There have been claims since many years that the Sun is shrinking overtime slowly. Some theories suggest that the Sun has decreased in diameter at variable rates over the entire observational period. Others claim it to be reducing its diameter at a constant rate of 5 feet per year throughout the observational period. It was considered that the force of gravity acts on the surface of Earth to it shrink, but the nuclear fusion is also underway which tries to blow it apart making the shrinkage theory less reliable.
Actually these e are two opposing forces, the intense gravity of the sun and the nuclear fission. The former tries to crush the Sun, while the latter one works to blow it apart. When the gravitational field causes the surface to shrink, it also builds incredible pressure inside the sun, thereby increasing the process of nuclear fusion. The increased fusion pushes the surface back out again, and the cycle starts over.
Lets assume that the Sun is contracting slowly as a result of Gravity then we would have detected some noticeable change in the size of he Sun over the past history, but no such evidences can be located. Moreover, if the Sun were a million years old then it would have swallowed Earth’s orbit inside its bloated mass. The fact that if the Sun had truely been shrinking at such a rate throughout the history, then wouldn’t have managed to see so many solar eclipses over the past three thousand years as the Sun would have been too big for the Moon to obscure. So these observations discard the fact that the sun is shrinking. Some minor changes in size calculation may be on account of lack of accuracy and channel noise.
Another question that prevails commonly is about the Sun’s mass becoming less in the process of producing energy, i.e., Fusion. Obviously its very true that the Sun is reducing its mass on account of nuclear fusion but its actual mass do not change due this. Actually the solar system is very active place, comets fall over the Sun quite often. The dust generated by asteroids hitting each other and comets creates tons of very fine dust particles that fall into the Sun every second. So the Sun also gains something in one process while loosing in the other.
So the shrinking of the Sun is just a myth and we see the same size of Sun as forefathers did and as our Grandchildren will see. It is basically based on the channel noise and inaccuracies in data collection and handling that the variations in size have been observed though not the very significant ones.