# The Age of the Sun

How old is the sun? How does the sun shine? These questions are two sides of the same coin, as we shall see.

The rate at which the sun is radiating energy is easily computed by using the measured rate at which energy reaches the earth’s surface and the distance between the earth and the sun. The total energy that the sun has radiated away over its lifetime is approximately the product of the current rate at which energy is being emitted, which is called the solar luminosity, times the age of the sun.

The older the sun is, the greater the total amount of radiated solar energy. The greater the radiated energy, or the larger the age of the sun, the more difficult it is to find an explanation of the source of solar energy.

To better appreciate how difficult it is to find an explanation, let us consider a specific illustration of the enormous rate at which the sun radiates energy. Suppose we put a cubic centimeter of ice outside on a summer day in such a way that all of the sunshine is absorbed by the ice. Even at the great distance between the earth and the sun, sunshine will melt the ice cube in about 40 minutes. Since this would happen anywhere in space at the earth’s distance from the sun, a huge spherical shell of ice centered on the sun and 300 million km (200 million miles) in diameter would be melted at the same time. Or, shrinking the same amount of ice down to the surface of the sun, we can calculate that an area ten thousand times the area of the earth’s surface and about half a kilometer (0.3 mile) thick would also be melted in 40 minutes by the energy pouring out of the sun.

In this section, we shall discuss how nineteenth-century scientists tried to determine the source of solar energy, using the solar age as a clue.

#### Conflicting Estimates of the Solar Age

The energy source for solar radiation was believed by nineteenth-century physicists to be gravitation. In an influential lecture in 1854, Hermann von Helmholtz, a German professor of physiology who became a distinguished researcher and physics professor, proposed that the origin of the sun’s enormous radiated energy is the gravitational contraction of a large mass. Somewhat earlier, in the 1840’s, J. R. Mayer (another German physician) and J. J. Waterson had also suggested that the origin of solar radiation is the conversion of gravitational energy into heat.1

Biologists and geologists considered the effects of solar radiation, while physicists concentrated on the origin of the radiated energy. In 1859, Charles Darwin, in the first edition of On The Origin of the Species by Natural Selection, made a crude calculation of the age of the earth by estimating how long it would take erosion occurring at the current observed rate to wash away the Weald, a great valley that stretches between the North and South Downs across the south of England. He obtained a number for the “denudation of the Weald” in the range of 300 million years, apparently long enough for natural selection to have produced the astounding range of species that exist on earth.

As Herschel stressed, the sun’s heat is responsible for life and for most geological evolution on earth. Hence, Darwin’s estimate of a minimum age for geological activity on the earth implied a minimum estimate for the amount of energy that the sun has radiated.

Firmly opposed to Darwinian natural selection, William Thomson, later Lord Kelvin, was a professor at the University of Glasgow and one of the great physicists of the nineteenth century. In addition to his many contributions to applied science and to engineering, Thomson formulated the second law of thermodynamics and set up the absolute temperature scale, which was subsequently named the Kelvin scale in his honor. The second law of thermodynamics states that heat naturally flows from a hotter to a colder body, not the opposite. Thomson therefore realized that the sun and the earth must get colder unless there is an external energy source and that eventually the earth will become too cold to support life.

Kelvin, like Helmholtz, was convinced that the sun’s luminosity was produced by the conversion of gravitational energy into heat. In an early (1854) version of this idea, Kelvin suggested that the sun’s heat might be produced continually by the impact of meteors falling onto its surface. Kelvin was forced by astronomical evidence to modify his hypothesis and he then argued that the primary source of the energy available to the sun was the gravitational energy of the primordial meteors from which it was formed.

Thus, with great authority and eloquence Lord Kelvin declared in 1862:

That some form of the meteoric theory is certainly the true and complete explanation of solar heat can scarcely be doubted, when the following reasons are considered: (1) No other natural explanation, except by chemical action, can be conceived. (2) The chemical theory is quite insufficient, because the most energetic chemical action we know, taking place between substances amounting to the whole sun’s mass, would only generate about 3,000 years’ heat. (3) There is no difficulty in accounting for 20,000,000 years’ heat by the meteoric theory.

Kelvin continued by attacking Darwin’s estimate directly, asking rhetorically:

What then are we to think of such geological estimates as [Darwin’s] 300,000,000 years for the “denudation of the Weald”?

Believing Darwin was wrong in his estimate of the age of the earth, Kelvin also believed that Darwin was wrong about the time available for natural selection to operate.

Lord Kelvin estimated the lifetime of the sun, and by implication the earth, as follows. He calculated the gravitational energy of an object with a mass equal to the sun’s mass and a radius equal to the sun’s radius and divided the result by the rate at which the sun radiates away energy. This calculation yielded a lifetime of only 30 million years. The corresponding estimate for the lifetime sustainable by chemical energy was much smaller because chemical processes release very little energy.

#### Who was right?

As we have just seen, in the nineteenth century you could get very different estimates for the age of the sun, depending upon whom you asked. Prominent theoretical physicists argued, based upon the sources of energy that were known at that time, that the sun was at most a few tens of million years old. Many geologists and biologists concluded that the sun must have been shining for at least several hundreds of millions of years in order to account for geological changes and the evolution of living things, both of which depend critically upon energy from the sun. Thus the age of the sun, and the origin of solar energy, were important questions not only for physics and astronomy, but also for geology and biology.

Darwin was so shaken by the power of Kelvin’s analysis and by the authority of his theoretical expertise that in the last editions of On The Origin of the Species he eliminated all mention of specific time scales. He wrote in 1869 to Alfred Russel Wallace, the codiscoverer of natural selection, complaining about Lord Kelvin:

Thomson’s views on the recent age of the world have been for some time one of my sorest troubles.

Today we know that Lord Kelvin was wrong and the geologists and evolutionary biologists were right. Radioactive dating of meteorites shows that the sun is 4.6 billion years old.

What was wrong with Kelvin’s analysis? An analogy may help. Suppose a friend observed you using your computer and tried to figure out how long the computer had been operating. A plausible estimate might be no more than a few hours, since that is the maximum length of time over which a battery could supply the required amount of power. The flaw in this analysis is the assumption that your computer is necessarily powered by a battery. The estimate of a few hours could be wrong if you computer were operated from an electrical power outlet in the wall. The assumption that a battery supplies the power for your computer is analogous to Lord Kelvin’s assumption that gravitational energy powers the sun.

Since nineteenth century theoretical physicists did not know about the possibility of transforming nuclear mass into energy, they calculated a maximum age for the sun that was too short. Nevertheless, Kelvin and his colleagues made a lasting contribution to the sciences of astronomy, geology, and biology by insisting on the principle that valid inferences in all fields of research must be consistent with the fundamental laws of physics.

We will now discuss some of the landmark developments in the understanding of how nuclear mass is used as the fuel for stars.

1 von Helmholtz and Mayer were two of the codiscoverers of the law of conservation of energy. This law states that energy can be transformed from one form to another but the total amount is always conserved. Conservation of energy is a basic principle of modern physics that is used in analyzing the very smallest (sub-atomic) domains and the largest known structure (the universe), and just about everything in between. We shall see later that Einstein’s generalization of the law of conservation of energy was a key ingredient in understanding the origin of solar radiation. The application of conservation of energy to radioactivity revealed the existence of neutrinos.

A Gimpse of a Solution