An "orbit" in a juggling pattern is the series of throws followed by a
particular ball. For example, in the pattern 423 two of the balls
just go up and down, staying in their own hand, while the third ball
goes from hand to hand. The first two balls are in the orbit "42"
whereas the third is just in an orbit "3". Try out this example
and look at the orbits window if this is your first time through.

When running a valid pattern, the orbits window will show how the throws
link up into orbits. Each throw of a ball gets an arrow pointing to the 
next throw of that ball, and following the arrows, one reads off an orbit.
The validity of the pattern is seen in the fact that there is exactly
one arrow coming to each throw (or more generally for multiplices, 
the number of arrows equals the number of throws).

This works in reverse: one can check validity of a pattern by drawing
arrows from all the throws, and seeing if the number of arrows coming in
(balls landing at that time) is the number of arrows going out (balls
thrown at that time). If not, some throw times will be unhappy because
they have too many balls coming, and some because they have too few.
This is the second function of the orbits window.

In practice, the orbits window is used as follows. You have entered a
pattern that doesn't work - say 6571 - and [MA][GNU]S suggests that 
you look at the orbits window to see why not. In this case, the first
two throws will have green-light happy faces, the next one a red-light
mad face indicating too many balls are coming (two), and the last 
a yellow-light sad face indicating that two few are coming (none).
So this can be fixed by redirecting one of the two throws landing
on Red to instead land on Yellow. Following the two arrows landing
on Red in reverse, we see that the 6 and 5 are landing there. To make
them land 1 later on Yellow, we could add 1 to one of them.
So we find that 7571 and 6671 are valid patterns.


