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Comment by kpwagner | Hacker News Reader

Fascinating that this relationship scales from solar systems in which the planets are close to the star to solar systems that are more spread out. I wonder if the mass of the star has an effect on the average distance that the mass of the rest of the solar system is from the star. I also wonder if the mass of the star has a correlation with the tightness of the logarithmic distance relationship exhibited in this article.

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I suspect some expert will come in and tell us that there is some fundamental of orbital mechanics which correlated to the observations. That is, stable planetary systems have orbits that correlate with the area of the orbit (the square of the distance from the star)

I recall one of the earliest breakthroughs in orbital mechanics was someone figuring out how the area of a slice of a elliptical orbit was the same anywhere in the orbit, when the angle of the arc is calculated as a unit of time and not degrees.

Not to say you’re wrong. I think you’re right, but the quality you’re attributing to the system is a behavior of the system that has an underlying link to physics that may already be well explored. Just nobody has bothered to put a pretty plot in front of us armchair types and students before.

> I recall one of the earliest breakthroughs in orbital mechanics was someone figuring out how the area of a slice of a elliptical orbit was the same anywhere in the orbit, when the angle of the arc is calculated as a unit of time and not degrees.

That would be Kepler's second law. It states that a line between the sun and the planet sweeps equal areas in equal periods of time.

There you go.

And calculus has an explanation for why that’s the case.

Based on the graph for our system, it seems more likely that the mass of the planets affects the correlation than the mass of the star. Mars is a bit small (relative to earth) and is a slight dip from a straight line, whereas Jupiter which is quite large is a jump up above the straight line. If hypothetically the planets beyond Jupiter were all small and rocky then it seems they'd dip back down past the straight line again.

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