# The flight from ambiguity essays in social and cultural theory

In planning certain types of trajectories of spacecraft within the solar system, engineers rely on a technique called gravitational assist (also gravity assist, slingshot, or swing-by). This technique underlies the feasibility of effecting a net change in both the speed and direction of motion of a spacecraft by passage through the gravitational field of a planet or a planetary satellite, typically in order to save propellant, time, and expense. A gravitational assist around a planet changes a spacecraft's velocity relative to the Sun by entering and leaving the gravitational field of a planet. The spacecraft accelerates as it approaches the planet and decelerates while escaping its gravitational pull. Because the planet orbits the Sun, this motion affects the spacecraft during the maneuver. To accelerate, the spacecraft flies across the trailing side of the planet, taking a small amount of the planet's orbital energy (as pictured in Figure ). To decelerate, the spacecraft flies across the leading side of the planet. The sum of the kinetic energies of both bodies remains constant. A gravitational assist can therefore be used to change the spaceship's trajectory and speed relative to the Sun. The resulting increase, or decrease, in the kinetic energy of the spacecraft appears to contradict the casual expectation that in such an encounter the kinetic energy of the spacecraft after the encounter would be the same as that before the encounter. However, the energy gained by the spaceship is equal in magnitude to that lost by the planet, though the planet's enormous mass compared to the spacecraft makes the resulting change in its speed negligibly small. These effects on the planet are so slight that they can be ignored in the calculation. Figure shows the motion of a spacecraft relative to a planet during a gravity assist maneuver. Encounters in space require the consideration of three dimensions; however, an approximate solution to the gravitational assist problem can be found using a simplified two-dimensional model. The following conditions are assumed:

• Orbits of planet and spacecraft are coplanar.
• Y-axis is parallel to the planet's position vector, positive outward from Sun.
• X-axis is in the orbital plane normal to the Y-axis, positive in the prograde direction.
• Planet's velocity (V p ) and flight path angle ( p ) are given.
• Spacecraft's initial velocity (V s i ), flight path angle ( s i ), and miss distance (d) are given.
The planet's velocity vector and the spacecraft's initial velocity vector are solved for using,

Seventeen months before the Bashkirian Airlines-DHL collision there had already been another incident involving confusion between conflicting TCAS and ATC commands. In 2001 two Japanese airliners nearly collided with each other in Japanese skies. One of the aircraft had received conflicting orders from the TCAS and ATC; one pilot followed the instructions of the TCAS while the other did not. A collision was only averted because one of the pilots made evasive maneuvers based on a visual judgement. The aircraft missed each other by about 135 metres (443 ft), and the abrupt maneuver necessary to avert disaster left 100 occupants injured on one aircraft, some seriously. [29] (pp2,176,134,22) In its report, published eleven days after the Überlingen accident, Japan called on the International Civil Aviation Organization (ICAO) to make it clear that TCAS advisories should always take precedence over ATC instructions. ICAO accepted this recommendation and amended its regulations in November 2003. [30]