**Problem about a geostationary satellite**
We want to put a satellite of mass $\displaystyle m_s$ in a circular orbit around the Earth at a distance $\displaystyle h$ from the ground. What is the angular velocity required to keep it in its orbit?
My guess was "the same angular velocity than the Earth has" but the answer given is $\displaystyle \omega=\sqrt{\frac{GM_E}{(R_E+h)^3}}$ where $\displaystyle M_E$ is the mass of the earth, $\displaystyle G$ is the universal gravitational constant and $\displaystyle R_E$ is the radius of the Earth.
How can I reach to the answer? (Please give me the full answer if you can because my exam is tomorrow and I promise I'll try to understand the exercise). Thanks in advance.
P.S.: I suppose I have to use the formula $\displaystyle F_g=\frac{Gm_sM_E}{R^2}$ and maybe also $\displaystyle \omega=\frac{v}{r}$ and probably $\displaystyle a_c=\frac{v^2}{r}$ with $\displaystyle F_c=m_sa_c$.
__________________ **Isaac** If the problem is too hard just let the Universe solve it. |