The Gravity Landscape and Lagrange Points

"We all are of the citizens of the Sky" Camille Flammarion

In 1858, by the set of its relations, it will allow Camille Flammarion, the 16 years age, to enter as raises astronomer at the Observatory of Paris under the orders of Urbain the Glassmaker, at the office of calculations.

There is a deep seated need to look beyond ourselves. We tend to look up in space, while there is this greater vision that lies even beyond what we are so used to in our everyday lives.


(Larry Niven's Ringworld, seen from space. Artwork by Harry Frank

Ringworld is a Hugo and Nebula award-winning 1970 science fiction novel by Larry Niven, set in his Known Space universe. The work is widely considered one of the classics of science fiction literature. It is followed by three sequels, and it ties in to numerous other books in the Known Space universe.

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Our view of space and living beyond the confines of Earth, is lived over in the minds of those who have struggled within science to make these travels possible.

Imagine that first look at the blue planet. How glorious this view, while here we mere mortals look at what those take for granted as they now use the machines they created to visit new planets.

L4 and L5

The L4 and L5 points lie at 60 degrees ahead of and behind Earth in its orbit as seen from the Sun. Unlike the other Lagrange points, L4 and L5 are resistant to gravitational perturbations. Because of this stability, objects tend to accumulate in these points, such as dust and some asteroid-type objects.

A spacecraft at L1, L2, or L3 is ‘meta-stable’, like a ball sitting on top of a hill. A little push or bump and it starts moving away. A spacecraft at one of these points has to use frequent rocket firings or other means to remain in the same place. Orbits around these points are called 'halo orbits'.

But at L4 or L5, a spacecraft is truly stable, like a ball in a bowl: when gently pushed away, it orbits the Lagrange point without drifting farther and farther, and without the need of frequent rocket firings. The Sun's pull causes any object in the L4 and L5 locations to ‘orbit’ the Lagrange point in an 89-day cycle. These positions have been studied as possible sites for artificial space stations in the distant future.

I draw you attention too,"ball sitting on top of a hill" in the previous article. One should get the idea right away, that what was revealed in the possibilities of the landscape, could have correspondences in how we look at the universe in it's gravitational considerations.



Who would have known that such "orbital tendencies" which would have seem so chaotic, could have let one seen Lissajous's by design. You might think of Lorentz's butterfly flapping it's wings, yet such probabilities are held "to a spot" that is a result of placement within the very nature of the landscape of the gravitational cosmos.

So would you have wondered, "if we considered "E8" as a dimensional attribute of such probabilities "by design in such a place" what would this place look like? Would you have selecedt the probability of this resulting ball to falling in the respective valley as a, moduli form?