Of all the changes in the stars in the night sky seen during the annual 500 million kilometre trip round the Sun, the two smallest, parallax and aberration, have the most far reaching implications. Stellar parallax, being the slight shift of a nearby star relative to a much more distant star (as discovered by Bessel), is found by comparing observations at the extremities of the orbit. Extremities in this case mean in relation to the line to the direction of the star, points P1 and P2 in the drawing. This is literally a far reaching result, the method can stretch astrogeometry to the limit.
Bradley detected a shift, but it was greatest when comparing the other extremities, marked A1 and A2 in the drawing. This is far reaching in its implications for physics, as well as for astronomy. Bradley realised that the aberration was related to the speed of the Earth (and so to the AU), which is why the aberration is in opposite directions at A1 and A2. It was discovered first because it is bigger than parallax, though only a hundredth of a degree. It is fortunate indeed for astronomers that the two effects are seen 6 months apart, otherwise aberration would smother and hide parallax. In fact Bradley, despite his excellent work on aberration, never did discover parallax. He took aberration as proportional to the sine of A, the angle marked ion the drawing, on the basis of interpreting light as a stream of corpuscles.
In other words, his analysis of the angles would indeed apply to a footballer running forwards and receiving a pass from the wing - you just take the sum of the vectors. Where light is involved, however, special relativity has to be used to add the two, and the aberration actually involves the square of the angle and not just the angle. Because the speed of the Earth is small, Bradley got away with it, and special relativity remained hidden.
In a closely related observation, in which the telescope is filled with water (do not try this at home!), special relativity was staring the experimenters in the face, but was again missed. The experimenters were Airy and Fizeau in 1871. The observation was amply accurate enough to discover special relativity, but the theoretical ideas were lacking and relativity had to await Einstein. We can hardly blame Fizeau for missing the fact that a bucket of water is all you need to discover relativity, because his observation was that it had no visible effect. This was explained away by a mysterious "ether", a meaningless ghost of an idea which was not laid for 30 years. When it was, special relativity led to general relativity, and hence to a cosmology which reaches the limits of the Universe.