Gravity and Height: Find the Height of a Physics Problem

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The discussion revolves around a physics problem related to gravity and height, specifically determining the height above a planet's surface. The correct orbital radius is identified as r = √2 * R, where R is the planet's radius. The height above the planet is calculated as (√2 - 1) * R, which simplifies to approximately 0.41 * R. Clarification is provided on how to derive the height based on the orbital radius. The conclusion emphasizes that substituting the planet's radius into the formula yields the desired height.
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I have a problem like the one below:

https://www.physicsforums.com/showthread.php?t=114812

I understand how they derived it(I did the same thing) but never say what is the height. So could someone tell what the height is?
 
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In that problem, height is relative to the radius of the planet. The correct answer for THAT question should have been
r = \sqrt{2}*R.
That would be the orbital radius. The "height" would be the altitude above the planet, which would be
(\sqrt{2}*R)-R
or(\sqrt{2}-1)*R
Which happens to be equal to 0.41*R

Substitute the radius of the planet in for R and you get the "height."
 
Ok I see now. Wasn't so obvious last night.
 

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