Satellite orbits

A satellite orbits the earth. The graviational force on the satellite is,

$\large \vec{F} = -\frac{Gm_e m_s}{r^2} \hat{r},$

where $G= 6.6726 \times 10^{-11}$ N m²/kg² is the graviational constant, $m_e = 5.97219 \times 10^{24}$ kg is the mass of the earth, $m_s$ is the mass of the satellite, and $\vec{r}$ is the position of the satellite measured from the center of the earth.

If the orbit falls below about 6400000 m, the satellite will crash into the earth. There are various kinds of orbits such as geosynchronous orbits, geostationary orbits, low earth orbits, elliptical orbits, and graveyard orbits. The difference just depends on the initial conditions of the satellite. A long time step should be used to calculate satelite orbits.