Part 4 — The Rumpus-to-Weight Ratio

As soon as you have checked in at the hotel, and have learned the local surface speed, it would be wise to calculate the planet's rumpus. Aside from giving you an idea of what to expect at the new year's celebration, you may wish to know the rumpus because any planet's weight is proportional to it. A planet where the speed is 10 dimes has a rumpus which is 10 thousand quartic dimes, and must weigh 10 thousand tons.

The ratio of a planet's rumpus to its weight is the same for every planet but how the ratio looks when you write it down depends on what units are used to measure speed and force. The ratio is officially called G and we already know what it looks like when speed and force are measured in dimes and tons:

G = dime⁴/ ton

Clearly it would be the same ratio if we put in a skimspeed of 10 dimes and a weight of 10,000 tons:

G = (10 dimes)⁴/(10,000 tons)

One way to imagine walking at ten dime speed, if you want to, is to think of taking heel-toe steps in time with a metronome. If your shoes are a foot long then one step per second is about right. If a metronome is not readily available think of snapping your fingers twice a second (which is a quick but comfortable snapping rate) and taking a heel-toe step with every two snaps. Its apt to look silly, mainly because it is so ridiculously slow for a walk. Silly or not, that is the surface-skimming orbit speed on a planet that weighs ten thousand tons.

In case you are curious, here what the same ratio looks like in metric terms:
G = 6.673×10^-11 (m/s)⁴/newton.

In metric terms the unit of force is newton and the unit of speed is meter per second (m/s). G still works as the ratio of any planet's rumpus to its weight. The determining choices for the metric system were made around 1790 in France during the Reign of Terror.

We can use this G ratio to weigh the sun. The earth's orbit speed is 10⁶ dimes. If we plug that in for the speed in the G ratio, the force that goes with it come out to be 10²⁴ tons. That is a trillion trillion tons. It is what a copy of the sun would weigh if placed at the distance we are from the sun. The ratio works for small satellites in any kind of circular orbit (not just orbits at ground-level) if you think of weighing the central body at the orbit radius. The discovery (by Ole Roemer around 1675) that the earth's orbit speed is a tenthousandth of the speed of light inspired the Monkeys and Parrot fable.