Transcript The Sun`s Energy Supply (PowerPoint version)

The Source of
the Sun’s Energy
In the Late 1800s
Physicists wanted to know:


What is the source of the energy of the
stars? (In particular, the Sun)
And how long can it last?
Here are Two Possibilities
(neither is correct!)


Perhaps the Sun is literally burning (undergoing
ordinary chemical reactions, like coal in a
fireplace); or
Perhaps the Sun is slowly contracting, using
gravity to keep itself hot (and indeed possibly to
progressively raise its temperature)
1. Burning
Ordinary Chemistry
Perhaps the Sun is
undergoing
purely chemical
1
reactions, like burning
(say, C + O  CO)
that release energy.
But this could provide the
Sun’s power for only
some thousands of years.
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!)
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.
Meet Lord Kelvin
He argued for slow
steady gravitational
contraction (“Kelvin
contraction”) as the
source of solar energy.
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.
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.
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:


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?
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.
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:


It would not give a long enough life (billions of years); and
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.
Problem Solved!
E=mc
2
Energy from Mass
Einstein showed that
E = m c2
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’.
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 10 14 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.)
Apply This to the Sun
The Sun emits 4 x 1026 joules of energy every
second (don’t worry about the numbers, or the
units!)
Using E = m c2, 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
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!
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.
Keeping Numbers in Perspective
Think About Gaining Weight
How much
weight does a
growing blue
whale gain per
day?
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...
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.
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?