<font color="yellow">1 What will be the magnitude limit of stars that you can see when you are standing on the nightside on the moon whit (no) Earth in the sky?</font><br /><br />Unfortunately, I think it would be pretty much the same value. With a very dark sky on Earth I don't believe your visual limit is determined by the sky background since a 6.5 magnitude star is still significantly brighter than the sky background (I believe the sky background should be something like 9 mags/square arcminute, where an arcminute is roughly the resolution of the human eye.). I could be wrong, but my impression is that the 6.5 mag limit is roughly set by the size of your eye and the effective integration time in your retina. So without a bigger eyeball (which is really what a telescope provides when you look through the eyepiece), I don't think you'll be able to see down to 8.75 anywhere.<br /><br /><font color="yellow">2 How will it look outside (hypothetical) if we can see stars down with the (unaided) eye to magnitude 8.75?</font><br /><br />For humans I don't think this is possible. Nonetheless, you can imagine what it would look like - if you used a sky simulator like starrynight or xephem (the latter is free, but not as user friendly) you can switch the faint magnitude limit between 6.5 and 8.5. Using the HD catalogue though, there are about 15,000 stars with photographic magnitude less than 6.5 and about 55,000 with photographic magnitude less than 8.5 - so you'd see something like 3-4 times as many stars in the sky if you could see down to 8.5. I suspect that the milky way would also be a lot more pronounced.<br /><br /><font color="yellow">3 What will be the magnitude limit of stars that you can see with (unaided) eyes at the clearest nights on the top of Mauna Kea Hawaii?</font><br /><br />As per above, I believe it's roughly the same as down here near sea-level. Though the chances of having a clear night on Mauna Kea are much better than <div class="Discussion_UserSignature"> </div>