Lagrangian Plane

We have seen the importance of Lagrangian Points in the posting "The Wonderful World Of Lagrangian Points. Whenever a smaller object is in orbit around a larger object, such as the earth around the sun, five Lagrangian Points are created. These are the points where the gravity of the two objects balances.

The following diagram shows the earth, at right, in orbit around the sun and the five Lagrangian Points that are formed, labeled L1 to L5. 

L2 is especially useful because a space telescope parked there will orbit the sun at the same rate as the earth, even though it is further from the sun, and so remain in the same place relative to the earth.

L3 is diametrically on the other side of the sun from the earth and forms an equilateral triangle with L4 and L5, which are 60 degrees ahead and behind the earth in it's orbit.

But the solar system and the galaxy are much more than one planet in orbit around the sun. All of the objects have gravity and so the effects of Lagrangian Points must go far beyond this. 

We have seen in "The Second Focal Point" an effect that I believe is related to Lagrangian Points. This describes how the gravity of the outer planets affected the formation of the inner planets. This created a virtual mirror image between the two sets of planets, with four planets each.

An interesting example of how the Lagrangian effect must go far beyond the basic points is the Hilda Asteroids. These are thousands of asteroids that are within the orbit of Jupiter and have a Lagrangian relationship with it. The Hilda Asteroids are not the same thing as the two groups of asteroids at Jupiter's L4 and L5, the Greeks and the Trojans.

The Hilda Asteroids are in a 3:2 orbital resonance with Jupiter. Each asteroid is in an elliptical orbit and orbits the sun three times while Jupiter orbits it twice. The elliptical orbits of the Hilda Asteroids are arranged so that asteroid reaches it's aphelion, the point furthest from the sun, when it is opposite Jupiter's L3, L4 or, L5. These Lagrangian Points are 120 degrees apart so that, the next time around, the aphelion is opposite the next Lagrangian Point. The asteroid's aphelion alternates being opposite these three Lagrangian Points.

But this is just within the solar system. What about the galaxy? Shouldn't we expect to find some kind of Lagrangian relationship since the galaxy is held together by gravity?

Our galaxy is a barred spiral galaxy, aligned along a central plane. The orbits of the planets in the solar system are also mostly aligned in one plane, which is known as the ecliptic. But the two planes are not the same. There is a difference of 60 degrees between the two. Our solar system is not near the center of the galaxy. It is about 2 / 3 of the way out, on a spiral arm of the galaxy.

The following diagram, which is not to scale, shows the orbital plane of the solar system as the short line at a 60 degree angle to the central plane of the galaxy.

The earth is also tilted on it's axis, relative to the plane of it's orbit around the sun, which is what gives us the seasons. The top right of the diagonal line represents the northern hemisphere winter, where the stars are outward from the center of the galaxy. The bottom left of the line represents the northern hemisphere summer, where a point in the southern hemisphere night sky is the direction of the center of the galaxy.

Away from bright lights, the Milky Way is visible at night. This is the dense band of stars when we are looking along the plane of the galaxy. The fact that the ecliptic and the Milky Way are different shows that the planes of the galaxy and the solar system are not the same.

We should expect that there would be some kind of Lagrangian effect within the galaxy, since it is held together by gravity. What catches my attention is that the 60 degree difference between the plane of the galaxy and that of the solar system is the same 60 degrees that define L4 and L5. This looks like what we could call a Lagrangian Plane.