Image 1 Caption: An animation showing the motion of the 5 Lagrange points (L-points) in a corotating reference frame specified by the circular orbits of 2 large astro-bodies around their mutual center of mass (CM). The of 2 large astro-bodies determine the 5 L-points).
Features:
In the special case of the animation, the 2 bodies are in astro-bodies around their mutual center of mass (CM).
Lagrange points
are most easily understood for
circular orbits
for the 2 bodies are
in astro-bodies
and that is all we will consider in here.
The
L4 and L5 points
complete
equilateral triangles
with the
2 finite bodies.
This means they are 60° away from the line joining the
2 finite bodies as seen
from either of the 2 finite bodies.
A stable equilibrium
is one where motions due sufficiently small
perturbation on a
test particle
placed at the
stable equilibrium
damp out and the
test particle average
position remains the
stable equilibrium.
The test particle NEVER escapes
to infinity.
However, the
gravitational perturbations
of an
n-body system
with more than 2
astro-bodies
make the
Lagrange points less than ideal.
In general, the larger planet,
the larger its gravitational force,
and the more ideal its
Lagrange points.
For example, in the Solar System,
Jupiter's
L4 and L5 points
are particularly close to ideal, and therefore very
stable equilibria.
For that reason,
Jupiter's trojan asteroids
accumulated near its
L4 and L5 points
and tended to stay there over the
Solar System's evolution.
The word trojan
has come to mean any small
astro-body
(e.g., an asteroid) that
orbits near
L4 and L5 points.
Lissajous orbits
are sort of like
quasi-periodic
epicycles come to life.
Lissajous orbits can
used for spacecraft at the
unstable
L1 point,
L2 point, and
L3 point
This L2 point is on
Earth-Sun line
at 0.010 AU
(∼ 1.5*10**6 km) from the
Earth.
An astro-body
at that distance from the
Sun, NOT at an
L2 point would
have an orbital period
about the Sun
that is slightly longer than a
sidereal year = 365.256363004 days (J2000).
An astro-body
in Lissajous orbit
about L2
has, of course, an
orbital period
about the Sun of exactly a
sidereal year = 365.256363004 days (J2000).
So spacecraft
at the L2 point are
NEVER
in the umbra.
In fact, their Lissajous orbits
probably NEVER put them
in the penumbra
either.
Going into
penumbra would
decrease the solar power
that powers most
spacecraft.
How early?
Well hopefully days, but maybe sometime only hours
(see
Wikipedia:
Coronal mass ejection: Physical Properties).
Early warning is particularly necessary for
super coronal mass ejection (CMEs)
(e.g., the Solar storm of 1859
(AKA the Carrington event)
and the May 1921 geomagnetic storm
(AKA New York Railroad Storm of 1921))
which could burn out the
electrical power grids worldwide
which would be a major disaster.
Simply breaking the
electrical power grid
connections for a few hours while
a super CME
passes over could prevent said major disaster.