Editing Launch Azimuth
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− | The '''launch azimuth''' is the angle between north direction and the projection of the initial | + | The '''launch azimuth''' is the angle between north direction and the projection of the initial orbit plane onto the launch location. It is the compass heading you head for when you launch. |
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==Relation between latitude and inclination== | ==Relation between latitude and inclination== | ||
− | Not all | + | Not all inclinations can be reached at a position on a celestial body, with even fewer possibilities if that body does not spin on an axis. The problem is, that the launch location has to be a point inside the target orbit plane. So, if the latitude of a launch location is higher than the inclination, or the spin is so slow that it's impractical to wait for the launch window, the orbit can't be reached directly. |
− | + | Using spherical trigonometry, we can [http://orbiter-forum.com/showpost.php?p=51004&postcount=5 calculate] the launch azimuth required to hit any allowed orbit inclination. | |
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<math>\cos(i)=\cos(\phi)\sin(\beta)\!</math> | <math>\cos(i)=\cos(\phi)\sin(\beta)\!</math> | ||
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This shows mathematically why the inclination must be greater than the launch latitude: Otherwise, the argument to the inverse sine function would be greater than 1, which is out of its domain. Therefore there is no solution in this case. | This shows mathematically why the inclination must be greater than the launch latitude: Otherwise, the argument to the inverse sine function would be greater than 1, which is out of its domain. Therefore there is no solution in this case. | ||
− | + | Also, note that frequently there are two solutions: one northbound and one southbound with launch windows one half day apart. There is only one solution if the inclination is precisely equal to the latitude, and that is the spin direction, or in Earth's case due east. There is only one solution if the inclination plus latitude exactly equals 180° (retrograde orbit), and that is the opposite of spin direction, or due west. | |
=== Example === | === Example === | ||
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[[Category:Tutorials]] | [[Category:Tutorials]] |