The Source of the Sun s Energy

Transcription

1 The Source of the Sun s Energy

2 In the Late 1800s Physicists wanted to know: n What is the source of the energy of the stars? (In particular, the Sun) n And how long can it last?

3 Here are Two Possibilities (neither is correct!) n Perhaps the Sun is literally burning (undergoing ordinary chemical reactions, like coal in a fireplace); or n Perhaps the Sun is slowly contracting, using gravity to keep itself hot (and indeed possibly to progressively raise its temperature)

4 Perhaps the Sun is 1. Burning Ordinary Chemistry undergoing purely chemical 1 reactions, like burning (say, C + O à CO) that release energy. But this could provide the Sun s power for only some thousands of years.

5 2. Slow Contraction Gravity Provides the Energy The slow, steady shrinking of the sun would keep it hot. Potential energy is slowly converted to the energy of movement (as the particles draw closer together) and thermalize (collide and jiggle heat!)

6 Very Important Early On! This is indeed exactly how the stars form (relatively quickly!) from distended clouds of interstellar gas, heating up as they do so. But once a star becomes dense enough to be opaque (that is, heat and light inside it cannot readily escape), the contraction slows down enormously.

7 Meet Lord Kelvin He argued for slow steady gravitational contraction ( Kelvin contraction ) as the source of solar energy.

8 Can We Test This Directly? What rate would be required? Would we notice the sun perceptibly shrinking? It would have to do so by about 40m (in diameter) every year. We ve been monitoring it seriously for ~2000 years. Over that span of time, it would need to shrink by about 80 km - that is, 0.006% of its diameter. This would be utterly unobservable.

9 How Long Could it Last? Kelvin contraction could keep the Sun incandescently hot for a reasonably long time tens of millions of years, depending on various assumptions. But it cannot explain how the sun can stay essentially unchanged for billions of years, as we now know to be the case.

10 Okay at the Time But in the late 1800s, this was not a critical problem! The age of the Earth was very uncertain, based on various indirect arguments. For example: n n How long would it take the oceans to become as salty as they are now? (minerals get leached out of the continental soils) How long would it take to erode away old mountains, leaving rounded hills like the Appalachians?

11 One Noteworthy Contributor: Charles Darwin His theory of the origin of species, new in 1859, suggested that the Earth had to be very old indeed, to allow the observed biological diversity to have taken place.

12 Important Implications 1. We have no direct observation that rules out the possibility that the sun is slowly shrinking. But we reject this possibility because: n It would not give a long enough life (billions of years); and n We now have direct measurements that prove that thermonuclear reactions are the actual energy source! [stay tuned for later details] 2. If nuclear reactions in the core of the sun were mysteriously to cease right now, it would resume a slow contraction and stay hot for millions of years yet to come.

13 Problem Solved! E = m c 2

14 Energy from Mass Einstein showed that E = m c 2 In other words, a small amount (m) of mass can, in principle, be converted to a lot of energy (E) if only we knew how! Ordinary matter can be thought of, loosely, as frozen energy.

15 An Unimaginably Rich Resource! Consider a dime, with a mass of 2.3 grams. (Or equivalently, simply pick up a pebble of that mass!) E = m c 2 tells us that this lump could (in principle) be converted to 2 x Joules of energy. That would be enough to supply the complete energy needs of a city of a couple of million people -- for a whole year! Alternatively, we would have to burn about 30 tonnes of coal a day. (Even that assumes 100% efficiency; actually, much more would be needed.)

16 Apply This to the Sun The Sun emits 4 x joules of energy every second (don t worry about the numbers, or the units!) Using E = m c 2, or equivalently m = E / c 2 we learn that the Sun is (somehow) converting mass into pure radiant energy at a rate of 4 million metric tons a second

17 Big-Time Mass Loss? As noted, the sun loses about 4 million tonnes of its mass every single second But the sun itself is 2 billion trillion times as massive as this!

18 Longevity Assured! In principle, therefore, the sun has enough mass to last 10 trillion years. [It will not last that long, however, because not all of its mass gets converted to energy. As we will learn, only about 0.1% of it does.] Still, that yields a potential lifetime of 10 billion years.

19 Keeping Numbers in Perspective Think About Gaining Weight How much weight does a growing blue whale gain per day?

20 Some Numbers An adult blue whale weighs about 100 tonnes (100,000 kg) Suppose it reaches maturity in 10 years. Average weight gain ~ 25 kg a day That s huge for an ant! But not so much for a whale...

21 Will the Earth s Orbit Change? Over billions of years, the inexorable loss of mass will slightly weaken the Sun s gravitational grip on the Earth, but this has an inconsequential effect.

22 The Big Question Exactly how does some of the matter in the Sun get converted to energy? [Knowing, from Einstein, that this is possible does not immediately tell us how it happens!] Can we utilize this same principle and process on Earth, in a controlled way?