As a result of a malfunction of the spacecraft’s control system, the thrust directions of its three engines changed.

As a result of a malfunction of the spacecraft’s control system, the thrust directions of its three engines changed. The thrust of the first engine called “Cygnus” turned out to be directed to the constellation Cygnus, the thrust of the second one, called “Cancer”, to the constellation Cancer. Where is the thrust of the third engine called “Pike” directed if the total thrust is zero, and the total work of the engines, as in Krylov’s fable, is completely useless? The powers of all three motors are equal.

In the problem statement, it is said that the powers of the three engines are equal, and their total action vanishes. This can be the case if the thrust vectors of the three engines are in the same plane at an angle of 120 ° to each other. Just at this angular distance from each other are the centers of the constellations Cygnus and Cancer, their approximate coordinates are a = 20h40m, 5 = + 40 ° and a = 8h40m, 5 = + 20 °, respectively. In addition, these two points are located on the same declination circle, which greatly simplifies the calculation of the coordinates of the third point to which the thrust of the Pike engine is directed. It is easy to see that the coordinates of this point are equal to a = 20h40m, 5 = -80 °, that is in the constellation Octantus, near the South Pole of the world.