In 1971 Hafele and Keating performed their wellknown experiment proving the SRT with the help of macroscopic clocks carried eastward and westward around the world.
IDEA OF THE EXPERIMENT Assuming all the motions to be inertial we obtain a formula describing the difference between the times indicated by the clocks Indications of the clocks were then compared to each other and the difference of indications have been assumed the proof of the SRT 

THE ABOVE REASONING MET CERTAIN DOUBTS 

According to SRT inertial frame should be bound with one of the clocks 
Binding the inertial frame with any other point  HERE WITH THE EARTH'S POLE  adds a velocity to all of the velocities (here  the Earth's rotational velocity) and this change the predicted difference between the clocks' indications 
HOWEVER...Hafele and Keating stated, that in case of rotational motion it is allowed to bind the inertial system with a center of rotation  HERE  WITH THE EARTH'S POLE ON THE OTHER HAND...If this statement is true then it should be true also for rotational motion around the Sun and the inertial system can then be bound WITH THE POLE OF THE SUN Binding the inertial frame with the Sun, we are increasing all of the velocities for the velocity of the Earth in relation to the Sun, being approx. 100 times higher than all the other velocities. Finally to the previous formula a new factor is added (here on the red background) and it gives a very strong dependance of the clocks' indications as a function of time of a day. This dependance changed the predicted clocks' indication up to 400 times
Such dependance had not occurred. It is a proof that the velocity V, in the formula above, being the velocity of the Earth in relation to the Sun, is equal to zero. 