Editing 2717: L6 Lagrange Point

{{comic
| number    = 2717
| date      = December 27, 2022
| title     = L6 Lagrange Point
| image     = l6_lagrange_point_2x.png
| imagesize = 399x400px
| noexpand  = true
| titletext = It's difficult to orbit L6 stably due to gravitational perturbation from Akron and Toledo.
}}

==Explanation==

In celestial mechanics, the {{w|Lagrange point}}s are points of equilibrium for small-mass objects under the influence of two massive orbiting bodies. Or in simpler terms, positions in space where objects can float motionless relative to the defining bodies.

There are five traditional Lagrange points. Two form equilateral triangles with the two massive objects (in this case the Earth and the Sun), and three more are collinear with the massive objects. The L<sub>1</sub>, L<sub>2</sub>, and L<sub>3</sub> points are unstable, as any drifting off the point (e.g. due to the gravity of other bodies) might quickly increase the tendency to depart the area. However, there are quasi-stable {{w|Halo orbit}}s around these points, like the one used by the {{w|James Webb Space Telescope}}. The L<sub>4</sub> and L<sub>5</sub> points can actually retain objects stably over long periods, resulting in the Sun-Jupiter L<sub>4</sub> and L<sub>5</sub> points capturing the {{w|Trojan (celestial_body)|Trojan Asteroids}}.

Randall claims that a sixth Lagrange point has been discovered outside of {{w|Cleveland}}, {{w|Ohio}}. This is pretty obviously farcical,{{Citation needed}} as this would be part of the Earth and thus not gravitationally balanced between Earth and the Sun, though it is balanced by the countering forces that hold anything stable on the surface of any body: {{w|gravity}} and {{w|electromagnetism}}. The joke here is that there actually is a small village named {{w|LaGrange, Ohio|LaGrange, OH}} (population 2,595 in 2020) just outside Cleveland ([https://www.google.com/maps/place/Lagrange,+OH+44050/ map]). However, the village name is spelled with a capital G, unlike {{w|Joseph-Louis Lagrange}} after which the Lagrange points were named.

There is, however, a {{w|Lagrange,_Maine|Lagrange in Maine}}, a {{w|Lagrange,_Virginia|Lagrange in Virginia}} and a {{w|Lagrange_Township,_Bond_County,_Illinois|Lagrange Township in Illinois}} which all use the lower case g in their spelling like Joseph-Louis Lagrange.  There are also {{w|https://en.wikipedia.org/wiki/Lagrange_(disambiguation)|twenty-six other communities}} in the United states with a spelling of LaGrange or La Grange, as well as four in France and two in Australia with one of the three spellings.  This includes {{w|La_Grange,_Texas|La Grange, Texas}} which became famous as the title of a {{w|La_Grange_(song)|ZZ Top song}}.

The title text mentions {{w|Akron}} and {{w|Toledo,_Ohio|Toledo}}, two other large cities in Ohio. It says that their gravitational influence is the reason why orbits around the LaGrange L6 are unstable. The Lagrange points are solutions for a simplified three-body system, and orbits around them may be disrupted if additional bodies such as moons or planets are close enough or massive enough to cumulatively exert significant gravitational forces over time (the Moon does factor into the Earth-Sun L1 and L2 Lagrange points, especially, but that can be accounted for in the station-keeping measures already required). Trying to orbit around a point on the ground would, of course, run into much more serious problems, {{w|lithobraking|such as the ground.}}

==Transcript==
:Grey on white diagram of the Earth orbiting the Sun, not to scale.  Earth is depicted as a circle with pale grey continents on darker grey seas, and shows a view from above the North Pole without any Arctic ice. The sun is drawn surrounded by radially symmetrical exaggerated wave pattern.
:Also in grey, approximate locations of Lagrange points 1 to 5 are marked with dots and labels: "L<sub>1</sub>" "L<sub>2</sub>" "L<sub>3</sub>" "L<sub>4</sub>" "L<sub>5</sub>". 
:In black, a point on the Earth's surface within the boundary of a continent that could be North America. Also in black, an arrow pointing towards the point, and the label "L<sub>6</sub>".
:Caption: "Huge space news: Astronomers have discovered a new Lagrange point just outside Cleveland."

{{comic discussion}}

[[Category:Astronomy]]
[[Category:Science]] <!-- This is a supercategory to Astronomy; should this comic then belong directly to Science? -->