# Would a space elevator theoretically be possible on a tidally-locked planet?

It's my understanding that many of the theorized methods of creating a space elevator rely on the upward centrifugal force of earth's rotation on a counterweight high above to keep the structure taut and counter the planet's gravity. So, is there any possibility that a space elevator could be at all plausible on a planet with similar mass and size of earth that's tidally-locked to a dwarf star? If so, where would it need to located on the planet (disregarding any potential planet-side environmental factors the material would be exposed to, such as extreme heat or cold)?

• Sep 29, 2016 at 20:28

Let's start with the naive estimate where we neglect the perturbations of the space elevator by the gravity of the star. The radius of the geostationary orbit is given by, $$\begin{equation} r=\sqrt{\frac{Gm}{\omega^2}} \end{equation}$$ where $$m$$ is the planet mass and $$\omega$$ its rotation angular velocity. For the tidally locked planet $$\omega$$ coincides with the angular velocity of its orbital motion around the star. Assuming that the orbit is circular with radius $$R$$ and denoting the star mass as $$M$$ this angular velocity equals, $$\begin{equation} \omega^2=\frac{GM}{R^3} \end{equation}$$ This yields, $$\begin{equation} r=R\sqrt{\frac{m}{M}} \end{equation}$$ Assuming that $$m\ll M$$ we get that $$r\ll R$$ i.e. the orbital elevator stays close to the planet. One may then naively expect that we indeed approximately describe it omitting the star gravity from our consideration.
Then we remember that there are 5 points - the Lagrangian points, where objects remain stationary with respect to planet and the star. Taking the image from wikipedia 