  Earth's magnetic field traps charged particles from the solar wind in the Van
Allen belts. These trapped ions execute three types of motion: helical motion
around magnetic field lines, longitudinal motion between North and South mirror
points, and latitudinal drift motion around Earth. Each is associated with an
adiabatic invariant, which expresses restrictions on each type of motion. This
study examines the effect on proton motion and the three adiabatic invariants
when the strength of Earth's magnetic moment varies with time. Using a Python 3
code developed in Google Colaboratory, each invariant was calculated and
graphed for a static magnetic field, for magnetic fields that varied with
periods shorter than the invariant period, and for magnetic fields that varied
with periods longer than the invariant period. The results demonstrate that if
Earth's magnetic moment changes quickly enough with time, the adiabatic
invariant is no longer constant, allowing a wider variety of ion movement.
Further study of these invariants and how they change in time-varying magnetic
fields could help predict ion motion and changes to the magnetosphere during
events that affect space weather, like solar storms or pole reversals.
