Part 2 — Planet-Hopping and Rumpus

In a dream, you and your friends are planet-hopping — you visit a series of small planets and whenever you arrive it always happens that the people there are celebrating their planet's new year. For them, the new year celebration is a birthday party for the planet: the beginning of a new circle around its star. They light bonfires, put on displays of fireworks, and all go into orbit — a kind of mass helter-skelter horizontal sky-diving in all directions.

In going from planet to planet you discover that on all of them speed is measured in dimes. Not only that, but they all use the same ton measure of force: one they call a "natural" ton, which is slightly larger than our ordinary tons.

One of the first things to do upon arrival at a small planet, after checking in at the hotel, is to discover the surface orbit speed, the skimspeed — where your path curving around the planet just matches falling. Since it takes no effort, this is the speed you and everybody else will be traveling. Never exceed the skimspeed unless you wish to leave the surface, which after all is where the party is. A hundred dimes wouldn't be unusual for a small planet's skimspeed.

Rumpus is tumult, according to Webster's: "a disorderly agitation or milling about". Experience shows that rumpus grows disproportionately with speed. In a milling crowd, whether of dogs or dancers, bumper-cars or celebrants, if you double everyone's speed you may get considerably more than twice the commotion. In some cases doubling the speed might increase the rumpus by as much as sixteen-fold. We can define a rumpus quantity that does increase exactly sixteen-fold when speed is doubled, simply by making rumpus the fourth power of speed. You obtain it by squaring the speed twice — a square square dime is a quartic dime.

If the skimspeed on a planet is 3 dimes, then the rumpus is 81 quartic dimes, which is a considerable amount of rumpus.

The local people say that what a planet weighs is actually proportional to its rumpus. (This is weight in gravity equal to whatever it is at the planet's surface, in other words what the planet itself thinks it weighs.) They say that heavy planets have a big rumpus, and that for every extra quartic dime of rumpus you can expect the planet to have an extra ton of weight. If the skimspeed on a planet is 3 dimes, they say, then the planet is sure to weigh 81 tons.