## Lighting the Sun’s Fire

The Sun produces energy at a prodigious rate. It has done so for a long time. To find out how it produces energy and what it took to get it lighted, scientists divided the total solar output by the Sun’s mass. This gave the energy each unit of mass produces. They then compared this production rate with the rates for various processes, like the simple cooling of a very hot body, or the burning of various kinds of fuels. The production rate is so high and the burning has gone on so long that nothing less than the burning of a nuclear fuel can explain it.

We can estimate the Sun’s mass accurately enough from three numbers. We need the period of the Earth’s orbit, 1 year. Then we need the Earth’s distance from the Sun, 93 million miles or 150 million kilometers. Finally, we need the amount of gravity mass produces, as measured in laboratory experiments. From this, a straightforward calculation based on Newtonian mechanics gives the Sun’s mass.

1 990 000 000 000 000 000 000 000 000 000 kilograms

We measure sunlight intensity in space at the distance of the Earth from the Sun. First we imagine a sphere centered on the Sun that has the Earth embedded in its surface. Then we consider that sunlight must have the same intensity anywhere it passes through the imaginary sphere. The radius of the sphere is 150 million kilometers, and from this we can calculate the surface area of the sphere. We multiply the power that flows through a square meter by the area of the sphere. In this way we obtain the Sun’s energy productivity as 2 ergs per second for every gram of mass. In modern units that is 200 microwatts per kilogram. Now, taking the estimated lifetime of the Sun at 10 000 million years (about twice its present age), and remembering that a year is about 31 million seconds, each kilogram of the Sun has to produce 63 000 000 megawatt-seconds or 18 000 megawatt-hours of energy.

A wood or coal fire produces plenty of power, but only while the fuel is burning. There is still some heat to radiate once combustion stops, but the heat dissipates quickly and the temperature of the ashes falls rapidly. A kilogram of coal produces at most about 10 kilowatt-hours of energy. If the Sun were burning coal it could only last a thousand years or so. Historical records are sufficient to establish that the Sun has been shining longer than that! Kelvin calculated how long the Sun could provide heat and light simply by glowing from the compression of its own gravity. Such gravitational collapse would produce energy at the Sun’s prodigious rate for a few million years, but not for thousands of millions of years.

Once people knew that the Earth and Sun are about 4 650 million years old, someone had to figure out where the Sun gets its energy. Hans Albrecht Bethe (German-born American physicist, 1906–2005) proposed this question to himself one day in 1938 while returning by train to Ithaca, New York, from a physics conference in Washington. He finished his calculations before sundown.[i] The fire is not chemical but nuclear.

[i] George Gamow tells the story in

We can estimate the Sun’s mass accurately enough from three numbers. We need the period of the Earth’s orbit, 1 year. Then we need the Earth’s distance from the Sun, 93 million miles or 150 million kilometers. Finally, we need the amount of gravity mass produces, as measured in laboratory experiments. From this, a straightforward calculation based on Newtonian mechanics gives the Sun’s mass.

1 990 000 000 000 000 000 000 000 000 000 kilograms

We measure sunlight intensity in space at the distance of the Earth from the Sun. First we imagine a sphere centered on the Sun that has the Earth embedded in its surface. Then we consider that sunlight must have the same intensity anywhere it passes through the imaginary sphere. The radius of the sphere is 150 million kilometers, and from this we can calculate the surface area of the sphere. We multiply the power that flows through a square meter by the area of the sphere. In this way we obtain the Sun’s energy productivity as 2 ergs per second for every gram of mass. In modern units that is 200 microwatts per kilogram. Now, taking the estimated lifetime of the Sun at 10 000 million years (about twice its present age), and remembering that a year is about 31 million seconds, each kilogram of the Sun has to produce 63 000 000 megawatt-seconds or 18 000 megawatt-hours of energy.

A wood or coal fire produces plenty of power, but only while the fuel is burning. There is still some heat to radiate once combustion stops, but the heat dissipates quickly and the temperature of the ashes falls rapidly. A kilogram of coal produces at most about 10 kilowatt-hours of energy. If the Sun were burning coal it could only last a thousand years or so. Historical records are sufficient to establish that the Sun has been shining longer than that! Kelvin calculated how long the Sun could provide heat and light simply by glowing from the compression of its own gravity. Such gravitational collapse would produce energy at the Sun’s prodigious rate for a few million years, but not for thousands of millions of years.

Once people knew that the Earth and Sun are about 4 650 million years old, someone had to figure out where the Sun gets its energy. Hans Albrecht Bethe (German-born American physicist, 1906–2005) proposed this question to himself one day in 1938 while returning by train to Ithaca, New York, from a physics conference in Washington. He finished his calculations before sundown.[i] The fire is not chemical but nuclear.

[i] George Gamow tells the story in

*The Birth and Death of the Sun*(New York: Mentor Book, The New American Library of World Literature, 1945).