Is there any chance of collision for an orbiting ring of planets around a star? (SF Novel)?

The planets are at risk for collision. That's because Kepler's laws are an approximation, they don't account for the interaction between the planets. Plus, the planets will not all be at *exactly* the same distance from the central star, especially since they are not all the same mass.

The orbits are not precisely around the central star, they are around the center of mass of the star-planet combination. With different masses, each planet orbits around a different focus point.

Depending on the details, I would guess that there will be a collision in less than 100 million years.

Such a configuration of planets is not stable. If the masses are different, it's not even an equilibrium. If the masses are EXACTLY the same, it's an equilibrium but not a stable equilibrium.

yup exactly.

PROOF

Centripetal acceleration is given by

m*V*V / r*r

Since it is gravitational, it is equal to Newton's force

G*m*M / r*r

where M is mass of star and m is mass of planet

Equating both

m*V*V / r*r = G*m*M / r*r

V^2 = G*M

V = (GM)^(1/2)

so the speed only depends on mass of star, and since star is same for all planets, the speed will also be same.

Perhaps. However I notice that we have not ever detected that configuration of exoplanets. This leads me to think that perhaps due to the gravitational effects of planets (or moons) themselves they tend to alter each others orbits slightly and over time they tend to collide or disturb each other's positions.

Absolutely. That is why there is no "ring of planets" orbiting a star.

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