  This work investigates the solar quasi-periodic cycles with multi-timescales
and the possible relationships with planetary motions. The solar cycles are
derived from long-term observations of the relative sunspot number and
microwave emission at frequency of 2.80 GHz. A series of solar quasi-periodic
cycles with multi-timescales are registered. These cycles can be classified
into 3 classes: (1) strong PLC (PLC is defined as the solar cycle with a period
very close to the ones of some planetary motions, named as planetary-like
cycle) which is related strongly with planetary motions, including 9 periodic
modes with relatively short period (P<12 yr), and related to the motions of the
inner planets and of Jupiter; (2) weak PLC, which is related weakly to
planetary motions, including 2 periodic modes with relatively long period (P>12
yr), and possibly related to the motions of outer planets; (3) non-PLC, which
so far has no obvious evidence to show the relationship with any planetary
motions. Among planets, Jupiter plays a key role in most periodic modes by its
sidereal motion or spring tidal motions with other planets. Among planetary
motions, the spring tidal motion of the inner planets and of Jupiter dominates
the formation of most PLCs. The relationships between multi-timescale solar
periodic modes and the planetary motions will help us to understand the
essential natures and prediction of solar activities.
