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Question
Hi Randy,

Recently discovered; Any planet in orbit has a relationship;

orbit Radius / planet Radius  =

Square Root of "orbit Sphere" Surface Area / planet Surface Area

(orbit Sphere = orbit Radius^2 x 4 Pi)

A top physicist states that this is just a thing that all planets have.  We state hogwash and that this is specifically a law that stems from the Density of the planet.

Do you have any insight as to whether this could be true if the orbit Radius wasn't directly connected to the Radius (Volume) of the planet, via Density.

Thanks,
AL

Answer
Let R = orbit radius and r = planet radius. We then have

orbit sphere = 4π・R^2 and planet surface area ("planet sphere") = 4π・r^2.

The ratios are then

orbit radius/planet radius = R/r and
sqrt[(orbit sphere)/(planet sphere)] = sqrt[4π・R^2/4π・r^2] =sqrt[(4π/4π)(R/r)^2] = R/r.

So, yes, the ratio of the orbit-to-planet radii is equal to the sqrt of the ratio orbit-sphere/planet-sphere.

This doesn't really have anything to do with planets, orbits, density, etc., just the definition of surface area.

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randy patton

Expertise

college mathematics, applied math, advanced calculus, complex analysis, linear and abstract algebra, probability theory, signal processing, undergraduate physics, physical oceanography

Experience

26 years as a professional scientist conducting academic quality research on mostly classified projects involving math/physics modeling and simulation, data analysis and signal processing, instrument development; often ocean related

Publications
J. Physical Oceanography, 1984 "A Numerical Model for Low-Frequency Equatorial Dynamics", with M. Cane

Education/Credentials
M.S. MIT Physical Oceanography, B.S. UC Berkeley Applied Math

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Also an Expert in Oceanography

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