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Comment by kevinslashslash | Hacker News Reader

My son likes to ask our Google Home the distance to different planets. The numbers, though generally technically correct (sun has worked in the past), are misleading as some are minimum, some average distance and some maximum.

For example "distance to mars" says 54.6 million km, which is the theoretical minimum. "distance to venus" says 261 million km which is maximum. I believe it was Jupiter that previously gave an average distance but now I'm seeing minimum.

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By the "[maximum] distance to different planets" do you really mean literally that, or do you mean the maximum distances to their orbits?

Wouldn’t those be the same? The periods of each planet’s orbit aren’t factors/multiples of one another, so eventually any two will be at opposite points in their orbit.

The maximum distance between two ellipses is not the same as the maximum distance between all pairs of points on them right? Like just imagine measuring the maximum distance from a circular orbit to itself. One measure would give zero (zero separation between the orbits) and the other would give twice the radius (individual points can be 2R away from each other).

If I'm doing this correctly I think the max distance between two points would come out to max_x max_y ||x - y|| whereas the max distance to the orbit would come out to max_x min_y ||x - y||.

There are orbital resonances, but you are right that none involve planets. https://en.wikipedia.org/wiki/Orbital_resonance

The closest is the 2:3 ratio of Pluto:Neptune. (It counts if you consider Pluto a planet. ;)

Otherwise, there's a nice table showing "near-integer-ratio relationships between the orbital frequencies". If I understand it correctly, each of the bigger-than-a-dwarf-planet planets will be at their furthest possible distances from each other in timescales no longer than about 50,000 years.

What's the difference?

See here: https://news.ycombinator.com/item?id=16211745

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