If we look to the sky at night, we will see stars that shine all the time. but the question is where did the stars get the energy to be able to emit light for a very long time? even up to billions of years for some stars.
For example, let us observe our sun. if we look at the fossils that exist on earth, we can know that our earth has existed since 3 billion years ago. But until now according to research shows that our earth did not undergo major changes caused by the instability of the sun.
The sun has shone long enough. The sunlight that we feel today is no different from the sunlight felt by early dinosaurs. the question is: Why is the sun so stable? where does the sun get such a huge energy source?
Gravity and Gas pressure
Let's try to count the mass of the sun. the distance between our earth and the sun is 1 AU or about 150 million Km, the time it takes the Earth to surround the Sun is 365.25 days (one year). Assuming the earth's orbits are circular, the speed the Earth needs to travel around the Sun is 100000 km / h.
The Earth's movement around the sun is caused by the force of gravity of the Sun, so according to the Law of Gravitation, the force of gravity of the Sun is produced by a mass of 2 x 1030 kg! or equal to 330000 times the mass of the Earth.
Here the question arises Why did the sun not collapse into its center due to such a large mass? Because there is something that sustains the structure of the sun. If there is no "something" that sustains the entire mass, then the sun will collapse toward its center in less than half an hour! We never see it happen, It shows that there is something that sustains the structure of the sun.
The sun is like a glowing gas ball. If that's true, we can think of gas in the sun as an ideal gas that emits electromagnetic radiation. The ideal Gas law says that compressed gas will produce pressure against the compression. When the gas emits electromagnetic radiation, then the Sun also produces radiation pressure that goes beyond the surface of the sun.
Energy from Shrinking Stars
In the 19th century, two great physicists, Lord Kelvin of England and Hermann von Helmholtz of Germany separately tried to answer this question: About the source of solar energy comes from the shrinking. The assumption that in the past the size of the sun is much larger than its present size. As time passes, the sun shrinks as a result of the gravitational pull of its mass. This shrinking will free up potential energy that can be converted into thermal energy or thermal energy that is about 4 x 1048erg. According to the virial theorem, when a gravity system (like the Sun) changes its equilibrium, half of its potential energy will be converted into thermal energy, while the other half will be emitted. Thus, the energy emitted by the sun is 2 x 1048erg. A huge energy, but is it a source of solar energy?
To know this, we need to re-analyze the light emitted by the sun. This can be calculated if we regard the sun as a perfectly fluorescent black body. The curve of the energy distribution of a black body we use to calculate the energy output of the black body throughout the wavelength, then we sum up all the energy at different wavelengths. From this method we will have a law called the Law of Stefan-Boltzmann, which states that the total energy of every second emitted from every unit of the surface area of a black body is only dependent on its temperature. Since we know how much the surface of the Sun (assuming the Sun is spherical with the radius of 700,000 km) and also its surface temperature is 5800 K, it can be calculated the total energy radiating from the entire surface of the Sun at this time is 3.8 x 1033erg per second !
Radioactivity
Earlier it had assumed the Sun was in equilibrium between the gravitational pressure and the radiation pressure, an equilibrium we call the hydrostatic equilibrium. from this assumption, we can calculate the gravitational pressure occurring in the center of the sun, ie 3.4 × 10{11}atm. If we suppose that the gas in the center of the sun is the ideal gas, then the ideal gas law allows us to calculate the temperature in the "stove" of the sun if we know how much pressure in the center of the sun. The temperature in the "furnace" of the sun is thus roughly 15 million Kelvin!
This extremely high temperature and pressure allow for fusion reactions. From the experiment, it is known that the mass of 1 Helium atom is slightly lighter than the mass of 4 Hydrogen atoms. There is a mass loss of 0.7% of the mass of 4 Hydrogen atoms, meaning that every 1 kg of Hydrogen will change to 0.993 kg of Helium, and the remaining mass loss of 0.007 kg will be converted into energy. How much energy is liberated by 0.007 kg of this mass? When Einstein examines the effects of special relativity, he finds that the energy (E) and mass (m) are apparently equivalent and can mutually change through the very famous equation, E = mc2, where c is the speed of light. The speed of light is 300 000 km per second (3 x 10{8} meters per second), a very high speed. Through this very famous formula of Einstein, we can calculate that the reaction of 1 kg of Hydrogen to 0.993 kg Helium will free the mass of 0.007 kg equivalent to the energy of 0.007 x (3 x 108)2 = 6.3 x 10{14} Joule energy. This is proportional to the energy produced by burning 100 000 tons of coal!
We know that the amount of Hydrogen in the Sun is about 75% of the total mass of the Sun. We can calculate how much energy will be released if 10% of this Hydrogen is melted into Helium:
Energy = 0.007 x 0.75 x 0.1 x (2 x 10{30}) kg x (3 x 10{8} m / s)2 = 9.4 x 10{43} Joule = 9.4 x 10{50} Erg.
A tremendous energy, almost a thousand times the energy liberated by gravitational shrinking! How long can this nuclear reaction support the Sun? As we know, the energy emitted by the Sun is 3.8 x 1026 Joules every second. This means the Sun can shine over 7.5 Billion years!
Nuclear Power
Our sun contains 34% Hydrogen and 64% Helium, and 2% is a combination of other elements. The centuries-old secret of the founders of the Sun has been answered. When astronomers direct their spectroscope to other stars. they find that the spectrum of stars is the same as the Sun. which means that the Sun is one of the stars that is very close to us. Stars and Suns are the same objects but the star distance is much greater than the distance of our Earth to the Sun.
Research in the late nineteenth and early twentieth centuries about the nature of atoms and radioactivity concludes that it is the nuclear reaction that generates the energy of the Sun. Previously we have seen that the abundant Hydrogen in the Sun can carry on a nuclear reaction for billions of years.
Fusion reactions can occur in extreme conditions, and it has been estimated that the Sun's core is extreme enough to carry out such reactions. As we know, the temperature at the core of the Sun is about 15 million Kelvins. In the theory of gas dynamics, the temperature of a gas denotes the kinetic energy contained in the gas, due to the atomic motions of the gas. The extremely high temperatures in a gas state the remarkable atomic movement. Extremely high pressures may also state the density of the gas. The denser the gas, the closer the atomic nucleus is to each other.
Reference :
http://www.astronomynotes.com/starsun/s7.htm
http://www.physics.rutgers.edu/filenotfound.shtml
https://www.quora.com/Why-do-a-star-get-trapped-by-its-own-gravity-and-starts-to-shrink
http://www.radioactivity.eu.com/site/pages/Solar_Energy.htm
https://www.universetoday.com/60065/radiation-from-the-sun/
https://en.wikipedia.org/wiki/Nuclear_fusion