According to this answer, energy has some (minimal) mass associated with it. Therefore, when lots of energy hits the earth (such as solar radiation in a 24 hour period) shouldn't the earth gain some small additional mass? And if so, how much?
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5$\begingroup$ Slight problem: we lose about as much energy to space as we gain, which is why the oceans are not boiling right now. Still you can calculate roughly what you are asking; the typical way to do this calculation is to look up the solar constant $\Phi$ on Wikipedia, look up the radius of the Earth $R$, Earth shows a circular cross-section to the Sun so compute $\Phi~\pi R^2~T$ for whatever time $T$ you want, that's the energy absorbed in that time. Then divide by $c^2$ to get mass. $\endgroup$– CR DrostCommented Jan 12, 2017 at 17:15
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2 Answers
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There's an answer to your question, but it's not all that meaningful.
The sun strikes the Earth with $1.5\cdot10^{22}J$ of energy every day. Using $m=\frac{E}{c^2}$ we find this has a mass equivalent of 166897kg.
However, the Earth does not actually gain mass this way. The Earth is also radiating energy into space, continuously. If we assume the average , so the amount of energy coming into the system equals the amount of energy leaving the system. As a result, the earth is not gaining mass by this at all. (or if any, its a small amount attributable to global warming).
We also gain about 40000kg of space dust every day, and lose about 95000kg of hydrogen from the atmosphere. You win some, you lose some.
answered Jan 12, 2017 at 17:18
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3$\begingroup$ Does the absorption of energy through photosynthesis increase the mass at all? $\endgroup$– Caleb707Commented Jan 12, 2017 at 20:16
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1$\begingroup$ @CalebMauer If you increase the energy stored in an object, then its mass increases accordingly. Of course, the amount of mass gained there is miniscule compared to the amount of mass gained by the CO2 molecules pulled from the atmosphere. $\endgroup$ Commented Jan 12, 2017 at 20:56
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4$\begingroup$ Wow I totally misread the question and was assuming it was asking about the mass from particle radiation, e.g. from the solar wind. $\endgroup$– MichaelCommented Jan 12, 2017 at 22:05
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3$\begingroup$ @CortAmmon Moving CO2 from the atmosphere to a plant has no net gain or loss of mass for the Earth. Since the energy has been trapped, this is a reasonable question to ask. Does the trapped solar energy from photosynthesis increase the mass of the Earth? This is probably also roughly in equilibrium because plants are dying all the time and gradually releasing their stored energy, some of which would escape into space. $\endgroup$ Commented Jan 12, 2017 at 22:52
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4$\begingroup$ @Devsman Yes. Calculating what that equilibrium is could be a bit time consuming, but we can comfortably say that there is some equilibrium temperature, and it's hotter than the cosmic background radiation and colder than the surface of the sun. Of course, rather than calculating, we could always just measure and say its currently 61F, but that kinda feels like cheating =) $\endgroup$ Commented Jan 13, 2017 at 21:44
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Not only does Earth not retain any significant amount of energy it gets from the Sun, but it actually loses its thermal energy (by radiating more than it is absorbing) while its core is cooling down. Core cooldown rate is estimated at about 50 terawatt, which translates to about 2 kg of mass lost per day.
As Cort's answer explains, there are other sources of mass gain / loss which are several orders of magnitude more significant than this mass loss due to radiation.
answered Jan 13, 2017 at 10:11
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$\begingroup$ $$\textit{> Core cooldown rate is estimated at about 50 terawatt} \\ \text{Does all of this energy make it to the surface, though?}$$ $\endgroup$– user78072Commented Apr 14, 2018 at 11:30
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$\begingroup$ @Josef Where else would it go? I'm not aware of any large-scale endothermic processes in the core. $\endgroup$ Commented Apr 16, 2018 at 7:51
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1$\begingroup$ @dimitry-grigoryev I read somewhere that the formation of basalts consumes a lot of the energy, but apparently not. From Wikipedia (en.wikipedia.org/wiki/Earth%27s_energy_budget): "The geothermal heat flux from the Earth's interior is estimated to be 47 terawatts.[10] This comes to 0.087 watt/square metre, which represents only 0.027% of Earth's total energy budget at the surface, which is dominated by 173,000 terawatts of incoming solar radiation." $\endgroup$– user78072Commented Apr 16, 2018 at 8:58