The Sun

The Sun is deeply familiar to us and the source of almost all energy on Earth. It is the main body in the Solar system, and because it is so nearby, it is the star that we can study in the most detail for its general properties, structure, and energy sources. This is our starting point for studies of other stars.

General Properties

1. Distance to the Sun

Mean distance from the Earth is 1 Astronomical Unit = 1.5 x 108 km, or 93 million miles = 8 light minutes

2. Diameter of the Sun

From the distance and measured angular diameter of the Sun (about 0.5 degrees), we can calculate the Sun's diameter = 1.4 x 106 km. This is about 100 times the Earth's diameter, and 10 times the diameter of Jupiter, the largest planet.

3. Mass of the Sun

We can measure the mass of the Sun using the orbit of any planet. For example, knowing the period of the Earth's orbit and its distance from the Sun, we can apply Newton's Law of Gravity to calculate the mass of the Sun = 2 x 1030 kg -- more than 300,000 times the mass of the Earth.

4. Density of Sun

Knowing the mass of the Sun, and using its diameter to calculate its volume, we can determine its mass per unit volume, or density. This is 1.4 gm/cm3, or about 1.4 times the density of water. It is much less than the mean density of rock or the Earth's density of 5.5 gm/cm3. This is a clue to the composition of the Sun, and suggests that its composition and/or structure of the Sun is different from the Earth. We'll explore this in more detail when we study the Solar System and planets. From spectra, the composition of the Sun and other stars is mostly hydrogen and helium.

Energy Production and the Sun

How is it produced and how long will it last?

1. Solar Luminosity

At Earth we receive a flux of 1.37 kilowatts/meter2 from the Sun -- equivalent to 13 100-watt bulbs + 1 70-watt bulb over a 1 meter x 1 meter area. This is a small fraction of the total radiated energy of 3.8 x 1026 watts, or Lsun=3.8 x 1033 ergs/sec = 1026 joules/sec -- the Solar luminosity, which we calculate knowing Sun's distance.

2. Energy Production

a) Burning fossil fuels

Life on Earth is connected with photosynthesis, where sunlight provides the energy for carbon dioxide and water to form organic compounds and oxygen. Energy is now stored in the chemical bonds of organic material, and can be released by burning fossil fuels such as coal, oil, wood, or gas. Alternative non-Solar energy sources like tides, nuclear energy, or geothermal energy make up only a small fraction of our energy use.

`Burning' coal corresponding to the mass of the Sun to produce the Solar luminosity would only work for about 1500 years. Whatever powers the Sun cannot be normal chemical burning.

b) Gravitational contraction

Gravitational potential energy can be converted into thermal energy. As gravity compresses a cloud of gas, the temperature rises, and energy will be radiated into space. We will see later that this is the energy source for forming protostars. For a star with the mass of the Sun, this process only works for about 30 million years, yet from dating rocks we know that the Earth is much older -- 4.5 billion years. Looking ahead, we can ask what stops this gravitational collapse process and what happens in the center of a star? This leads us to the next possible answer:

c) Nuclear Energy

Contraction and compression raises the central temperature of the Sun to 15 million degrees Kelvin, forcing hydrogen nuclei to fuse together, liberating energy. This process of thermonuclear fusion (fusion=joining) occurs when light elements combine to make heavier elements, releasing energy. The proton-proton or p-p chain of nuclear reactions is the source of energy for our Sun. This reaction combines 4 hydrogen nuclei (protons) into a helium nucleus, generating energy, and also producing a particle which can be detected at the Earth, called a neutrino.

The helium nucleus has about 0.7% less mass than the hydrogen nuclei; the difference in mass is coverted into energy according to Einstein's formula

Each second 4 million tons of material is turned into energy, to produce the Sun's luminosity. If we divide this power consumption rate into the mass of the Sun, we find there's enough (hydrogen) fuel in the Sun to last about 10 billion years -- twice the current estimated age of the Solar System.

Nuclear fusion requires high temperatures (> 10 million degrees) and pressures to overcome the natural repulsion of positively charged nuclei, and force these together. Although this is often referred to as `nuclear burning' it is quite unlike the chemical burning of wood, gas, or coal. Fusion of heavier nuclei to form carbon, nitrogen, or other heavier elements up through iron, requires even higher temperatures. For elements heavier than iron, energy is released when massive nuclei such as uranium are split into less massive components in a process termed fission.

The Solar Interior

Pressure balance

Moving into the interior of the Sun, the gas is compressed by the weight of the gas above it, in a balance between gravity and pressure. This compression causes the gas to heat up, and at the center of the Sun we calculate a temperature of 15 million degrees, and a density of 150 gm/cm3 with a huge pressure. This pressure stops further gravitational collapse of the Sun, and this balance will continue as long as nuclear reactions continue.

The Solar Plasma

These high temperature conditions mean that the Sun is hot enough for atoms to be ionized, losing one or more electrons. This state of ionized gas is called a plasma. Energy flows outward from the higher temperature core to the surface; we see some evidence of this in the `boiling' motion of convective cells just below the photosphere.

The Solar Atmosphere

1. Photosphere

This is the visible `surface' of the Sun. There is no hard surface; this is simply the point at which interior gas becomes opaque, like the edge of a flame. From the thermal spectrum of the dense gas just below the photosphere, we can apply Wien's Law, and calculate a temperature of about 5800 degrees Kelvin. The temperature continues to decrease for a while as we move outwards, and the spectral absorption lines indicates the presence of cooler, lower density gas

2. Chromosphere

This is the thin layer just above the photosphere, where the temperature is beginning to rise. The name comes from the red color arising from Hydrogen emission lines found in this hotter layer.

3. Corona

The outer layer of the Sun's atmosphere is the Solar Corona

It is very thin and spreads out farther than the diameter of the Sun. It is very hot, about 1 million degrees but we do not properly know why. Because the Corona is so hot, the wavelength of its radiation is very small (X-rays)