Salida del sol

Salida del sol
 

When the sun rises it appears/come up/enters into view, so it's hard for me to hear la salida del sol without imagining "the sun's exit/departure/leaving" - since all the door signs I see in stores say ENTRADA and SALIDA for ENTRANCE and EXIT.
So why wouldn't la entrada del sol make sense to say for sunrise?

Because "entrar" gives us an idea of entering a closed space, and there is nothing more open than the sky, so the sun comes out of the darkness to light it all up. :)

When used with the sun:
salir = rise up, come up

So that's a special use of salir, right?
Angélica makes a good point too. Thanks to both for the help

'Salir' isn't used in that sense just to mean the rising of the sun. When plants poke out of the soil for the first time, we use 'salir' (or 'brotar') for that as well.

Another use of salir/entrar that seems foreign to English speakers is on stage. Salir means to "enter" or come out on stage, and "entrar" means to leave or exit the stage. Angelica's explanation applies here perfectly.