The Trojan asteroids lie in Jupiter's orbit equidistant from
Jupiter and the sun. They are an example of what is known as the
restricted three-body problem: the motion of a small body, an
asteroid, under the influence of two massive bodies whose motion
is not affected by the presence of the asteroid. The
gravitational forces exerted by the sun and Jupiter combine to
give the asteroid a stable orbit with Jupiter's period of
rotation. (Some trigonometry is needed to show that the Trojan
site forms an equilateral triangle with the sun and Jupiter). In
the applet, the massive bodies executing circular orbits about
their common centre of mass can have mass ratios ranging from 9
up to the value for sun-earth system. It is convenient to view
the motion of the asteroid in a frame rotating with the massive
bodies. This is a non-inertial frame, and both centrifugal ( - m
w x (w x r) ) and Coriolis ( - 2 m w x v ) forces appear in
Newton's Law. Viewed in the rotating frame, the asteroid in a
stable orbit remains at rest