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 of 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 three numerals, and some words:

In our language the speed of light is ten billion dimes. Your speed is ___ dimes.

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 100 dimes.

Whatever else is strange about the people on this planet, they do seem to be ten-users — a reassuring thought. You can't always be sure ahead of time what people are going to choose for units of measurement or what names they'll give them. These people say that the speed of light is ten billion dimes, so they must have a unit of speed called "dime" which is one tenbillionth of the speed of light.

We know the speed of light so we can figure out how much that is in our conventional earth terms. They may not have minutes like ours, or city blocks like ours, or miles, or centimeters, or anything else we would recognize. Their measures of force and time and distance may be unknown to us, but at least we know their measure of speed.

A ten-to-the-tenth part of light speed is roughly a pace a minute. It is a speed I've seen ants running, along a slender branch in our lemon tree. That would be a dime, for these people. How to imagine ten dimes? Perhaps, if your shoes are about a foot long, think of snapping your fingers about twice a second and taking heel-toe steps once a second or once every two snaps. It is apt to look silly. On the other hand, a hundred dimes is more like a speed you or I might run—a ten-to-the-eighth part, or about 6.7 miles per hour.

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.