# Astrodynamics/Satellite Ground-Track

## Effects of Earth's Rotation

The earth rotates with respect to the orbit, which means that the orbital plane is essentially stationary in space while the earth rotates. The sine wave formed by the ground track is displaced by the number of degrees each orbit by the number of degrees that the earth rotates during the orbital period. The image below shows a satellite ground track through two of earth's rotations:

## Launch Inclination and Latitude

It should be apparent that the point and orientation of launch heavily affects the orientation of the satellite's orbit. A satellite is launched from a point A on the surface of the earth. The launch latitude and longitude are given by L and λ respectively. The satellite is launched with an azimuth angle of β.

The satellite's orbit passes through the equator on the ground-track map (the ascending node) at point B with an inclination angle from the equator of i. We can calculate i as:

${\displaystyle \cos(i)=\sin(\beta )\cos(L)}$

We can see from this result that a direct orbit must have a launch azimuth between 0° and 180°. A retrograde orbit must have a launch angle between 180° and 360°.

We can see that satellites cannot be put into an equatorial orbit if the launch site is not on the equator. We can also see that a launch site cannot obtain an orbital inclination smaller than the launch latitude. For that reason, launch sites closer to the equator have a larger range of possible orbits. A launch site directly on the equator can put a satellite into any orbit.

Example: USA Launch Sites

The United States has a series of launch sites in southerly states: Florida and Texas are the most well known, but there are plans for a new launch site in New Mexico as well. Launch sites in Florida have a latitude of 25°