Hey guys, maybe some of you could shed some light on this. I was always under the impression that Gravitational Potential Energy (GPE) tends to decrease the higher up you go, due to the inverse square law. Then why is it that the potential energy of a rocket, after it has exited the atmosphere is still LARGE...shouldn't it be smaller?

I'd appreciate your explanations

This can be confusing.. but its an excellent question. I'll take a whack at it... If u don't like thorough answers, my apologies, I'm pretty sure someone will post a one-liner later...

First, force is a vector, typically we represent F=GMm/r^2 but technically it's F=-GMm/r^2 (usually with a unit vector to da right). The negative sign tells you that the force is ATTRACTIVE.

Second g=10m/s^2 is simply an approximation of gravitional force field, it's also a vector. A field is just "force density" in a specific direction. Therefore g= gravitational Force/unit mass and E= electric Force/unit charge.

g= Force/1kg = -GMm/

mr^2 = -GM/r^2

(where m is a test mass =1kg, M=mass of Earth).

therefore F=

mg=-GM

m/r^2 (consider them equivalent)

Work/Energy = Fd(CosQ), GPE =Fr = GMm/r

Now to ur questions/statements:

"I was always under the impression that Gravitational Potential Energy (GPE) tends to decrease the higher up you go, due to the inverse square law" Technically GPE INCREASES by the inverse law (not inverse squared law), r is NOT squared for GPE. But GPE INCREASES with r. Why?? See Below..

"Then why is it that the potential energy of a rocket, after it has exited the atmosphere is still LARGE...shouldn't it be smaller?"

1. Lets look at this form a perspective of work, W=Fr, what happens to F as r increases, it gets bigger... yes bigger.. F=

-GMm/r^2 (a negative number gets bigger as it's magntude decreases, -1>-100).

As F increases with r, GPE = Fr increases as well. Most people get confused bcos they neglect the minus sign.

FYI, gravitational Force is maximum (F=0N) where r is infinite and minimum (F~ -infinity) when r is zero, If u want to prove this to urself, take the limits of F(r) =-k/r^2 as r approaches 0 and infinity... (I've substituted GmM as k since it's constant for rocket/earth system)

2. From a Field perspective, Work done on an object in a conservative field, is stored as potential energy, gravity is a conservative field so the rocket's engine does work against gravity to move it into space and this work is stored as GPE.. (Well, in reality there's a myriad of frictional forces etc... so not all the work is conserved.. regardless some of the work is stored as GPE therefore)

Hope this helps...