# 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, $$$$r=\sqrt[3]{\frac{Gm}{\omega^2}}$$$$ where $$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$$ this angular velocity equals, $$$$\omega^2=\frac{GM}{R^3}$$$$ This yields, $$$$r=R\sqrt[3]{\frac{m}{M}}$$$$ Assuming that $$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.