The diagram at left shows the L4 Lagrange point displaying the forces acting, which vector sum to zero.
In 1788, Joseph Lagrange published, in Mechanique Analytique, an
analysis of the apparent gravitational forces that act on a very small
body placed in a two body rotating system (eg the sun and a planet).
He showed that there exist five points (now known as Lagrange points)
in such a system where the resultant force acting on the small body is
zero. These points are shown in the diagram below.
These points exist because the true gravitational forces exerted by both the Sun and the planet are just cancelled by the centrifugal force at these points. The points L1, L2 and L3 which are colinear with the Sun and the planet are points of unstable equilibrium. That is, a small displacement from these points will result in an ever increasing force away from the point. L4 and L5 are conditionally stable. However, even at the unstable points, it is possible to set a spacecraft in a reasonably stable orbit around these points. The L2 point in particular is the site of several spacecraft in the Sun-Earth system. From here they can monitor space weather from the Sun before it reaches the Earth. On the average they can give about one hour's warning of an event.
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The L4 and L5 points in the Sun-Jupiter system are interesting
because they are the homes of trapped asteroids called the
Trojans. In the Sun-Earth system the L1 and L2 points are
approximately 1.5 million kilometres from the Earth. L4 and
L5 exist on an equilateral triangle with equal distances from the
Sun and the Earth, and L3 lies just a tiny fraction further from
the Sun than does the Earth.
The diagram at left shows the L4 Lagrange point displaying the forces acting, which vector sum to zero. |
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