# What is the difference between Saddle points and Lagrangian points between Earth and the Sun?

I am studying MOND bubble effects in the Solar System (Paper). In "mond habitats.." (last reference) first page, the author says MOND bubbles reside on the saddle points but I fail to understand the differences from Lagrangian points. Can anyone explain this to me?

• I believe those saddle points are Lagrangian points. I think the author calls them saddle points because not all Lagrangian points are saddle points (namely L4 and L5). Dec 7 '14 at 21:17
• He makes a direct reference to L1 not being a saddle point, though.. Dec 8 '14 at 11:46
• when using classical Newtonian physics, then those Lagrangian points are saddle points, however with MOND for example the L1 point turns into one stable point surrounded by two unstable points, see the figure on page 6. Dec 8 '14 at 15:36
• We (NASA) have actual tests of the L1 and L2 points (from the Earth-Sun system) due to spacecraft orbits around these potential minima. We know from experience that they are not stable orbits, they are saddle points because we need to perform station keeping maneuvers every few months or so. So I am confused as to why one would use MOND if it gives the wrong answer. Is there an advantage to this theory for some purpose? Jan 1 '15 at 18:26
• Oh, one should also be careful of micron-sized dust and nanodust. These particles are moving at tens of km/s and can produce accumulated damage to spacecraft. A recent astronomy mission ran into issues with their ability to focus their images because they underestimated the amount of nanodust. Apparently, the dust levels were high enough to produce enough vibrations to blur their images. Jan 1 '15 at 18:28

## 1 Answer

In case you still want to know, here is my two cents. In MOND (the paper you referenced uses TeVeS the relativistic cousin of MOND) the potential is modified due to the introduction of an acceleration parameter a0. At accelerations below this value MONDian behaviour takes over. This means that the saddle point of the potential between two bodies is shifted away from the purely Newtonian L1. See for example figure 7 in this report:

https://engineering.purdue.edu/people/andrew.d.cox.2/pubs/2016_AAS_CoxHow.pdf