## Maneuver Between Leo And Geo Change In Altitude At Same Orbital Inclination

The nominal LEO is 100 nautical miles (185.2 km) or 200 km (108 nautical miles). To reach a higher-altitude orbit is usually a two-step process, as shown in Figure 5.6 for GSO for example. For a general elliptical orbit the lowest altitude is the periapsis and the highest is the apoapsis. Specifically for selected bodies:

General Sun Earth Moon

Periapsis Perihelion Perigee Perilune

### Apoapsis Aphelion Apogee Apolune

The first step is an elliptical transfer orbit to the orbital altitude desired, which requires a propulsion burn to leave the low-altitude orbit; the second step is a propulsion burn to match the circular orbital velocity at the desired higher orbital altitude. This process to return to the low orbital altitude requires a burn to match the elliptical orbital speed at the higher altitude, then a second propulsion burn to match the lower circular orbit speed. This is a minimum energy transfer orbit, or a Hohmann transfer. Equation (5.1) provides the magnitude of the circular orbital velocity at the desired altitude.

Figure 5.6 shows the geometry for an elliptical transfer orbit from LEO to GSO, as an example. The information needed is the elliptical orbit velocities for the lowest

Figure 5.6. Transfer ellipse to change orbital altitude.

orbital altitude (periapsis) and the highest orbital altitude (apoapsis). Equation set (5.6) provides the orbital parameters for Keplerian elliptical orbits.

Vp = Velocity at periapsis vp =

0 0