Expert: Philip Stahl - 2/15/2006

Question
I have been doing some research about the sun and have gotten interested in the energy the sun provides to the earth but my question is,

How does the Sun's energy arrive at the Earth?

I keep finding that only one billionth of the energy reaches earth and plenty of proportions on that but can not seem to understand how exactly it arrives to the Earth.  

Answer
Hello.

Okay, let's first start at the beginning and how the Sun's energy originates in the first place. This occurs deep inside its CORE at a temperature of some 10
million degrees F, which enables nuclei of hydrogen to *fuse* together in what we call nuclear fusion.

The basic reaction - actually compiling three separate ones together - is:

H1 + H1 + H1 + H1 ->  He4  + energy

That is, four hydrogen nuclei (protons) fuse to form one helium nucleus and energy given off.

The energy given off is in accord with the famous equation discovered by Einstein:

E = mc^2.

Which in terms of the above is more formally written:

E = (mass of reactants - mass of products) x speed of light squared

Now, since the mass of reactants (left side) will always be LESS than the mass of the product(s), in this case helium, that amounts to the difference in mass converted directly into energy, E.

Millions of such fusion reactions are ongoing in the Sun's core and the energy released is then transported toward the Sun's surface by the processes of *radiation* (actually radiative diffusion via photons), and convection. (The transfer of heat via heated elements -which acquire an excess of bouyancy in the Sun's fluid plasma medium, release their heat, then descend back toward the core to acquire more-before rising again)

It is estimated that, on average, it takes a photon generated in the typical core fusion reaction to take up to ONE MILLION years to get to near the solar surface. Fortunately, so many photons are formed at different times, that we (on Earth) don't notice any 1 million year delays in getting our heat and light!

Now, having reached the solar surface (or photosphere), how does the Sun's energy travel across the vacuum  of space and reach Earth?

This occurs by the process of RADIATION.

RADIATION specifically is conveyed in WAVES - which we call ELECTRO-MAGNETIC waves. (Or E-M waves). They get this name because they have electric (E) and magnetic (M) parts ("vectors") that vibrate at right angles to each other and perpendicular to the direction of propagation.

Thus:

E
^
!
!
!
X---------->M

With 'X' marking the direction of propagation - coming out of the screen TOWARD you.


These waves travel or propagate with a velocity = c, the speed of light, or 186,000 miles per second. This means the radiation from the Sun takes about 8 and 1/3 minutes to arrive at Earth.

The waves have differing *wavelengths*, some short and some long. The shorter the wavelength the higher the energy carried, and the longer the wavelength the lower the energy.

A simple relationship that gives how much energy is carried at a particular wavelength is:

E  = hc/ L

where h is Planck's constant (6.625 x 10^-34 J/s), and c is the speed of light (3 x 10^8 m/s) and 'L' is the wavelength.

As you can see, if L is small E must be large, and vice versa. (Given the product hc = constant)

Some short wavelength examples are: x-rays, ultraviolet (UV) radiation, and gamma radiation. You may be familiar with UV radiation as the type that can get through the Earth's atmosphere and cause sunburn.

Some long wavelength examples are: radio waves, microwaves, and *infrad-red radiation*.  The last is the type that primarily conveys HEAT, and when it is trapped by Earth's atmosphere, leads to a "greenhouse effect" - which we are now experiencing.

The factoid you found that "one billionth of the Sun's energy" reaches Earth is somewhat misleading. This fraction is based on *the total radiation emitted by the Sun in ALL directions*!

Obviously, at some distance x (in this case 93 million miles) a particular planet like Earth will only intercept a tiny fraction from the "radiation sphere" moving outwards as a wave front. (Since for a radiative "sphere" of 93 million miles in radius, a planet of only ~ 8,000 miles in diameter - will occupy only a very very tiny "sliver" of the sphere's surface *at that distance*).

Then again, bear in mind that the *intensity* of this radiation (of any form) falls off as the inverse square of the distance. So at 93,000,000 miles the intensity of energy received at Earth will be only:

(1/93)^2 of what would be received say at 1 million miles.

Be all this as it may, we are able to reckon just how much solar energy (on average) arrives at each square meter on Earth.

It turns out to be about:

1360 WATTS per sq. meter

Or, about equivalent to the power of 14 one hundred watt bulbs going into an area of about 3.3 ft by 3.3 ft.

This is what we refer to as "the solar constant".

Hopefully, this answer has aided your understanding of how the Sun's energy gets to Earth.