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# Geometry/Geometry Planets

Question
Hi Scott,

Recently discovered; Any planet in orbit has a relationship;

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

Let the orbit radius be O and the planet radius be P.

The surface area with radius r is known to be 4*pi*r^2.

The surface area of the orbit sphere would then be 4*pi*O^2.
The surface area of the planet would then be 4*pi*P^2.

Since we are dividing these two, the 4*pi cancels, leaving sqrt(O^2/P^2).
Taking the sqrt gives O/P.

This is what was given at the start, so it is correct and the physicist is not full of hogwash.

Geometry

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#### Scott A Wilson

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