Hi, I am a bit confused with the relationship between gravitational field strength and gravitational potential. As far as I know, gravitational field strength is defined as:
g=[itex]\frac{F}{m}[/itex]=[itex]\frac{GM}{R^{2}}[/itex]
and gravitational potential is defined as:
V=[itex]\frac{-GM}{R}[/itex]
Now if I differentiate V with respect to R, I get:
[itex]\frac{dV}{dR}[/itex]=[itex]\frac{GM}{R^{2}}[/itex]=g
However, the formula booklet that I'm using at school suggests that
[itex]\frac{-ΔV}{ΔR}[/itex]=g
Why doesn't my derivation above agree with the formula in the formula booklet? (i.e. why are the signs different?) A friend of mine suggests that I cannot use differentiation to replace the symbol Δ, but I see no reason why it is so.
Thank you very much!
g=[itex]\frac{F}{m}[/itex]=[itex]\frac{GM}{R^{2}}[/itex]
and gravitational potential is defined as:
V=[itex]\frac{-GM}{R}[/itex]
Now if I differentiate V with respect to R, I get:
[itex]\frac{dV}{dR}[/itex]=[itex]\frac{GM}{R^{2}}[/itex]=g
However, the formula booklet that I'm using at school suggests that
[itex]\frac{-ΔV}{ΔR}[/itex]=g
Why doesn't my derivation above agree with the formula in the formula booklet? (i.e. why are the signs different?) A friend of mine suggests that I cannot use differentiation to replace the symbol Δ, but I see no reason why it is so.
Thank you very much!