You are standing on a planet which is perfectly spherical with radius .
A rope was been wrapped around its equator. Adding meters to this rope,
how high will you be able to lift the rope with it still being in the plane of the equator?
The planet has a radius of (the units don't matter).
At the equator, the circumference (length of the rope) is: .
Add meters to the rope.
The rope is now a circle with circumference .
Let be the radius of this new (larger) circle.
Then the circumference of the circle is:
So we have: .
We see that the new radius is meters larger.
Therefore, the rope can be raised meters (all around the equator).