Newton gravitational potential theory

[look416]

Homework Statement

we all know to measure g.p,e(gravitational potential enery) we would likely to use g.p.e = mgh,
however from the theory of Newton gravitational potential energy theory, g.p.e = G$$\frac{m1m2}{r}$$, my lecturer told me that mgh is not equal to G$$\frac{m1m2}{r}$$

Homework Equations

my question is anyone know why they are not equal?

The Attempt at a Solution

 

[Fightfish]

First and foremost, $$-G\frac{m_{1}\,m_{2}}{r}$$ measures the gravitational potential energy of the object with respect to infinity, at which the GPE is chosen to be zero. It is the absolute GPE as we define in physics.

$$\Delta GPE = mg\Delta h$$ is the true form of the gpe = mgh equation that you mentioned. This makes it clear that we are measuring the change in gpe and NOT the true gpe. It must also be noted that this formula holds only for uniform gravitational fields. In the case of objects on the earth, then it only applies for distances close to the surface of the Earth where we can approximate the gravitational field to be uniform.

Obviously the gravitational field of the Earth is not uniform, and so we can apply the approximation only in certain situations.

 

[look416]

fightfish
if you say so, the both equation are valid when the object is near the gravitational sink, however both equation are not equal to each other when the object is far from the gravitational sink as the gravitational field is not uniform?

 

[Fightfish]

I stand corrected with my initial choice of words, which were a bit clumsy and awkward admittedly. The earlier post has been edited to reflect a more appropriate exposition.

It's not a matter of being close to a gravitational 'sink' - I was overgeneralising a bit there - but more so of the nature of the gravitational field present. It happens that at small distances from the surface of the Earth (or any massive body) (and over a small region of space), the gravitational field can be approximated as being uniform.

I stress again that both equations do not mean the same thing: the first measures the absolute gpe wrt infinity as the zero point, while the latter measures the change in gpe. The first equation holds for spherical and point masses, whereas the latter holds for uniform gravitational fields.

 

[look416]

oh now you make me clear of it by stressing the last part
XD