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For example, sunlight captured by plants would count in the "arrived as sunlight" category, whilst heat energy in the core of the earth would count in the "kinetic energy during formation" category.

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    $\begingroup$ Interesting question, but I believe that the energy gets transformed into the another form so rapidly that it is nearly impossible to accomplish this. $\endgroup$
    – User123
    May 24 at 20:21
  • $\begingroup$ If you have a bucket of water, add some new water, and then drain that same amount... how much is new vs old?! Likewise if you have to keep adding to counteract a leak. Same ideas here... things like gravitational\kinetic energy don't change much, but do participate in processes with "newer" energy such as in atmospheric circulation. And internal energy (temperature) doesn't change much... but does need the sun's warmth to maintain it from slowly decreasing. So it's an interesting question, but I'm with User123 that it's tough\impossible to really characterize. $\endgroup$ May 26 at 14:03
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When the Earth first formed, it had a rotational speed of about 12 hours. The Moon has been slowly stealing rotational speed over that time. This site estimates Earth's kinetic energy from rotation at $2.138×10^{29} J$, and since this varies with the square of rotation speed, the energy was about $8.5×10^{29} J$.

The Wikipedia article on solar energy says

The total solar energy absorbed by Earth's atmosphere, oceans and land masses is approximately 3,850,000 exajoules (EJ) per year.

This is $3.8×10^{24} J$ per year. Over 4.5 billion years, this would aggregate to about $10^{34} J$.

Now, I'm going to have to be handwavey here. The Sun's production of energy, as well as the Earth's ability to capture that energy, have varied a lot over time. But this isn't enough to overcome 4 orders of magnitude -- by the beginning of the Phanerozoic, about 600 million years ago, the Sun's brightness was 97% of its current value.

The aggregate amount of solar energy received during the Precambrian (assuming 25% luminosity at the beginning) - $$3.8×10^{24} J×4×10^9×.62 = 9.4×10^{29} J$$ already matches the initial kinetic energy, but the amount received during the Phanerozoic $$3.8×10^{24} J×6×10^8×.98 = 2.2×10^{33} J$$

is at least 3 orders of magnitude greater.

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We can try to compare sunlight energy arriving from the Sun and geothermic energy coming from the Earth's interior.

The Earth gets about 340 W/m2 from the Sun(1) while the average geothermic flux is about 0.1 W/m2.(2) Therefore, the current energy of sunlight is way larger than that from kinetic energy during Earth formation.

Additionally, it should be noted that a large part of geothermic energy doesn't come from Earth cooling by getting rid of its formation heat but from radioactive decay, making the comparison with sunlight even more one sided.

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