It is a well-documented fact that Jupiter emits more energy than it receives from the sun. The implication is that there is some source of energy powering Jupiter from the inside. Is that source thermonuclear, or chemical? In this article we examine the known sources of energy which could be providing the excess energy with and eye on whether or not these sources constrain evolution.

What goes in must come out

During each second of its existence, the sun radiates 3.9 x 10³³ ergs into space. This is over 100,000,000,000 (one hundred billion) megatons¹ of TNT per second, or equivalent to some 25 billion hydrogen bombs exploding every second. The sun throws its energy in all directions so that little by comparison reaches earth, which is but a speck in the sky when seen from the sun. By comparison, the fraction of that energy that reaches Jupiter is that fraction of the total sky which Jupiter's disk covers when seen from the sun. Jupiter is about 88,700 miles in diameter and it is 489 million miles from the sun. By the time sunlight reaches Jupiter's distance, it has been diluted over a shell whose area is 4pD₄² = 3 x 10¹⁸ square miles. (Here D is the Jupiter-sun distance.) Jupiter's disk itself, by contrast, covers an area of 2.5 * 10¹⁰ square miles. The ratio of the two areas signifies that Jupiter receives seven billionth of the sun's energy or a total of 3.2 x 10²⁵ ergs/sec. Now Jupiter emits about 1.9 times the energy it receives, so it radiates 6.1 x 10²⁵ ergs per second. This means that Jupiter is radiating 2.9 x 10²⁵ ergs per second of its own energy.

Mass energy

Jupiter's mass if 318 times the earth's which amounts to a total of 1.9 x 10³⁰ grams. If all the mass were converted into energy, (mind you, no mechanism to do that exists as far as we know,) then by the famous E=mc² formula, Jupiter's total available store of energy is 1.7 x 10⁵¹ ergs. At the rate it is losing energy, Jupiter could last for another 3 x 10²⁵ seconds or about 10¹⁸ years. This is much, much older than any the age of the universe according to the big-bang model.

That all of Jupiter's mass should be converted into energy, as assumed in the previous paragraph, is unlikely. According to stellar structure models, Jupiter is too small to convert hydrogen into helium and so there should be no nuclear furnace inside. Of course, some might argue that the same model doesn't predict the right result for the sun, so why trust it for Jupiter? Good question, but the model predicts more energy from the sun than is observed, so it stands to reason that it errs on the conservative side. Thus it seems a safe call that Jupiter's core is not thermonuclear.

Chemical Energy

Another potential energy source is chemical energy. In order to arrive at an estimate for it's lifetime, we need to find the number of nucleons in Jupiter. Since Jupiter's mass is 1.9 x 10³⁰ grams, and since each proton is 1.7 x 10^-24 gm, it follows that Jupiter's mass is made up of 1.1 x 10⁵⁴ protons. If we assume that Jupiter is made up entirely of hydrogen (the most optimistic case from the evolutionist's perspective; actually, 30% of Jupiter's mass resides in helium and about 5% in heavier atoms), and that each hydrogen atom will release 10eV (1.6 x 10^-11 erg) in chemical energy, then the total energy available is 1.6 x 10⁴³ ergs and this will last Jupiter for a good 18 billion years.

Gravitational Energy

Next, consider Jupiter's gravitational energy. Jupiter's gravitational potential is V_G=GM₄/R₄. From this it can be derived that Jupiter's total gravitational energy is 1.9x10⁴³ ergs, about equivalent to its chemical energy. Actually, by the Virial Theorem, only half of that energy is available to heating up the planet so that its lifetime is of the order of 10 billion years. By contrast, if the sun were powered by gravitational energy, it could only last for a few tens of millions of years.

Conclusion

Although Jupiter radiates about twice as much energy as it receives from the sun, its huge mass provides it with enough chemical and potential gravitational energy that it could persist in its present state for billions of years. Thus, unlike the case for the moon and sun, Jupiter's excess energy does not allow a straight-forward contradiction of the evolutionary time scale.