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[sci.astro] General (Astronomy Frequently Asked Questions) (2/9)
Section - B.16 What are the Lagrange (L) points?

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	John Stockton <jrs@merlyn.demon.co.uk>

The Lagrange points occur in a three-body system.  Take a system
consisting of a large mass M, orbited by a smaller mass m, and a third
mass u, where M >> m >> u.  There are five points where u can be and
have the same orbital period as m.

Three lie on the line connecting M and m.  One (L1) lies between M and
m, one (L2) lies outside the orbit of m, and one (L3) lies on the
other side of M from m.

Two are in the orbit of m, 60 degrees ahead (L4) and 60 degrees behind
it (L5).

Pictorially, we have something like this (not too scale!), with the
direction of revolution indicated for m:

                                 L4
                                  \ 
                                   \ orbit of m    ^
                                    \              |
                  L3   M         L1   m  L2        |
                                    /              |
                                   /
                                  /
                                 L5

The Lagrangian points are often considered as places where objects,
such as satellites can be "parked" for long periods.  For instance,
the SOHO satellite sits at the Sun-Earth L1 point in order to have a
continuous, unobstructed view of the Sun, and the Wilkinson Microwave
Anisotropy Probe observed from the L2 point.  There is a group of
asteroids, known as Trojans, which occupy the Sun-Jupiter L4 and L5
points.  There are also various groups advocating human colonization
of space which support putting a colony at the Earth-Moon L5 point.

In fact, the L1, L2, and L3 points are "unstable equilibria."  That
is, an object placed there will slowly drift away if there are any
other gravitational tugs on it (which there always will be due to
other objects in the solar system).  Thus, placing a spacecraft at the
Sun-Earth L1 or L2 point requires regular "course corrections" so that
it doesn't move too far from the L1 or L2 point.  The L4 and L5 points
are generally stable so that one should be able to remain at them
indefinitely.

Additional diagrams for the L points is at the WMAP site,
<URL:http://map.gsfc.nasa.gov/m_mm/ob_techorbit1.html>.

User Contributions:

1
Keith Phemister
Sep 13, 2024 @ 11:23 pm
Copied from above: If the Universe were infinitely old, infinite in extent, and filled
with stars, then every direction you looked would eventually end on
the surface of a star, and the whole sky would be as bright as the
surface of the Sun.
Why would anyone assume this? Certainly, we have directions where we look that are dark because something that does not emit light (is not a star) is between us and the light. A close example is in our own solar system. When we look at the Sun (a star) during a solar eclipse the Moon blocks the light. When we look at the inner planets of our solar system (Mercury and Venus) as they pass between us and the Sun, do we not get the same effect, i.e. in the direction of the planet we see no light from the Sun? Those planets simply look like dark spots on the Sun.
Olbers' paradox seems to assume that only stars exist in the universe, but what about the planets? Aren't there more planets than stars, thus more obstructions to light than sources of light?
What may be more interesting is why can we see certain stars seemingly continuously. Are there no planets or other obstructions between them and us? Or is the twinkle in stars just caused by the movement of obstructions across the path of light between the stars and us? I was always told the twinkle defines a star while the steady light reflected by our planets defines a planet. Is that because the planets of our solar system don't have the obstructions between Earth and them to cause a twinkle effect?
9-14-2024 KP

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