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Does Jupiter's Excess Energy Imply A Young Planet?

Gerardus D. Bouw, Ph.D.

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 VG=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.


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.


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1 One megaton TNT equivalent = 3.4 x 1022 ergs.

Translated from WS2000 on 4 September 2005 by ws2html.