The answer is Lagrange points, briefly called L- points. The Lagrange points are the points in the space where a small object is stable and can orbit relatively along with two larger objects. These are the special places where the gravitational forces of the two large bodies balance their centrifugal forces. There are five Lagrange points for a given two large mass bodies like Sun and Earth. Let us see what L-points are.
As shown in the picture below (Image source: Wikipedia),
There are a total of five L-points out of which L1, L2, and L3 were discovered by Leonhard Euler whereas L4 and L5 were discovered by Joseph - Louis Lagrange.
The objects at L1, L2, and L3 require few orbit corrections since they are metastable points. The state of a ball placed on the tip of a convex circle is called a metastable state. Whereas, L4 and L5 are the stable Langrangian points. L1, L2, and L3 are collinear points whereas L4 and L5 each are positioned as the third vertex of an equilateral triangle formed with the centers of the two large bodies.
L1 is an equilibrium point between the two masses. It's near to the smaller object. Earth's gravity pull counterbalances the Sun's centripetal effect.
Sun-Earth L1 point is suitable to study the sun since it provides an uninterrupted view of the sun. Currently, it has been a station for the Solar and Heliospheric Observatory Satellite (SOHO).
L2 is positioned in line with two large bodies and it is farther from the larger mass. The gravitational forces of both large bodies balance the centrifugal forces at this point. The L2 position is used for space observation. L2 currently has the Planck satellite and will have James Webb Space Telescope soon in November 2021.
L3 is positioned in line with two large bodies and it is nearer to the larger mass. L3 doesn't have much use as of now as it always remains hidden behind the sun. Since it is far away from the Earth, the gravitational force by other planets plays more role than Earth's. Usually, it is shown as a place for Counter-Earth (hypothetical space body supplementary to Earth) in comic science fiction books.
L4 and L5 are stable Lagrangian points when the following condition is met,
The ratio of masses of two large bodies M1/M2 > 24.96
This condition holds in the case of the Sun-Earth system and the Sun-Jupiter system.
Many space objects are found orbiting at these naturally stable Lagrangian points L4 and L5. These are called Trojans. The Sun-Earth system has one such Trojan name as 2010 TK7. The Sun-Jupiter system has more than nine thousand trojans. The nomenclature 'Trojan' is based on the Trojan war in Greek mythology. Few Jupiter astroid trojans - 911Agamemnon, 588Achilles, and 624Hector have been named from Greek mythology as well.
In nutshell, since centrifugal and gravitational pull takes all the balancing effort, the additional efforts required to put the satellite (at L1) or telescope (at L2) in a determined place are less. Thus, these are the ideal places for placing satellites and telescopes in space. L3 can be used to study deep space being its position far enough, but as of now, it has no specific use being the least stable L-point. L4 and L5 are the stable Langrangian points where we find interplanetary dust for systems such as Earth-Moon whereas astroid trojans for systems like Sun-Jupiter, Sun-Mars, Sun-Earth, and many more.
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