Part 1 — An Orbit Dream

In a dream, you are flying over a round planet of unknown size. The radius might be only a couple of miles or it might be more, you can't be sure. You are in a skimming orbit around the planet, close enough to see your shadow moving across the planet's surface beneath you. Occasionally you nearly brush a hilltop. Seeing your shadow helps you judge the scale of surface features and estimate your speed.

It looks like you are going at the speed of an easy run — but not actually running since you are in orbit. In what feels like a minute you see your shadow travel over the surface by maybe a hundred paces, the length of a city block. You must be orbiting the planet at something like one hundred paces a minute: not really a serious run, more like a relaxed lope.

Ahead of you on a low hilltop you see a radar speed-sign of the type they have along the highway some places. The sign has a window with space for numerals, and some words:

In our language the speed of light is a billion cents. Your speed is ___ cents.

As you approach, it registers your speed and numerals light up in the window, and as you reach the sign it says:

Your speed is 10 cents.

You can't do much about your speed — it comes with the planet. On a round planet there is always some speed which is right for level skimming orbits. It's the planet's skimspeed — the speed at which falling exactly matches curving around the planet, so that falling bends your path around into a circle. Slower would let you spiral inwards and crash — faster would make you swing out from the surface.

By the way, this planet does not have large mountains that you might bump into. There is an atmosphere of dream-air. You can breathe it but it doesn't slow you down. Enjoy your flight.