THE SUN Chaisson & McMillan, Chapter 16: The Sun

The Sun is a massive (10³⁰ kilograms; the Earth has a mass of 6.0x10²⁴ kilograms), gaseous ball held together by gravity which radiates energy at the prodigous rate of 3.9x10²⁶ Watts. The Sun is a more or less normal star; it is slightly more massive than average (the average star in our Galaxy is 30 % the mass of the Sun).

Question: How do astronomers differentiate stars from planets^* and/or other types of celestial bodies?

Answer: In general, stars are objects which produce energy internally; planets, for the most part, do not produce large amounts of energy (but, ...). We are not too picky about the way in which stars produce energy. Some stars produce energy through nuclear fusion, other stars produce energy through gravity , and so on. There is also some ambiguity in this definition of a star as some celestial objects radiate energy and are not considered stars, e.g., the planets Jupiter, Saturn, and Neptune. However, despite the exceptions, a reasonable working definition for a star is an object which generates its own energy (internally).

The Sun is a prodigous source of energy. As such, it is of fair amount of interest to us.

Question: How energetic is the Sun?

Answer: A not too useful statement is that the Sun radiates at a rate of 3.9x10²³ kilo-Watts (kW). This is a high rate as it corresponds to the brightness of 3.9x10²⁴ 100 W light bulbs! A more striking statement is that at $0.10 a kW-hour, the Sun produces $ = 3.9x10²³ kW x 1 hour x $0.10 ===> $ 3.9 x 10²² worth of energy in one hour!!

An aside-- A Watt is a measure of power, the rate at which energy is used or produced. A Watt is 1 Joule (J) per second (s) and the Sun's luminosity is 3.9x10²⁶ J/s.

Question: How much is a Joule?

• If I drop a rock of mass 1 kilogram (1 kg = 2.2 pounds on Earth) from a perch 5 meters (m) off the ground, the rock will hit the ground with speed of ~10 m/s. The kinetic energy (energy of motion) of the rock when it hits the ground is the 0.5 x mass x speed². If I measure the mass in kg and the speed in m/s, the energy of the falling rock will be in Joules. The rock hits the ground kinetic energy of ~50 J.
• A slow moving mosquito (1 gram) has an energy of about 10^-7 J ===> a pack of 10 million mosquitos has an energy of ~ 1 J.

Question: Are there more useful yardsticks for the power of the Sun?

Answer: Yes, in 1972 the US consumed 1.7 trillion kW-hours of energy = 6x10¹⁸ J (with a fairly large increase over the last 30 years--note one BTU = 1,055 Joules). By 2002, the U.S. consumed energy at the rate ~ 3.4x10⁹ kW. The Sun produces power at the rate 4x10²³ kW; the Sun would not notice us stealing energy. This, however, is not the complete picture.

Question: How much of this energy is available to us on the Earth?

Answer: Since we are 93,000,000 miles from the Sun, we cannot utilize all of the energy produced by the Sun. Because of our great distance from the Sun, we intercept only a small fraction of the Sun's total energy output. At the orbit of the Earth, we intercept only 0.46 billion-ths of the Solar output. The energy flow from the Sun falls off with an inverse square law dependence. At the top of our atmosphere, the flow amounts to ~1,365 Watts per square meter (W/m²). A flow of energy per unit area is referred to as an energy flux . The energy flux from the Sun at the Earth's orbit is called the Solar Constant.

The amount of energy that actually reaches the surface of the Earth is smaller. The amount that doesn't penetrate the atmosphere and cloud layer and which is thus prevented from reaching the ground is variable--it ranges from 30 % to more than 50 %. The globally averaged flux that reaches the surface of the Earth is ~ 341 W/m² of which 31 % is further reflected.

In the absence of an atmosphere, this energy input would heat the surface of the Earth to only 250 Kelvin (~ -23 Celsius or ~ -9 F which is well below the freezing point of water at standard temperature and pressure). However, the heated surface produces infrared radiation which is absorbed in the lower atmosphere by Greenhouse gases. This absorption with its subequent remission process traps some of the heat raising the temperature in the lower atmosphere of the Earth to roughly 288 K (~60 F, a nice comfortable temperature for life as we know it).

Although 341 W/m² does not sound like a large flux of energy, if we could tap it efficiently we would easily satisfy our energy needs. (Question: If we had a Solar collector that was 100 % efficient, how large would it need to be to acquire enough energy to satisfy the energy needs of the U.S.?)

Question: How does the Sun produce energy?

Answer: This question was a mystery for many years given that the Earth (and therefore the Sun) is very old and the Sun is very bright. The combination of these two things means that the Sun must have a large store of energy. The understanding of the energy source for the Sun (and hence other stars) relied on the work of Einstein in the early 1900's. The pioneering workers (e.g., R. d'E. Atkinson in the 1920's) realized that if the Sun generated energy through nuclear fusion ( fusing hydrogen into helium) then it had ample energy to radiate at its current rate for around 10 billion years, easily long enough to explain lifetime of the Solar System. We return to this important topic later. Other sources of energy such as fossil fuel burning (chemical burning), gravity, stored internal heat are just not efficient enough to have powered the Sun from 4.6 billion years (the lifetime of the Solar System).





Solar-Terrestrial Connections




The Sun is a variable star. The Sun shows shows variability on time scales ranging from milliseconds to billions of years. As an example (because of its possible effects on short-term global climatic changes) we consider what is known as the Solar Activity Cycle.



The principal observable manifestation of the Solar Activity Cycle is the variable number of sunpots visible on the surface of the Sun. As discovered in 1843 by Heinrich Schwabe, a German apothecary, the number of Sunspots varies roughly periodically with a period of 11 years (the cycle based on other markers suggests that the period is actually 22 years). There are other features of the Sun that vary with the number of sunspots e.g., prominences (quiescent and active), faculae, and coronal activity. Although, it is clear that the appearance (activity) of the Sun varies with strongly with the Solar Activity Cycle, the actual change in the luminosity of the Sun is small, less than 1 %.





Based on the historical record, it has been shown that the Sunspot Cycle can stop, that is, there are times when there are no visible Sunspots. There have been several such intervals in recent history. The most prominent one is referred to as the Maunder Minimum which occured in the 1600's. The interesting thing is that during this time Europe experienced what is known as the Little Ice Age when the average temperature was depressed by over a degree. There is a clear indication that the varying activity of the Sun affects the overall climate of the Earth. The annoying thing is that the changes in the luminosity of the Sun are small. The challenge is to figure out how small changes in the Sun can lead to global climatic changes.

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^* The IAU therefore resolves that planets and other bodies in our Solar System be defined into three distinct categories in the following way:

• A planet is a celestial body that (a) is in orbit around the Sun, (b) has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape, and (c) has cleared the neighbourhood around its orbit.

• A dwarf planet is a celestial body that (a) is in orbit around the Sun, (b) has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape, (c) has not cleared the neighbourhood around its orbit, and (d) is not a satellite.

• All other objects except satellites orbiting the Sun shall be referred to collectively as Small Solar-System Bodies