We’ll suppose each planet has an independent uniform probability of being at each point in its orbit
This happens to be true of Earth, and a very useful assumption, but I think it’s pretty neat that some systems have a mean-motion resonance (eg Neptune-Pluto, or the Galilean moons, or almost Jupiter-Saturn) which constrains the relative position away from a uniform distribution.
Yeah, that is very neat, and I don’t know how you would take it into account in the calculation. The paper does have a table comparing predictions from their formula, the old model (taking the difference of the radii) and a simulation they did, and eyeballing it, the Jupiter/Saturn distance doesn’t seem to have a bigger error than other entries in the table. (Unfortunately the table only shows the planets of the Solar System, without Pluto.)
This happens to be true of Earth, and a very useful assumption, but I think it’s pretty neat that some systems have a mean-motion resonance (eg Neptune-Pluto, or the Galilean moons, or almost Jupiter-Saturn) which constrains the relative position away from a uniform distribution.
Yeah, that is very neat, and I don’t know how you would take it into account in the calculation. The paper does have a table comparing predictions from their formula, the old model (taking the difference of the radii) and a simulation they did, and eyeballing it, the Jupiter/Saturn distance doesn’t seem to have a bigger error than other entries in the table. (Unfortunately the table only shows the planets of the Solar System, without Pluto.)