~ Asteroids that escort planets? ~ L4, L5 & The moon ~

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1.Lucy spacecraft is flying by Eurybates.
Credits: Southwest Research Institute.

In these regions of space in which the interaction of the gravitational forces of two celestial bodies are balanced forming "valleys" in which some asteroids were trapped. According to some hypothesis some as big as Mars ...

First discovered..

2.Credits: NASA's Goddard Space Flight Center/Dan Gallagher, producer

The first to be registered was Achilles in 1906 by Maximilian Franz Wolf, German astronomer at the LSW Observatory near the German city of Heidelberg. This astronomer was a pioneer in the application of astronomical photography to automate the discovery of asteroids and in that way he was able to find more than two hundred and forty asteroids. In the long exposure photographs, the asteroids are shown as short lines due to their movement with respect to the fixed background of the stars, facilitating their detection.
One of which was (588) Achilles. The first was discovered, inside the orbit of Jupiter one of the gaseous giants of our solar system. Located at point L4 of the Sun - Jupiter system with his observation the existence of the Lagrange points was confirmed...

L4 & L5

3.Diagram of Lagrange points by NASA's J.F. Kennedy Space Center and Goddard Space Flight Center.

These regions of space L4 and L5 are known by Trojan points or triangular Lagrange points. Located L4 behind and L5 in front of the small body at sixty degrees inside the same orbit. In those regions the gravitational forces of the bodies of the system create regions similar to "valleys".
The reason that these points are in equilibrium is that the point L4 and the point L5 are at the same distance from the two masses.

In the Sun - Earth system we also have a Trojan satellite 2010 TK7. More Trojan asteroids have been found on other planets such as Mars, Saturn or Neptune. Even on a Saturnian moon, Trojan asteroids have been found. Precisely the accumulation of asteroids in those points of Lagrange gave rise to a hypothesis about the formation of the Moon …

Moon formation ( hypothesis)

4.StarChild Project NASA/GSFC Image Credit: Joe Tucciarone.

The hypothesis of the great impact.
It is believed that the Earth collided with a twin planet the size of Mars 4.5 million years ago , called Tea formed in one of the Lagrange points.
Dr. William K. Hartmann and Dr. Donald R. Davis, were the first to suggest the leading modern hypothesis of the moon's origin, in a paper published in 1975.

Quote:
”Exploratory calculations using accretionary theory are made to demonstrate plausible sizes of second-largest, third-largest, etc., bodies at the close of planet formation in heliocentric orbits near the planets, assuming asteroid-like size distributions at the start of the calculation. Many satellite-sized bodies are found to be available for capture, cratering, or collisional fragmentation. In the case of earth-sized planets, the models suggest second-largest bodies of 500 to 3000 km radius, and tens of bodies larger than 100 km radius”.
”Collision of a large body with earth could eject iron-deficient crust and upper mantle material, forming a cloud of refractory, volatile-poor dust that could form the moon. Other satellite systems may have been affected by major capture or collision events of chance character.”
Hartmann, W. K. and D. R. Davis 1975 Icarus, 24, 505.

This hypothesis is the most accepted because it can prove that Tea's iron melted and became part of the Earth's core and explain why there is no iron in the Moon.
It has also been proven with the samples collected on the moon that the earth and the moon share the same oxygen isotope. Mars rocks and meteorites from other parts of the solar system have different oxygen isotope compositions. And although this hypothesis is not perfect, if it is able to explain many facts more than the previous hypotheses…

References

1
https://www.nasa.gov/feature/goddard/2017/nasa-selects-mission-to-study-jupiter-s-trojan-asteroids
2
https://www.nasa.gov/feature/goddard/2017/osiris-rex-begins-earth-trojan-asteroid-search
3
https://www.nasa.gov/missions/solarsystem/f-lagrange.html
4
https://starchild.gsfc.nasa.gov/docs/StarChild/questions/question38.html
Q
http://dx.doi.org/10.1016/0019-1035(75)90070-6