Figure 5.3. Velocity increment to 200 nautical mile orbit for orbital inclination. Some launch centers indicated.

latitude is:

La = latitude of the launch site (5.2)

For a due east launch, the inclination of the orbit is equal to the latitude of the launch site. Figure 5.3 shows the velocity increment for the launch A V as a function of the launch site azimuth for a due east launch with a number of launch sites indicated. In reality the launch azimuth will not always be due east. The launch azimuth for a non-rotating Earth at a given orbital inclination and launch site latitude is:

Az = launch azimuth from true north i = orbital inclination (5.3)

Equation (5.3) defines the minimum inclination for an orbit as the latitude of the launch site and a true east or west launch (90° or 270°). For the rotating Earth case a correction to the launch azimuth and velocity must be made by the vector addition of the eastward velocity of the Earth and the launch velocity vector. But equation (5.3) will give the minimum azimuth and a good first-order value. For a Sun-synchronous orbit (98°) from a launch site at 45° latitude this value is -11.4° degrees or an azimuth of 348.6°. For a space station orbit (55°) from Kennedy (28.5°), the azimuth angle is 40.7° or just north of northwest. So if Shuttle launches from Kennedy, the spacecraft must roll so the wing plane is perpendicular to 40.7°, and then proceed along its launch trajectory.

Given the incremental velocity required to achieve a circular orbit, the next step is to determine the quantity of launch propellant required to place a given quantity of propellant into LEO for inter-orbit maneuvering.

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