What would it be like to orbit the moon at an altitude of one inch?

I’ve long been fascinated by the idea that on an airless world, you could send a spacecraft into orbit at an altitude that would just barely miss the highest point beneath your orbit.
Say you were orbiting our moon at an altitude on one inch (ignore the mascons that make the moon’s gravity lumpy). I understand the physics well enough – what I am interested in is what the physical sensations would be for an occupant of the spacecraft (it would have nice big viewing windows, of course). Obviously you would be in a weightless free fall, but what would it look like? Would you be able to see the surface clearly, or would it be shooting beneath you so fast that it would be a blur? Would there be any sense that your spacecraft was falling towards the surface, or would you be shooting straight at the horizon? Would it seem like your spacecraft were motionless while the planet spun furiously beneath you? I am trying to imagine it, but it’s pretty far outside my day-to-day experience.
Thanks, dopers

Go here: put in 1 lunar mass in the upper-right box; put in 1738.2 km in the lower-right box (Equatorial radius of the moon + 100 meters). The box on the right will give you 1.679 km/s, which is a bit more than one mile per second (3755 mph). Depending on the local altitude, you may be able to briefly make out some of the lower (more distant) features, but the highlands and mountain peaks with flash by probably faster than you can see anything but grey.

Yes to both. That’s how orbits work.

As to what it’d look like, you’d feel weightless, and would see a surface blurring past you at extreme speed. At that kind of speed, and a distance of a mere inch, it probably wouldn’t look like anything except a uniform gray, maybe gradually changing color as you passed over different sorts of terrain.

One of the peculiarities of the Moon is that it has a certain asymetry. What I’m talking about is that the Center of Mass (CM) is not at the Center of Figure (CF). Instead of being at the same place like most spherical astronomical bodies, the Moon’s CM is about 2 kilometers closer to the Earth than its CF. The CM is what the craft is orbitting, so this offset is the equivalent of the entire far side being on a two kilometer high plateau. If you combine that with the fact that the far side is also much more mountainous, you’ll find that a typical orbit will average 3 or 4 kilometers or even more above the surface when over the near side. If it happens to go over the highest point of the moon (about 10,000 meters high), it’ll be much higher when over the near side.

So you may apparently be going from peak to peak while over the far side, but on the near side, you’ll be soaring well above the maria.

You could do a circumpolar at the earth-terminator.