Satgen 525  Hesitation Waltz   by GM4IHJ  (BID SGEN525)  1999-04-17

Modern disco dancers will never have heard of it. But if memory serves
aright. This was a dance where the music stopped briefly and the tempo
then changed. Apparently Comets, Comet Dust and Asteroids know all
about the Hesitation Waltz.

The hesitation arises when a Comet or Asteroid , finds itself near a
Lagrangian point. A critical balance point, where the gravitational
attraction of the distant Sun, and that of a nearby planet, are
balanced. Leaving the Comet /Asteroid in doubt as to which object to
orbit.

Sometimes this results in orbital resonance. Whereby, a comet coming
from deep space is captured by a planet , such that it continues on
round the Sun , but in an orbit restricted to going not much further
out again than the planet ie taking up a short period orbit inside the
solar system. Comet Oterma has presently got an 18 year orbit and
Jupiter has a 12 year orbit. So Oterma does 2 orbits to every 3 orbits
of Jupiter. But this situation is not permanent. Some time ago Oterma
hesitated at the Sun/Jupiter Lagrangian point in its orbit and,
shifted from a 2:3 resonance , to a 3:2 resonance with Jupiter. A much
shorter 8 year orbit for the Comet.

Then 3 orbits or so later Oterma hesitated again and reverted to a 2:3
18 year orbit, in resonance with Jupiter.

Many other heavenly bodies exhibit these resonances . Planet Neptune
has resonances with Pluto and a number of Kuiper Belt objects slightly
further out than Pluto. Almost all short period comets ( orbital
period roughly 200 years or less), are in orbital resonance with one
or other of the planets with mighty Jupiter and Saturn having captured
the majority. From time to time, the hesitation waltz can and does
upset these orbits and those of the Asteroids , as they pass through
the various Sun/planet Lagragian points on their way into and out of
the inner solar system. Resonance changes which might in some
circumstances bring them, and in the case of Comets, their dust trails
and associated meteors, much closer to the earth than they come at
this present time.

In a different approach to this aspect of orbiting in a busy solar
system. The mathematics suggests that we may be able to deliberately
direct space craft into positions which place them in new resonances
with moons or planets at much lower cost in fuel than the present fuel
economy routes which use, the favourite, fuel economy Hohmann transfer
orbit . Hohmann orbits use Solar gravity to travel between the
planets. But neither the Hohmann orbit nor any potential resonance
assisted orbit can provide a speedy passage between planets or moons.
So these orbits are unlikely to appeal to Military or Commercial
organisations. But they might at some time provide excellent but slow
fuel economy transfers from Earth to Moon, or Earth to another planet
for radio amateur probes or comsats.