Beta angle result of the beta angle of the space station at those times. When the orbiter was in-flight (not docked to ISS) and it flew to a beta angle greater than 60 degrees, the orbiter went into "rotisserie" mode, and slowly rotated around its X-axis (nose to tail axis). For flights to ISS, the shuttle could launch during an ISS beta cutout if the ISS would be at a beta less than 60 degrees at dock, and throughout the docked phase. Therefore, the mission duration affected launch timing when the beta cutout dates were approaching. Beta angle The beta angle (formula_1)
Angle of parallelism e where e is the base of the natural logarithm. Then the relation between "φ" and "a" can be deduced from the triangle {("x", 0), (0, 0), (0, "y")}, for example: Angle of parallelism In hyperbolic geometry, the angle of parallelism formula_1, is the angle at one vertex of a right hyperbolic triangle that has two asymptotic parallel sides. The angle depends on the segment length "a" between the right angle and the vertex of the angle of parallelism. Given a point off of a line, if we drop a perpendicular to the line from the point, then "a" is