- #1
AbsoluteZer0
- 125
- 1
Hi,
The derivation of the Gravitational Potential formula, as I understand, is:
[itex] W = Fd [/itex] (1)
[itex] W = G \frac{M_1m_2}{r^2}d [/itex] (2) Substituting the Gravitational Force formula
[itex] W = - \int_R^∞G \frac{M_1m_2}{r^2} \, dr [/itex] (3) Integrating within the boundaries of the initial distance (R) and Infinity
Which allows us to arrive at:
[itex] E_p = - \frac{GM_2m_1}{R}[/itex] (4)
However, what I don't understand is how we are able to proceed from step 3 to step 4.
What method must be used in order to proceed as such?
My proficiency with Calculus is still in the works.
Thanks,
The derivation of the Gravitational Potential formula, as I understand, is:
[itex] W = Fd [/itex] (1)
[itex] W = G \frac{M_1m_2}{r^2}d [/itex] (2) Substituting the Gravitational Force formula
[itex] W = - \int_R^∞G \frac{M_1m_2}{r^2} \, dr [/itex] (3) Integrating within the boundaries of the initial distance (R) and Infinity
Which allows us to arrive at:
[itex] E_p = - \frac{GM_2m_1}{R}[/itex] (4)
However, what I don't understand is how we are able to proceed from step 3 to step 4.
What method must be used in order to proceed as such?
My proficiency with Calculus is still in the works.
Thanks,