I just thought of an interesting question.Is the sun actually moving? I have learnt that the way the lunar landers and the space ships of the Mercury and Apallo missions moved and controlled their positions through the use of thrusters.NoW apply that same concept to the sun are the constant explosions on the surface of the sun enough to move it?
Whether the velocity of the sun changes because of explosive mass ejections depends on whether we include or exclude the ejected mass in the resulting system. The center of mass of "the sun+the ejected mass", considered as a single system, continues at constant velocity. The velocity of the center of mass of "the sun", considered as one system, and the velocity of the center of mass of "the ejected mass", considered as another system, are both changed. So, my classical physics Answer to your Question is no and yes.
The velocities of "the sun" and "the ejected mass" change so that the total momentum is conserved. "The ejected mass" is very small compared to the mass of "the sun", so the change of the velocity of "the sun" is very small, though still in proportion to the velocity of "the ejected mass". A spacecraft's velocity changes quite a lot with its ejection of fuel because the fuel is ejected as fast as we can safely engineer, and the mass of the fuel ejected is ultimately a significant fraction of the initial mass of the spacecraft.
There are various qualifications if we consider the motion of the sun relative to the center of mass of the galaxy. The sun is in orbit around the center of mass of the galaxy, so in classical physics terms the sun is constantly accelerating towards the center of mass of our galaxy, just as the earth is in orbit around and is constantly accelerating towards the center of mass of the solar system. In general relativistic terms, however, a more sophisticated description of the changes of configuration of the earth relative to the sun and of the sun relative to our galaxy is necessary.
Two points about how you can think about your question. (1) It's helpful to distinguish between position, velocity, and acceleration, and (2) it's helpful to be as explicit as possible about what the position, velocity, and acceleration are relative to, and to be careful what we choose to use as reference points. I'm moving at a constantly changing velocity relative to you because we are not at the same place on the earth's surface; describing my motion relative to you is considerably more complicated than describing my motion relative to the center of mass and to the rotational axis of the earth. Ultimately, a lot of systematic care has to be taken. When it comes to a technological application like GPS, a lot of systematic care is taken to describe and analyze relative positions, velocities, and accelerations.
All motions are relative and yes the sun is in motion about the center of our Milky Way galaxy, which is itself moving within the local group, which is moving about the center of Virgo cluster, which is a part of Coma supercluster, which is moving towards "the Great Attractor".
The constant explosions on the surface of the sun is not causing any significant movement of the sun since explosions are not taking place in any particular direction and more or less taking place on the whole surface. Therefore no significant movement of the center of mass due to these explosions takes place.