Parabolic antenna

A satel­lite's orbit is called geosta­tionary if as the Earth turns, the satel­lite stays above the same point of our planet's surface. Such orbits are often used in posi­tioning and commu­ni­ca­tion systems.

he satel­lite you see on the picture is the symbol of the Russian space program. This is SOUZ-TM.

And this is how the begin­ning of the main Russian tele­vi­sion news program "Vremia" looked like some time ago.

In our movie we'll see how signal trans­duc­tion works, say, in modern satel­lite tele­vi­sion.

Draw a line and call it a direc­trix. Take a point that is not contained in it. The locus of points equidis­tant from the direc­trix and the given point (called a focus) is called a parabola.

If we direct a beam parallel to the parabola's symmetry axis they'll meet at it's focus. This is what one calls parabola's optical prop­erty.

The converse is also true. If we put a lamp in the focus, the rays reflected from the parabola will go in the same direc­tion and the light front will be a straight line.

Rotating a parabola around it's symmetry axis one gets a second-order surface of rota­tion — a parab­o­loid. As in any plane section passing trough the symmetry axis we get the same parabola, the optical prop­erty is preserved for parab­o­loids as well. If we place a lamp in the focus, the reflected rays will be parallel. The converse is also true.

Exactly this prop­erty is used in satel­lite para­bolic antennas. As satel­lites are too far from antennas, rays can be consid­ered as parallel and the receiver is placed in the focus of a parab­o­loid.

Other etudes in “Quadratic surfaces”