# Would 6 Earths Separated by 60 Degrees Have Day-Night Cycles?

This picture is taken from one of Sean Raymond's Planet Planet articles, Cohorts of co-orbital planets.

What the article doesn't explain, however, is the basis for the question. In a solar system in which six rocky planets, each one the size of Earth and each one orbited by a single moon 1/4 the mass from a distance of 238,900 miles, orbit their sun from one same distance, would a 60-degree difference allow each of the "Earths" to spin in day-night cycles?

• Why do you think this would prevent their rotation?
– Mary
Aug 29, 2021 at 3:18
• My first impulse was to think @Mary had a good point, then I started to think about the compounded gravitational forces. Call the Earth on the right of the image "A" and letter the Earths clockwise. Earths B and F are exerting a gravitational pull on A along with the star. I can imagine that the extra gravitational "umph" would favor tidal locking due to both the increased pull and the spread of the pull. I'm looking forward to the group's Celestial Mechanics' input on this one.
– JBH
Aug 29, 2021 at 3:26
• That should probably go in the question.
– Mary
Aug 29, 2021 at 4:20
• @JoinJBHonCodidact: The tidal force exercised by the "neighbours" on any given planet would be so tiny as to be completely negligible. (Tidal forces are inversely proportional to the cube of the distance.) More interesting are the gigantic satellites. Aug 29, 2021 at 5:05
• Agree with AlexP.. Q: do you mean a moon 1/4 of our moon's mass, or a moon that has 1/4 of the planet's mass ? Aug 29, 2021 at 8:48

Rotation will be maintained

When planet-sun distance and planet mass are similar to Earth's, there is no reason for tidal lock, because the other planets are far away. Tidal locking depends on size, orbit and mass of the orbiting object and the sun's mass. There is no need for symmetry: rotations could differ. The rotation of a celestial body does not affect gravitational interactions with other bodies, because the center of gravity does not move.

https://en.wikipedia.org/wiki/Tidal_locking

Age would count

In a simulation model, like the one used in the article, you just launch an isolated configuration and wait a few thousand years, until things collide. If they don't collide, conclusion is "stable".

But your picture shows 6 mature, developed planets. In the real universe, planets like Earth exist for >4x10e9 years. In that timespan, orbits get disturbed, eventually causing issues with distances. For example, our moon was supposedly formed by an early collision with a planetary size object. Little is known about earths orbit before that event occurred, but I think "shakeup events" must be included in the simulation ! A subtle orbit disturbance could have grave consequences in due time.

https://en.wikipedia.org/wiki/Giant-impact_hypothesis