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Comment by aceazzameen | Hacker News Reader

Wow. I had no idea a horseshoe orbit was possible.

It must be noted that it's a horseshoe only relative to the Sun-Earth system. Relative to the Sun it's just a normal elliptical orbit that keeps changing shape.

Same! The animation is wild.

Apparently it will oscillate between being in orbit around earth to going back into a bouncy horseshoe orbit. Over and over throughout the millennia.

There are even more animations here, though the one in the article is great:

https://en.wikipedia.org/wiki/469219_Kamo%CA%BBoalewa

https://en.wikipedia.org/wiki/469219_Kamo%CA%BBoalewa#/media...

This is only animation from all of these I've seen that makes any sense to my brain, I still can't figure out what's going on in the others:

https://en.wikipedia.org/wiki/File:Asteroid2016HO3-SunEarthO...

Thank you. But I am having the hardest time understanding how this entirely reasonable-looking orbit "around the sun":

https://en.wikipedia.org/wiki/File:Animation_of_2016_HO3_orb...

Somehow turns into this loop-de-loop "relative to the sun and earth":

https://en.wikipedia.org/wiki/File:Animation_of_2016_HO3_orb...

Is this essentially the origin of epicycle model of the planets? Do all planets look like that loop-de-loop graphic, but for whatever reason we never plot them that way, but for some reason this article is plotting the asteroid this way? (Just to confuse us?)

The second plot fixes Earth and Sun in place, and so you see the position of the asteroid relative to Earth. What is happening is that the asteroid is in an orbit so similar to Earth that they do not usually pass each other, and alternatively speeds up and slows down very slightly related to us. (When it approaches Earth from "behind" on it's orbit, earth's gravity accelerates it forwards, which makes it's orbit slightly longer, which makes it take a longer time to go around it, causing it to start lagging us. When Earth catches up to it, Earth's gravity will accelerate it backwards, as in slow it down, which will shrink it's orbit, meaning it will go around faster than us.)

The tight loops are caused by orbital inclination: As the asteroid is not orbiting in the same plane as Earth, each orbit around the Sun it will travel slightly above us and slightly below, this causes the loop.

3+ body orbits can be wild!

It doesn't make any sense in a 2-body orbit (those are all conic sections).

Another fun one is the long term orbits of expended Apollo hardware. The below article shows the booster entering by way of L1 into something like a Molniya orbit until leaving again.

Yeung’s discovery, formally named J002E3, became the focus of an intense analysis with a unique result. The object was not an asteroid captured by Earth in a cosmic game of coincidence. This was a relic of humanity’s space race: an Apollo-era rocket that had been placed in orbit around the Sun — and then returned to Earth.

https://www.astronomy.com/space-exploration/how-a-long-gone-...

Horseshoe orbits come from the most counterintuitive behavior of orbits: if you thrust forward, you go slower. And if you thrust backward, you go faster. (The reason is that thrusting forward puts you in a higher orbit.)

In a horseshoe orbit, when the small body approaches the medium body "from behind" (that is, the small body is moving faster than the medium body), the medium body tugs the small body forward. That is an effective forward thrust for the small body, which rises into a higher orbit and slows down as a result. That means the small body starts to fall behind, losing ground relative to the medium body.

After it loses enough ground, it approaches the medium body from the front (or, if you prefer, the medium body catches up to it from behind). Then the medium body's gravity tugs it backward, dropping it into a lower and faster orbit, and the cycle repeats.

The most exceptional example of this is two of Saturn's moons, Janus and Epimetheus, which share an orbit and periodically trade places in it as a result of these dynamics.

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