Layman question on sun as seen from mercury

[Constantinos]

Hey!

Here's a question. This is Mercury as seen from some telescope during one of its transits
The white disk in the background is the Sun.

So suppose now that I am where this telescope is and start approaching Mercury. As I approach, both the Sun and Mercury would become larger from my point of view right? Given the picture above, it seems to me that if I stand just above the surface of Mercury, the sun would look HUGE. It would look like the whole sky in front of me is just Sun. Here is another picture, as I would come closer to mercury.

Regardless, the Sun as seen from Mercury is postulated to be much smaller than I would expect. According to this article, the Sun from mercury is 2.2 to 3.3 times bigger (I suppose in radius?) than the Sun on earth. That doesn't sound like much at all, certainly not the whole sky as I assume it.

So where do I go wrong?

Not a physicist, computer engineer though, so I guess I can understand basic math if need be?

Thanks!

 

[Matterwave]

When you approach Mercury, because you are closer to Mercury than the Sun, Mercury will grow in size more than the Sun will, you can't assume that they will "grow at the same rate". When you get to the surface of Mercury, your whole field of view will be Mercury and not the Sun. You can get this same effect on Earth by looking down, your whole field of view will be the Earth. :)

 

[Constantinos]

hmm... yes I think you are right! How did I miss this intuition? It would be the same thing as, for example, finding an object closer to the galactic core and going towards it. The galaxy wouldn't grow much larger in my point of view of course.

Hmm, I think I will now draw some geometric shapes and see how the math goes, it might be interesting. Thanks!

 

[Matterwave]

hmm... yes I think you are right! How did I miss this intuition? It would be the same thing as, for example, finding an object closer to the galactic core and going towards it. The galaxy wouldn't grow much larger in my point of view of course.

Hmm, I think I will now draw some geometric shapes and see how the math goes, it might be interesting. Thanks!

You can do this yourself. Put a quarter up against one eye and set it against a backdrop, e.g. your TV, which at first much larger than the quarter. As you bring your eye to the quarter, you will find the quarter will eventually become larger than this backdrop. The backdrop won't grow much, but the quarter will grow until it obscures the view from your eye.