Template talk:Earth orbits

$$v= \sqrt{\mu\left({2\over{r}}-{1\over{a}}\right)} $$

$$T = 2\pi\sqrt{a^3/\mu}$$

$$\epsilon = -{\mu \over{2a}}\,\!$$

where

$$\mu$$= 398,600 km3s-2 (standard gravitational parameter for the Earth)

$$a\,\!$$ is semi-major axis of the orbiting body.

Calculation examples:


 * speed: (398600*(2/6600-1/7500))^.5
 * period (in minutes): 2*pi*(6600^3/398600)^.5/60
 * specific orbital energy compared with stationary on Earth: 398600*(-1/2/6600+1/6400)

The largest speed occurs in the orbit with the distance to the center of the earth ranging from the minimum to the maximum; the semi-major axis is the mean value of the two (for the LEO range: 7500 km). In this orbit the largest speed occurs at the lowest altitude.