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?
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.