The Sun is Shrinking

…and this happens enormously fast – thinking in terrestrial dimensions. Nuclear fusions in which hydrogen is transformed into helium permanently happen in the sun’s core. At it, a helium atom is formed out of four hydrogen atoms, to put it simply. But why is the sun that hot? – The answer can be obtained by making a very peculiar observation: First, take the building blocks of a helium atom (two protons and two neutrons), “weigh” them individually, and add their masses together. Then, “weigh” a helium atom (the atom as a whole, not its components!) and note its mass. You’ll find that the sum of each two protons and two neutrons is surprisingly bigger than the mass of a full helium atom! But how is this possible? Our atomic building blocks become lighter if combined into a helium atom. Why?

A schematic proton-proton chain reaction as it happens in stars the size of our Sun or smaller.

Obviously, there’s a mass difference between “source material” and “end products”. Did mass get somehow lost in this process? Isn’t mass a conserved quantity and, therefore, can’t just vanish or appear from nowhere? – The answer is: No, mass is preserved only in classical, Newtonian physics! As Albert Einstein figured out, it is indeed possible to convert mass into energy and vice versa. “Mass” and “energy” are closely linked by his famous equivalence of mass and energy formula E=Δm·c². (We write “Delta m” – this is Δm – instead of just m to elucidate our fiddling with mass differences.) So as it turns out, no mass gets lost at the process of nuclear fusion at all, but instead it is transformed into energy – “some kind of a more universal conservation law is at work”. The resulting energy is radiated, moves from the sun’s core to the surface in more than 100,000 years, and finally finds itself on an eight minute trip to Earth, where it possibly warms our ice cream or our beer. (Was it worth while then? 😉 ) 

However, this is what the sun looks like right now.

By the way: This just-discussed and so-called “mass defect” also allows us to obtain energy from nuclear fission. We exploit this effect in nuclear power plants by splitting heavy elements like, e.g., enriched uranium. For elements heavier than iron, the mass defect works inversely: The sum of the masses of the individual building blocks (i. e. protons and neutrons) is smaller than the nucleus as a whole. Hence, if we want to obtain energy from a nuclear reaction, we have to split the nuclei. For all elements lighter than iron, it’s necessary to merge or fuse nuclei in order to have a positive energy budget.

How much energy does the Sun emit?
–> 3.9·1026 joule per second.

Let’s put this number, together with the speed of light c = 3·108 meters per second (approx. 670 million miles per hour), in Einstein’s equation E = Δm·c2:

E / c2 = Δm
(3.9·1026) / (3·108)2 = Δm = 4.3·109 kg

Our result might seem surprising: The Sun loses 4.3·109 kilograms per second because of radiating energy. This is more than 4 million tons per second!

Would you like to have a little illustration? –> Click here(The number on the left represents the Sun’s mass loss in million tons while the number on the right counts the mass of hydrogen transformed into helium in billions of tons.)

But… how long will it take until the Sun has “radiated itself away”?

Don’t worry, this will take a looong time! Before this happens, the Sun will run out of “fuel” in some billion years and life on Earth will be gone at the latest at that time. (Assuming, of course, that we will, until then, be spared from big asteroid impacts and that we won’t blow ourselves away in a disastrous nuclear war, which, I think, represents one of the biggest threats to the well-being of human kind. After all, us human beings aren’t that intelligent in the long term, are we?)
Surely, the Sun loses some 4,000,000,000 kilograms per second, but its mass loss, projected over ten billion (= 10,000,000,000) years, adds up to just about 0.1 per cent of its total mass.

…now the time seems right to say “Wow, the Sun has to be enormously big indeed!”. 😉


Finally, I’d like to show you a gorgeous video which shows the Sun’s previous three years in only three minutes.
We owe this footage to NASA’s Solar Dynamics Observatory (SDO). If you watch closely, you’ll notice a slight increase of the solar activity in the course of the video. This activity cycle repeats itself every eleven years.


About tempse

I think about physics, other stuff, and physics. Besides, I share some thoughts on the internet.

Posted on September 21, 2013, in astronomy, physics, science, Solar system, Sun, video and tagged , , , , , , . Bookmark the permalink. 1 Comment.

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