the Earth from all directions there would be no alternation of day and night, because no rotation of the Earth could shield any part of its surface from the light. A certain amount of energy flows constantly from the Sun to the Earth’s surface, and that energy is necessary to sustain life.
However, some other arrangement could provide the equivalent energy inflow. Suppose, for instance, that we could place the Earth inside a hollow cubical cavity in some sort of massive body at 280 kelvins or 7º C, about 45º F. The walls of the cavity would have to be very strong to keep it from collapsing. This idea is quite hypothetical because there is no known material strong enough to make a rigid cavity big enough to hold a planet. Even if there were, the walls would not provide light. Materials at room temperature or below are not hot enough to emit light. Anyone who doubts this can enter a closed room, turn off the lights, and notice that the walls do not look bright. The Earth inside a warm cavity would be in perpetual night. The warmth would have no directionality. It would impinge equally on the Earth from all directions.
Warmth from all directions could not provide the timekeeping information we have from the Sun even if the Earth in the cavity continued to rotate at the same rate. More importantly, however, there would be no food for bacteria, plants, or animals.
Incoming solar energy maintains all life on Earth by powering molecular heat engines that photosynthesize carbohydrates and release oxygen. Chlorophyll is the most important component of these engines. It reflects green light and absorbs red, blue, and violet light. Chlorophyll is what makes green plants green. The upper surface of a leaf is transparent, allowing sunlight to reach the chloroplasts, small bodies in the leaves containing chlorophyll. The absorbed colors correspond to rays of specific photon wavelengths and photon energies. The energies are those needed to move the electrons in the chlorophyll molecule from the state of lowest energy (the ground state) to certain excited states. The important excited states of chlorophyll are metastable. That is, they are not completely stable, but they persist for relatively long times. Their metastability enables them to retain the excitation energy long enough to catalyze the chemical reactions that turn water and carbon dioxide into a kind of sugar called glucose. Other molecular engines turn the sugar into starch. Starch and sugars are carbohydrates, food for the plant.
When chemical substances absorb light, they absorb one photon per molecule. Of course, two photons, each of low energy, might combine their energy to make the equivalent of a red, blue, or violet photon. This is possible, but chemical substances seldom absorb two or more photons at once. Light moves very fast. It is very unlikely that two photons would arrive at a given molecule close enough to the same time so that their energy could combine.
The Sun provides red, blue, and violet photons. Its maximum emission is yellow photons. It provides some ultraviolet photons, but not too many. Photons of too much energy are destructive. They rip electrons off of atoms and cause molecules to break up. On the other hand, infrared photons don’t have enough energy to put chlorophyll into excited states that can make sugar from carbon dioxide and water. At a temperature of 280 kelvins, 7º C, or 45º F, the dark walls of a cavity emit infrared photons with a wavelength of 10 micrometers. Their energy is only about 4% of the energy needed to make violet light. Twenty-five of them would have to gang up on chlorophyll to have the same effect as one violet photon. The heat photons from the walls of a warm cavity never gang up that way. There would be no photosynthesis of carbohydrates if sunlight did not provide daylight on the Earth. Many schoolchildren have performed the science experiment of depriving a green plant of light. The result is always the same. The plant dies for lack of red, blue, and violet light.
Animals depend on green plants for food and oxygen. There are some plants that do not have chlorophyll and do not use sunlight to make their food. Most of these plants obtain carbohydrates from other organisms. If the organisms are living, the plants that feed on them are parasites. Plants that feed on dead organic material are saprophytes. Both parasites and saprophytes clearly depend on green plants and chlorophyll.
The Sun’s light comes to the Earth’s surface from one direction only at any given time. If sunlight came to the Earth from all directions there would be no alternation of day and night, because no rotation of the Earth could shield any part of its surface from the light. A certain amount of energy flows constantly from the Sun to the Earth’s surface, and that energy is necessary to sustain life.
However, some other arrangement could provide the equivalent energy inflow. Suppose, for instance, that we could place the Earth inside a hollow cubical cavity in some sort of massive body at 280 kelvins or 7º C, about 45º F. The walls of the cavity would have to be very strong to keep it from collapsing. This idea is quite hypothetical because there is no known material strong enough to make a rigid cavity big enough to hold a planet. Even if there were, the walls would not provide light. Materials at room temperature or below are not hot enough to emit light. Anyone who doubts this can enter a closed room, turn off the lights, and notice that the walls do not look bright. The Earth inside a warm cavity would be in perpetual night. The warmth would have no directionality. It would impinge equally on the Earth from all directions.
Warmth from all directions could not provide the timekeeping information we have from the Sun even if the Earth in the cavity continued to rotate at the same rate. More importantly, however, there would be no food for bacteria, plants, or animals.
Incoming solar energy maintains all life on Earth by powering molecular heat engines that photosynthesize carbohydrates and release oxygen. Chlorophyll is the most important component of these engines. It reflects green light and absorbs red, blue, and violet light. Chlorophyll is what makes green plants green. The upper surface of a leaf is transparent, allowing sunlight to reach the chloroplasts, small bodies in the leaves containing chlorophyll. The absorbed colors correspond to rays of specific photon wavelengths and photon energies. The energies are those needed to move the electrons in the chlorophyll molecule from the state of lowest energy (the ground state) to certain excited states. The important excited states of chlorophyll are metastable. That is, they are not completely stable, but they persist for relatively long times. Their metastability enables them to retain the excitation energy long enough to catalyze the chemical reactions that turn water and carbon dioxide into a kind of sugar called glucose. Other molecular engines turn the sugar into starch. Starch and sugars are carbohydrates, food for the plant.
When chemical substances absorb light, they absorb one photon per molecule. Of course, two photons, each of low energy, might combine their energy to make the equivalent of a red, blue, or violet photon. This is possible, but chemical substances seldom absorb two or more photons at once. Light moves very fast. It is very unlikely that two photons would arrive at a given molecule close enough to the same time so that their energy could combine.
The Sun provides red, blue, and violet photons. Its maximum emission is yellow photons. It provides some ultraviolet photons, but not too many. Photons of too much energy are destructive. They rip electrons off of atoms and cause molecules to break up. On the other hand, infrared photons don’t have enough energy to put chlorophyll into excited states that can make sugar from carbon dioxide and water. At a temperature of 280 kelvins, 7º C, or 45º F, the dark walls of a cavity emit infrared photons with a wavelength of 10 micrometers. Their energy is only about 4% of the energy needed to make violet light. Twenty-five of them would have to gang up on chlorophyll to have the same effect as one violet photon. The heat photons from the walls of a warm cavity never gang up that way. There would be no photosynthesis of carbohydrates if sunlight did not provide daylight on the Earth. Many schoolchildren have performed the science experiment of depriving a green plant of light. The result is always the same. The plant dies for lack of red, blue, and violet light.
Animals depend on green plants for food and oxygen. There are some plants that do not have chlorophyll and do not use sunlight to make their food. Most of these plants obtain carbohydrates from other organisms. If the organisms are living, the plants that feed on them are parasites. Plants that feed on dead organic material are saprophytes. Both parasites and saprophytes clearly depend on green plants and chlorophyll.
A relatively small number of bacteria are as autotrophic as green plants, that is, they also form their own carbohydrates. Such bacteria need carbon dioxide and the energy of sunlight, but they use hydrogen sulfide (H2S) instead of water (H2O). Even though they don’t use chlorophyll, they require low-entropy sunlight for photosynthesis.
In the middle of Earth’s ocean floors there are deep-sea hydrothermal vents where heat from the Earth’s magma warms the water. Sunlight never penetrates to the depths of the ocean. There another kind of autotrophic bacteria oxidizes sulfides and uses the energy to synthesize organic compounds. The bacteria rely on oxygen dissolved in the sea water. This comes from photosynthesis near the surface.
Taking into account green plants, chlorophyll, and the autotrophic bacteria, we conclude that the entire staff of life on Earth depends on photosynthesis and sunlight.
Taking into account green plants, chlorophyll, and the autotrophic bacteria, we conclude that the entire staff of life on Earth depends on photosynthesis and sunlight.
Olbers’ Paradox
In 1826 Heinrich Wilhelm Matthäus Olbers (German physician and astronomer, 1758–1840) realized that if the universe is unlimited, every line of sight from Earth should end on the surface of a star. No matter how many stars the line missed, eventually there would be one in the way. The whole daytime and nighttime sky should always be as bright and hot as the surface of an average star. The effect would be like having the sky packed solid with many copies of our Sun. The fact that the stars are much farther away than our Sun makes no difference because the Earth has had time to come to equilibrium temperature with them. The Earth’s temperature should be like the Sun’s, 10 000º F or 6 000º C. At such elevated temperatures life on Earth would be impossible. Life based on atoms requires very complex compounds of atoms, but even the simplest compounds of two or three atoms break up at such high temperatures. We should be burned far worse than a crisp.
But we are not roasted, and the night sky is dark. This contradiction is called Olbers’ paradox. Olbers did not know of the expansion in the heavens that cools the light. Hubble discovered that in 1929. Neither did Olbers know that the universe was created a finite time ago. The age of the universe was not known until recently. These two factors, the expansion and the limited age of the universe, keep the sky cold.
The finite age of the universe makes it impossible for us to see beyond a certain limit. We run out of previous time before we run out of space. The limit we can see is not the edge of the universe, but the beginning. Some lines of sight stop when they reach the surfaces of stars, but many lines of sight stretch back to times long before the stars.
The darkness of space is now cold. It is far less energetic that the darkness of the first night. The beginning and the expansion caused the present darkness of space. Let’s try to understand this from a simple example.
But we are not roasted, and the night sky is dark. This contradiction is called Olbers’ paradox. Olbers did not know of the expansion in the heavens that cools the light. Hubble discovered that in 1929. Neither did Olbers know that the universe was created a finite time ago. The age of the universe was not known until recently. These two factors, the expansion and the limited age of the universe, keep the sky cold.
The finite age of the universe makes it impossible for us to see beyond a certain limit. We run out of previous time before we run out of space. The limit we can see is not the edge of the universe, but the beginning. Some lines of sight stop when they reach the surfaces of stars, but many lines of sight stretch back to times long before the stars.
The darkness of space is now cold. It is far less energetic that the darkness of the first night. The beginning and the expansion caused the present darkness of space. Let’s try to understand this from a simple example.