Tek

Apoapsis altitude ha hp = Periapsis altitude a = Semi-major axis of transfer ellipse a =[(Rq + ha) + (Ro + hp)]/2 e = Eccentricity (defines the shape of the orbit)

The Keplerian orbits are conic sections. In this general sense an orbit is a path through space defined by a conic section. There are two closed orbital solutions (circular and elliptical) and two open (not returning) orbital solutions (parabolic and hyperbolic). For a circular orbit the eccentricity (e) must be equal to zero. For an elliptical orbit, eccentricity (e) must be less than one. For a parabolic orbit, eccentricity (e) must be equal to one. For a hyperbolic orbit, eccentricity (e) must be greater than one.

The velocity increments to achieve an orbital altitude change are then

Increasing orbital altitude

DV1 = Vp — Vcircular, p DV2 = Va — Vcircular, a

Decreasing orbital altitude

DV1 = Vcircular, a — Va DV2 = Vcircular, p — Vp

So to increase orbital altitude there is a propulsion burn at periapsis to accelerate to elliptical orbit speed, then at apoapsis there is a propulsion burn to increase the spacecraft speed to circular orbit speed at the higher altitude. To decrease orbital altitude there is a propulsion burn at apoapsis to slow the spacecraft to elliptical orbit speed, then at periapsis there is a propulsion burn to decreases the spacecraft speed to circular orbit speed at the lower altitude. Specifically, in transferring from a 100 nautical mile (185.2 km) LEO to a 19,323 nautical mile (35,786 km) GSO orbit

(refer to Figure 5.6 for the geometry of the transfer maneuver and the location of the velocities called out) the orbital velocity for a 100 nautical mile (185.2 km) circular orbit is 25,573 ft/s (7,795 m/s). For an elliptical transfer orbit, the orbital velocity at the 100 nautical miles (185.2km) perigee is 33,643ft/s (10,254m/s) and 5,235ft/s (1,596m/s) at the 19,323 nautical miles (35,786km) apogee. The orbital velocity for a 19,323 nautical miles (35,786 km) circular orbit is 10,088 ft/s (3,075 m/s).

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