I recently bought a fast aperture lens which can be used only in manual mode. I bought this lens specifically for low light landscape photography.

However, that has got me thinking about how does focus set to infinity get impacted by wide open aperture (f/2.8) vs closed aperture (f/8 or f/11)? 

In other words, if I am taking a landscape photo in low light conditions with infinity focus, is it better to take picture with 

1. open aperture, short shutter speed,
acceptably high ISO (not grainy)
2. closed aperture, long shutter speed, low ISO

Both approaches will use a tripod. *It is my understanding that with focus set to infinity, everything from min. focussing distance should be in focus.*

**Is lens aperture a factor with focus set to infinity? Would you be able to get razor sharp photos with all apertures (f/2.8 - f/22) regardless? Or it depends on best performing aperture for the specific lens?**

Does 2nd approach result in softer images because of long shutter speed? (thus 1st approach is better)?

I understand a very important factor is what is the landscape. But taking out that factor, which is better?