# What (actually) is a 1:1 resonance, and is 2016 HO3 in one with the Earth?

In my question How was Earth's "quasi-satellite" 2016 HO3 "first spotted" and it's orbit determined? I link to two videos of simulations of views of 2016 HO3's orbit seen in two different frames.

In this NASA JPL video (above) the view is rotating around the sun following Earth. You can see the earth move slightly closer and farther from the sun since the Earth's orbit is not quite circular.

This video (above) from http://arksky.org/calendar/alerts/714-what-is-it-the-strange-new-object-2016-ho3 shows a projection of 2016 HO3's motion against the stars as seen from Earth's location, but in a fixed direction. You can see the the sun and planets tend to follow the ecliptic, while 2016 HO3 does a figure-eight every year.

The NASA JPL news brief announcing the discovery of 2016 HO3 states:

The asteroid's orbit also undergoes a slow, back-and-forth twist over multiple decades. "The asteroid's loops around Earth drift a little ahead or behind from year to year, but when they drift too far forward or backward, Earth's gravity is just strong enough to reverse the drift and hold onto the asteroid so that it never wanders farther away than about 100 times the distance of the moon," said Chodas. "The same effect also prevents the asteroid from approaching much closer than about 38 times the distance of the moon. In effect, this small asteroid is caught in a little dance with Earth."

note: Paul Chodas is the manager of NASA's Center for Near-Earth Object (NEO) Studies

I think that the fact that it's orbit slowly oscillates on the order of decades (tens of orbital periods) with respect to Earth's orbit means it is in a 1:1 resonance with Earth. But I'm using the term orbital resonance without knowing it's exact definition - if there is one. Perhaps it's a soft term - some orbits may be clearly in resonance, others only roughly in resonance.

Is there a good working definition of orbital resonance, and is 2016 OH3's orbit in 1:1 resonance with Earth's orbit?

bonus: Are Trojan asteroids (at a planet's $L_4$ or $L_5$ triangular libration points) also considered to be in a 1:1 resonance orbit?

• Did you read the Wikipedia article on orbital resonance? – Russell Borogove Aug 26 '19 at 15:04
• @RussellBorogove I'm not satisfied with that article, it's pretty vague, and mostly tries to explain the concept in simple terms. I'd rather have an answer that cites some authoritative source. After reading my question, if you feel it's definitively answered by that article, by statement that are themselves well-sourced, and can be used to address 2016 HO3 directly, then that could be the basis of an answer. – uhoh Aug 26 '19 at 15:08
• slightly related: Just how “locked” are resonant-chains of exoplanets thought to be? – uhoh Aug 26 '19 at 15:12
• @RussellBorogove for example, the answer to Is Dawn's upcoming low periapsis orbit for XMO7 “resonant”? is in my opinion no. While there was an effort to make the two periods have some rational number relationship, it was not actually "resonant" in any way. A real resonance involves a periodic exchange of energy between two oscillators (again in my opinion at least) and so there's a difference between a real orbital resonance and a Coincidental ratio. – uhoh Aug 26 '19 at 15:34