[chintan (OP)]

If there were and are meteorites and asteroids falling on earth since the beginning of time. How much the mass of earth have changed !? []

[chris]

The Earth is losing between 50,000 and 60,000 tonnes of mass each year.

How do we arrive at this figure?

We need to consider the "mass balance"; that is, how much material is arriving here that wasn't here to start with, and how much material is leaving the planet.

First, let's consider how the Earth is gaining mass:

Earth is continuously gaining mass in the form of dust particles, and sometimes larger bodies, that fall in from space. Scientists estimate that this adds up to about 40,000 tonnes of material each year.

At the same time, using planet-wide temperature readings from NASA and other sources, one can see that the planet is warming up, or gaining thermal energy. This is coming from the Sun, and if energy is added to a system, then since E=mc^2, there is a corresponding increase in mass. Based on present data, this is probably adding a small amount of mass to the planet each year, of the order of 200 tonnes or so.

So the total mass gained by the planet each year is about 40,000 tonnes.

At the same time, the Earth is losing heat energy from its core as radioactive elements decay. Based on estimates of how much energy exits in this way, the mass loss is trivial though at about 16 tonnes per year.

More significant is what happens in the outer reaches of our atmosphere where the gravity field is weaker and lighter elements, like helium and hydrogen are hard to hold on to.

Earth loses about 1600 tonnes of helium to space each year like this. More dramatically, physicists estimate that we're losing about 3 kilograms per second of hydrogen in the same way. This adds up to 95,000 tonnes of hydrogen over a year.

So the net change in mass each year is 40,000 tonnes coming in, minus 96,000 tonnes going out. So the Earth loses about 56,000 tonnes of mass every year.

That sounds like a lot, but actually, as a proportion of the mass of the planet, which is 6 x10^21 tonnes, it's about 0.000000000000001% per year, so probably not worth losing any sleep over!

[chiralSPO]

I was inspired by this response (I added bold for emphasis for the purposes of my question):

...At the same time, using planet-wide temperature readings from NASA and other sources, one can see that the planet is warming up, or gaining thermal energy. This is coming from the Sun, and if energy is added to a system, then since E=mc^2, there is a corresponding increase in mass. Based on present data, this is probably adding a small amount of mass to the planet each year, of the order of 200 tonnes or so.

...

At the same time, the Earth is losing heat energy from its core as radioactive elements decay. Based on estimates of how much energy exits in this way, the mass loss is trivial though at about 16 tonnes per year...

I had a question regarding the relationship between energy and temperature and mass, but thought it was different enough to warrant another thread:

[syhprum]

The largest loss that the Earth suffered was in the collision that ejected the matter that eventually collapsed into our moon.
The moon is about 1.2% the mass of the Earth so the mass loss to the Earth must be at least that. 

[PmbPhy]

If there were and are meteorites and asteroids falling on earth since the beginning of time. How much the mass of earth have changed !? []

That's quite impossible to state since there's absolutely no way to determine it. It's not even a well defined quantity.