
Apparently the “moving” towards a distant planet observer will “see” that apparent size of this planet is smaller, than the same planet as seen by “stationary” wrt to this planet observer.
For the sake of clarity let’s consider how will look pictures as taken by “stationary” photocamera (Fig. 1) and “moving towards the planet one” (Fig.2) at the moment, when their apertures coincide.
We can analyze this problem from the frame of the planet or from the frame of the observer. The picture should not depend on the chosen frame.
In the frame of the photo camera the planet is moving (Fig. 3) ; but we must bear in mind light - time correction. The rays of light always travel faster than the planet. That means that at the picture the planet will not appear where it actually is, but when it was in the past, when it’s apparent size was smaller. While rays of light are moving towards the aperture, the planet is moving closer.
In the frame of the planet the photocamera moves; but distance between its aperture and the film Lorentz – contracts plus the film moves further while rays travel from the aperture towards film. At the moment when “moving” and “stationary” apertures coincide, the same rays, or the same information goes through the aperture (Fig.2). Rays from the edges of the planet to aperture and from aperture to the film form similar triangles. However, the “moving” camera is shorter; hence image on it will be smaller.
It will be exactly of the same size as in the first scenario, but smaller than on the picture as taken by the “stationary” camera.
By the way. There is the relativistic aberration formula:
$$\tan(\phi) = \frac{u_y'}{u_x'} = \frac{u_y}{\gamma(u_x+v)} = \frac{\sin(\theta)}{\gamma(v/c + \cos(\theta))}$$
While light travels distance $ct$, "moving" observer travels distance $vt$, so in the "classical" case aberration angle $\tan \theta = ct/vt$.
What $\gamma$ does in the denominator of the relativistic equation? Distance $vt$ in relativistic case turns into $vt \cdot \gamma$, it is not $\gamma$ times shorter, but $\gamma$ times longer, because effect of aberration is "tied" with moving observer.
Since measuring rod of "moving" observer becomes $\gamma$ times shorter, he measures horizontal distances with "squashed" ruler and distant object appear to him even more further away.
The Feynman Lectures - Relativistic Effects in Radiation