# Is it possible for one celestial body to trail another indefinetly?

• MickN
In summary, it is not possible for one object to simply trail behind another indefinitely under the influence of gravity, unless there are multiple massive bodies involved in a specific scenario. The concept of Lagrangian points explains how this can occur, with only two points (L4 and L5) being stable. However, this only applies to specific circumstances and a comet breaking up into parts will not result in a static trailing configuration.
MickN
In other words, are there any circumstances in which one object, captured by the gravity of another, would simply trail behind it indefinitely, instead of revolving around it or crashing into it? Is it possible? It seems reasonable to me that under certain circumstances it could happen, but someone tells me it's impossible, and that, except in the case of one object breaking up into several (like a commit breaking up), it can't happen.

Thanks

As long as there are just two bodies under each other's gravitational influence, it's not possible.
Take a simplified scenario, where one of the bodies is much less massive(m) than the other(M), so that only the massive one attracts the light one. The m body will always feel the force of gravity, constantly accelerating towards M. To preserve the intial setup where both are at rest with respect to each other, you'd have to constantly keep pushing the body M away at the same rate as it pulls in the body m.

If you introduce a third massive body, that both M and m are orbiting, then you can get a class of solutions that is close to what you're asking for. Namely, M and m can follow one another as they orbit the central mass. In this case, the body m is at all times under the gravitational influence of M, as well as the central mass, so it can be said that it is trailing M.

These solutions are called the Lagrangian points.

(the blue blob representing M, the red dot m)
Of these five points, only L4 and L5 are stable.

To reiterate, if by trailing you mean being affected by the gravity of another body but neither obiting it nor changing the distance to it, then L4 and L5 should do.

By the way, a comet(or any other body) breaking into parts will not stay in a static configuration indefinitely. Either the parts will move towards each other under mutual gravitational attraction, or move away from each other affected by whatever force caused the breakup in the first place(tidal forces for example).

## 1. Is it possible for one celestial body to trail another indefinitely?

Yes, it is possible for one celestial body to trail another indefinitely. This phenomenon is known as orbital resonance, where two objects orbiting a larger body can maintain a specific distance and ratio between them, resulting in one object always trailing the other.

## 2. How does orbital resonance work?

Orbital resonance occurs when the orbital period of one object is an exact fraction of the orbital period of another object. This results in a gravitational interaction that maintains the stable distance between the two objects, causing one to trail the other indefinitely.

## 3. Are there any examples of celestial bodies that trail each other indefinitely?

Yes, there are several examples of orbital resonance in our solar system. One famous example is the relationship between Jupiter's moons, Io, Europa, and Ganymede. The orbital periods of these moons are in a 1:2:4 ratio, resulting in a stable orbital resonance where Io always trails Europa and Ganymede.

## 4. Can orbital resonance ever break or change?

While orbital resonance is a stable phenomenon, it can be disrupted by outside forces such as gravitational interactions with other bodies or changes in the mass or orbit of the objects involved. In some cases, orbital resonance can also evolve over time, resulting in a different ratio between the two objects.

## 5. Could a smaller celestial body eventually overtake and pass the larger one in an orbital resonance?

In most cases, the larger body will maintain its dominant position in an orbital resonance. However, there are some rare scenarios where the smaller object can gradually gain energy and overtake the larger one, resulting in a switch in their positions. This is known as a "resonance flip" and is more likely to occur with smaller objects orbiting a massive body like a planet or star.

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