how does a smaller focal ratio allow shorter exposure times?

how , lets say on a 4" scope can a lower f ratio mean shorter exposure times? if i have 2 scopes, both 4", one an f5, one an f10, how will the f5 give shorter exposure, as both have the same light gathering power. i understand the smaller f ratio gives a wider field of view, but i cant see how it gives shorter exposure times.

A F5 gives a smaller image of an object when compared to a F10, take the orion nebula for example, if you had 2 scopes with the same light gathering power (aperture) but one a F10 and the other a F5, the F5 makes a smaller image compared to the F10 scope. The F5 concentrates the same amount of light into a smaller area so it appears brighter as there is more photons per square millimeter, if its brighter then it can get by with a shorter exposure compared to the F10 scope. I hope this makes sence.

perfect. thanks!!

I had a look on this and i couldn't figure it out! Sometimes the simplest things are just to hard to realize ty Dave

one thing, if the smaller f value scope gives a smaller image, concentrating the light on a smaller area, can the same effect not be acheived in a large focal ratio scope with a lower magnification eye piece, as it will give a smaller image ( im not sure if it will be brighter or not )

Yes, but you can end up with problems like vignetting and field curvature, practically all astrophotography is done without an eyepiece in the scope for this reason. Think of it as the scope becoming the camera lens.