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Non-conservative forces

If gravity cannot be assumed to be constant then:

g=GM(rsummit−∫0ssin⁡θ(σ)dσ)2.\begin{aligned} g=\dfrac{GM}{\left(r_{\mathrm{summit}} - \int_0^s \sin{\theta(\sigma)}d\sigma\right)^2}. \end{aligned}

Substituting Equation (0) into Equation (??) yields:

Fr=GMmCrrcos⁡θ(s)(rsummit−∫0ssin⁡θ(σ)dσ)2\begin{aligned} F_r &= \dfrac{GMmC_{rr}\cos{\theta(s)}}{\left(r_{\mathrm{summit}} - \int_0^s \sin{\theta(\sigma)}d\sigma\right)^2} \end{aligned}
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Last modified: October 23, 2026.