Change of variable $$F$$ to $$F_{\rm gravity}$$ and $$m_1$$ to $$m_{\rm Earth}$$ and $$m_2$$ to $$m_{\rm satellite}$$ and $$x$$ to $$r$$ in Eq. \ref{eq:2820438}; yields Eq. \ref{eq:F0}. $$F_{\rm gravity} = G \frac{m_{\rm Earth} m_{\rm satellite}}{r^2} \label{eq:1917654}$$ Eq. \ref{eq:8242154} is an initial equation. $$F = \frac{m v^2}{r} \label{eq:8242154}$$ Change of variable $$F$$ to $$F_{\rm centripetal}$$ and $$m$$ to $$m_{\rm satellite}$$ and $$v$$ to $$v_{\rm satellite}$$ and $$8242154$$ to $$6845877$$ in Eq. \ref{eq:#9}; yields Eq. \ref{eq:F0}. $$F_{\rm centripetal} = \frac{m_{\rm satellite} v_{\rm satellite}^2}{r} \label{eq:6845877}$$ Eq. \ref{eq:2154616} is an assumption. $$F_{\rm centripetal} = F_{\rm gravity} \label{eq:2154616}$$ Substitute LHS of Eq. \ref{eq:1917654} and LHS of Eq. \ref{eq:6845877} into Eq. \ref{eq:2154616}; yields Eq. \ref{eq:4948724}. $$\frac{m_{\rm satellite} v_{\rm satellite}^2}{r} = G \frac{m_{\rm Earth} m_{\rm satellite}}{r^2} \label{eq:4948724}$$ Change variable $$C$$ to $$d$$ in Eq. \ref{eq:1115424}; yields Eq. \ref{eq:5369477}. $$d = 2 \pi r \label{eq:5369477}$$ Substitute LHS of Eq. \ref{eq:5369477} into Eq. \ref{eq:5114041}; yields Eq. \ref{eq:8090893}. $$v = \frac{2 \pi r}{t} \label{eq:8090893}$$ Change variable $$t$$ to $$T_{\rm orbit}$$ in Eq. \ref{eq:8090893}; yields Eq. \ref{eq:2392562}. $$v = \frac{2 \pi r}{T_{\rm orbit}} \label{eq:2392562}$$ Raise both sides of Eq. \ref{eq:2392562} to $$2$$; yields Eq. \ref{eq:6390693}. $$v^2 = \frac{4 \pi^2 r^2}{T_{\rm orbit}^2} \label{eq:6390693}$$ Divide both sides of Eq. \ref{eq:4948724} by $$\frac{m_{\rm satellite}}{r}$$; yields Eq. \ref{eq:2009493}. $$v_{\rm satellite}^2 = G \frac{m_{\rm Earth}}{r} \label{eq:2009493}$$ LHS of Eq. \ref{eq:2009493} is equal to LHS of Eq. \ref{eq:6390693}; yields Eq. \ref{eq:2871066}. $$G \frac{m_{\rm Earth}}{r} = \frac{4 \pi^2 r^2}{T_{\rm orbit}^2} \label{eq:2871066}$$ Multiply both sides of Eq. \ref{eq:2871066} by $$r T_{\rm orbit}^2$$; yields Eq. \ref{eq:7188516}. $$T_{\rm orbit}^2 G m_{\rm Earth} = 4 \pi^2 r^3 \label{eq:7188516}$$ Divide both sides of Eq. \ref{eq:7188516} by $$4 \pi^2$$; yields Eq. \ref{eq:6238570}. $$\frac{T_{\rm orbit}^2 G m_{\rm Earth}}{4 \pi^2} = r^3 \label{eq:6238570}$$ Raise both sides of Eq. \ref{eq:6238570} to $$1/3$$; yields Eq. \ref{eq:7139326}. $$\left(\frac{T_{\rm orbit}^2 G m_{\rm Earth}}{4 \pi^2}\right)^{1/3} = r \label{eq:7139326}$$ Eq. \ref{eq:9978909} is an assumption. $$T_{\rm geostationary orbit} = 24\ {\rm hours} \label{eq:9978909}$$ Change variable $$T_{\rm orbit}$$ to $$T_{\rm geostationary\ orbit}$$ and $$r$$ to $$r_{\rm geostationary\ orbit}$$ in Eq. \ref{eq:7139326}; yields Eq. \ref{eq:4507350}. $$\left(\frac{T_{\rm geostationary\ orbit}^2 G m_{\rm Earth}}{4 \pi^2}\right)^{1/3} = r_{\rm geostationary\ orbit} \label{eq:4507350}$$