Yes you can, but you'll need a hack to override the camera iso and shutter speed limits. Google CHDK
In some ways the 40 was better for night shots, but you can do it with the 50. Look for users on flickr that use the 50. I've taken shots of aurora's and meteors with both the 40 and 50. Better off with a better camera, but it will work. Unless there's a moon figure 1600 or 3200 and limit it to 25 seconds, 20 and less is better for sharpness. Start zooming in and it changes everything.
It's not made for it. That said I used the 40, 50, and 60 for night shots. There's a hack for doing it and it works fairly well but eventually you'll toast the sensor. That is why I had all three. The 50 was the better one for me. I've got a dslr now, but wish I still had a working 50 or 60 for some stuff. You can find the hack by googling chdk. Lot of info out there on it. The hack is put on the sd card, the card made bootable and away you go. Gets around the ISO issue so you can run high ISO's for long exposures. I've got stuff on flickr you can look at to get an idea of what you can do. You may find focus can be a real pain from what I remember. Also, there's something called the 400, 500, and 600 rule for avoiding star streak. Divide one of those by the focal length and it will give you an about how long you can expose without the streak. A 50 mm would be about 8 seconds. Wide open landscape on the 50sx would be 20 seconds or less, though that varies a bit depending on what part of the sky you're shooting because the speed of rotation is slower as you move towards the poles. Like a merry go round. I've got some stuff on Flickr from all three camera's of night stuff. Rocky Raybell