# Apollo 11 CSM spacecraft orbit

How long would it take to orbit the earth at a medium altitude (with equation). I need a equation that would help me figure out how long it would take to orbit at that altitude.

• Assuming a two-body problem, the orbital period of any particular body is a function of nothing other than the semimajor axis (put more simply, the average height) of the orbit. What research have you done, and where are you stuck? – Tristan Oct 12 '17 at 14:51
• I have looked up how long it would take for the spacecraft to orbit the earth at a low orbit, but i need to find out how long it would take for it to orbit for a medium orbit and an equation for it. – Mexican15 Oct 12 '17 at 18:53

According to wikipedia, the equation for orbital period of a small body is $$T = 2\pi\sqrt{\frac{a^3}{\mu}}$$
Where $µ$ is the gravitational parameter of the body you're orbiting -- the product of the mass of the body and the gravitational constant $G$ -- and $a$ is the length of the semi-major axis of the orbit, that is, the radius of Earth plus the altitude of the orbit above the Earth's surface.
For Earth, $µ$ is $3.986004419×10^{14} m^{3}/s^{2}$. For the ISS orbiting at around 400km altitude, $a$ is $6371000 + 400000 = 6771000 m$.
Make sure to be careful of the units; the $µ$ figure I've given assumes meters, so you need the radius and altitude to be in meters as well, with the result in seconds. Low Earth orbits (100km to 2000km) should yield periods from about 90 minutes to 2 hours.