The value of g above and below the earth

[takando12]

Homework Statement

The value of g at a point P inside the Earth and at another point Q outside the Earth is g/2. Maximum possible distance in terms of radius of Earth between P and Q is? (g being the acceleration due to gravity on the surface).

Homework Equations

g_h = (1+h/r)^-2g
g_d = (1-d/r)g

The Attempt at a Solution

I don't understand what maximum distance is. The value of g reduces whether we go above or below the Earth's surface and there is only one point above and below that correspond to g/2 and so there is only one distance between those two points. How does maximum distance come into this?
Just using the formulas I get:
d= R/2
h = R(√2-1) or -R(√2+1) // what does that negative sign actually mean in the second one?
Distance between the two points =
-(2√2+1)R/2 or (2√2-1)R/2 // again a negative sign.
And I suppose maximum means I should choose the first and the answer is right. But I just don't get what the answer means. How can there be more than one distance between P and Q? What do those negative signs mean?
Please point out where my understanding is flawed.

 

[RUber]

The positive R can be thought of as toward the North pole, and the -R can be though of as toward the South pole.
Maximum distance would not be where both points were in the +R position, right?

 

[ehild]

P can be anywhere on the green sphere.

 

[takando12]

ohhh.That never struck me at all.
Thank you ehild and RUber.