Can Earth's mass increase due to sunlight? With how much? Asking this just out of curiosity:
I am no physics buff but considering the particle nature of light, each photon has energy (however small it may be). Given this, can the earth's mass increase given that it has been receiving the sunlight and thus photons for a considerable period of time.
 A: Yes, but it’s very small rate of change, and it is almost perfectly balanced with an equal loss.
The total power of all the sunlight striking the earth is $\pi r_{earth}^2 {solarirradiance} = 173.9 PW$, divide that by $c^2$ and we get $1.935 kg/s$.
However, a lot of this is simply reflected, and even that which is absorbed is almost perfectly balanced by an equal loss of energy in the form of re-emitted thermal radiation. The small remaining difference is things like organic carbon sequestration — the sort of thing that will form new coal and oil deposits over million-year timescales.
The Earth is also losing mass as the radioactive elements slowly decay. I wouldn’t be surprised if that turns the whole thing into a net loss mass, but I don’t have concrete numbers to hand.
A: As you can see from the comments, the net change is probably close to zero.
Though, a photon does have stress-energy, and as it gets absorbed by the atmosphere or the land or waters on the surface, it transfers its energy to the energy of the parts of Earth.

All internal energy such as thermal, rotational, and internal potential energy contributes to the rest mass of an object. In fact, the vast majority of the mass of an atom is due to the internal energy between quarks that make up the nucleus rather than the rest mass of the quarks themselves.
  So, yes, a hot object has greater rest mass and would weigh more when measured, if a scale were sensitive enough.

Will heating up an object increase its mass?
So basically if you just look at the effect of a single photon as it gets absorbed, yes it does make the Earth in theory heavier.
