# Mass accumulation rate and orbit-time of earth

According to me following reason of mass accumulation of earth has been completely overlooked so far. The sunrays that fall on the oceans travel deep into water and finally get converted into mass which eventually results in "mass-accretion of the earth". So earth is continuously getting heavier due to the mass being added to it due to this reason year by year. Therefore, should this also not be one of the reasons why the orbit-time of the earth (time taken by it to take one round of the sun) is bound to change (increase or decrease) with time?

• The Earth is roughly in thermal equilibrium, so the small amounts of mass-energy that it gains from the sun are radiated away, at longer wavelengths. Total change in mass energy is about zero – James K Mar 22 '18 at 20:17
• The Earth has been collecting actual mass in the form of meteorites, comet debris, etc. for billions of years. AFAIK that accretion far out-masses the loss due to atmospheric gas escaping. – Carl Witthoft Mar 23 '18 at 12:52
• While it's theoretically possible to convert light into mass, does this actually happen on Earth, outside of laboratories? – user21 Mar 24 '18 at 14:07

OK. Let's do the numbers. The Earth presents an circular "profile" of radius about 6 million meters to the Sun so it's cross-sectional area is about $10^{14} m^2$. The solar irradiance at the top of the atmosphere is about 1400 $W/m^2$ so the total power received from the sun is about $10^{17}W$, by coincidence, more-or-less equal to $c^2$ in SI units. So the mass equivalent of the sunlight received by Earth is about $1 kg/s$ or about $3 \times 10^7 kg/year$. This is about one part in $10^{17}$ of the mass of the Earth per year, so even if were all absorbed and none of it re-radiated (which would be thermodynamically impossible) the increase in mass is so small that the orbital change would be unmeasurable. In fact as @James K has already pointed out in a comment, more or less the same amount of energy (and therefore mass) is radiated away as heat radiation, so even this tiny change does not really occur.

• Indeed, a much bigger effect is the fact that the Sun is losing about 1 part in $10^{14}$ of its mass every year. – ProfRob Mar 22 '18 at 21:54

Steve Linton is of course correct, but I just wanted to point out a very basic misconception in your post. The orbital radius and period of the Earth hardly depend on the mass of the Earth at all.

The semi-major axis of the Earth's orbits depends (via Kepler's third law and conservation of angular momentum) on the sum of the mass of the Sun and the mass of the Earth (the former of course being many orders of magnitude larger).

The Sun is losing mass continually via radiation and via the solar wind. This is lost at a rate of $-9.3\times 10^{-14}$ solar masses per year ( Noerdlinger 2008). This results in the growth of the Earth's orbit by about 1.4 cm per year. Any mass accreted (or indeed lost by for instance the loss of atmosphere into space) has a totally negligible effect on the Earth's orbit compared to this.

• I think this question got very nice answers and an important comment Plus 1 to all of them! – Alchimista Mar 23 '18 at 12:09
• hmmmm.... 1.4 cm/year * 4.5 billion years = total increase of 0.04% of the orbit radius (1 AU) . Space is really really big! – Carl Witthoft Mar 23 '18 at 12:56
• My query related to the light that entered the oceans through refraction, that is, which does not get radiated back into space. – S C Sawhney Mar 27 '18 at 6:13