why are parabolas used in satellite dishes?
338606
First off, what are the mechanics of your basic parabola?\nEvery parabola has several main parts:\n\n1. The vertex - essentially the point at the which the "curves" of the parabola begin\n2. The focus - the point (often seen as the satellite trans-miter) that all the waves the bounce off the satellite dish come into contact with\n3. The directrix - the line that is equidistant from the parabola as the vertex\n4. The focal diameter - the distance from the focus to the directrix\n5. The lattis rectum - the distance across from one side of the satellite to the other\n6. "P" - the distance from the focus to the vertex or the directrix to the vertex, the focal diameter is 2p  and the lattis rectum is 4p\n\nThe main reason is the nature of the parabolas. Satellites in space can see signals down to satellite dishes on Earth. No matter where on the inner dish the signals hit, they will always bounce off and come into contact with the focus (the trans-miter). The parabola is the most efficient design in accomplishing the goal of a satellite dish.
29646
The blocks are called "digitizing".  Thats caused by an almost low enough signal to lose it all together.  It can be caused by the dish not being pointed properly, bad fittings or wiring, or something in the way between your dish and the satellite in space.  You need to try aiming it better before anything else and get your signal strength into the 90's.  you won't get 100 on most transponders so don't go nuts trying to.  If you cannot raise the signal strength the problem is in the wiring or some piece of equipment is going bad.\n\nRight now try the cable that goes to "Satellite In" on the back of your receiver, that could also be loose. Should be finger tight and nothing inside the fitting such as wire mesh from the cable or lint.
265330
You asked for the general equation of a parabola, not the general equation of a parabola that is a function of x or y, so the following is the most general form you will encounter, with the parabola opening in any direction you choose.\nThe definition of a parabola is the set of all points that are equidistant from a point (called the focus) and a line not passing through the focus (the directrix; it determines the direction the parabola opens).\nThus, let the focus be the point (f, g) and let the directrix be the line ax + by + c = 0 when the parabola is imbedded in a Cartesian coordinate system. Then, using the distance formula and the application thereof in the source link http://mathworld.wolfram.com/Point-LineDistance2-Dimensional.html , we want the set of all (x,y) satisfying (f-x)^2 + (g-y)^2 = (ax + by + c)^2/(a^2 + b^2) . We have squared both sides to remove the square root and absolute value operations. After multiplying everything out, we get the standard equation Ax^2 + By^2 + Cxy + Dx + Ey + F = 0 where the capital letters are simple functions of f, g, a, b, and c that you can make explicit by simplifying the above expression. While it is a derivation, it does not yet say what each coefficient does to the usual parabola. For that explanation, we use linear algebra.\nConsider the simple parabola y=x^2 with vertex on the origin. It has parametric form (x,y) = (t, t^2). All the parabolas above are simply rotations, linear scalings, and translations of this parabola. A rotation by a is given by the matrix [cos(a), sin(a); -sin(a) cos(a)] and a scaling of r in x and s in y is given by [r, 0; 0, s]. A translation to the vertex (h,k) is given by simply adding (h,k) to the parametric form.\nThus, a standard parabola that has been rotated by angle t, scaled in x by r, scaled in y by s, and has had its vertex translated to (h,k) has the parametric equation \n(x,y) = [cos(a), sin(a); -sin(a), cos(a)][r, 0; 0,s](t + h, t^2 + k).\nBy inverting the matrix, we get:\n(t+h, t^2+k) = [1/r, 0; 0, 1/s][cos(a), -sin(a); sin(a), cos(a)](x,y).\nAfter a bit of tedious algebraic manipulation, and substituting the expression for t into t^2, we get the standard equation that we derived before except now we know that A = (cos(a)/r)^2, B = (sin(a)/r)^2, C = -sin(2a)/r^2, D = -(sin(a)/s + 2*h*cos(a)/r), E = 2*h*sin(a)/r - cos(a)/s, and F = h^2 + k.\nUsing the above, you can find the properties of any given parabola, or create a parabola with the properties you want.
719360
It opens down because the coefficient of the x^2 term is negative.\nIf the parabola opens down, then the vertex will be a maximum.
531807
If the satellite is designed for use in GEO, It would not be much use in any other orbit. That is because satellites in GEO are always in the same part of the sky as seen from the ground. Home TV broadcast satellites are in GEO, so you just have to point your dish antenna at the satellite when you install it and then fix it permanently it in place. To communicate with a satellite in any other orbit you have to have a computer controlled motorized antenna that follows the satellite as it moves across the sky. And the moving satellite will rise and set, like the sun, and be impossible to communicate with it when it is below the horizon, because radio signals travel in strait lines and cannot go through the Earth. In very low orbits the satellite may be above the horizon at your city for only few minutes each week!
453979
They might be able to obtain some paralax measurements of the stars and/or planets as they move around the Earth in their orbit, so they could deduce that they were orbiting something, though they might not know just what it was.
649189
Because most satellites are geosychronous (ie. Follow the earths rotation) a satellite dish can receive and transmit signals just as a you can receive satellite TV. This information is (should be at least) encrypted or scrambled so that only the person/organisation with the key or password can communicate with the satellite. The US have however failed to use this in the past several times and military satellite signals have been known to be able to be received by ordinary citizens given they point their dish in the right position.\n\nFor satellites that are not geosynchronous, ie. imaging satellites that work in a vertical plane such as the ones used by NASA to take pictures of the earth and spy satellites. These satellites are not in constant contact with land - they store their information and then relay it back in the short period of time it is in contact with the base station on earth.\n\nSatellites such as ones that visit Mars and that do not orbit the Earth simply use a higher output signal and a higher gain to receive signals. A larger satellite dish is required to receive these signals, and like the imaging satellites, they are usually not always in contact with earth.\n\nCheers
105012
You can build all (or most of) the platonic and archimedaic solids using Origami.\n\nYou can also buid conic sections (hyperboles, parabola, ellypse and circle) by repeatedly folding a piece of paper along the tangents, point by point, using fundamental properties of each one. (= you get them as the envelope of their tangents).
921378
Projectiles without the presence of air pressure creates a parabolic trajectory (path taken by a projectile).\n\n^_^
954394
Newtonian reflectors are difficult to use for terrestrial observation because the image is inverted. Cassegrain-type reflectors (Schmidt-Cassegrain, Maksutov-Cassegrain, etc.) can be used with erecting prisms, or with a star diagonal if you're willing to put up with a mirror image view. The main problem with the Cassegranian reflectors is that their focal lengths are usually so long that you can't go lower than 40 or 50 power with them. Terrestrial spotting scopes are  most often used in the 20x to 40x range.
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I'm guessing that PV stands for Photo-Voltaic, so this would be a reflective magnifier for photovoltaic solar cells, to greate electricity from solar power.\n\nAny old satellite dish is parabolic, but that's a saucer cicle shape.  If you want a trough, you'll need to construct one by calculating a parabolic arc and getting reflective material in that shape.  Here's a funny article about someone who made a solar reflector, maybe it will help you:\n\nhttp://www.cockeyed.com/incredible/parabola/parabola.html
1008088
Extremely doubtful.  The best resolution for US spy satellites has been guessed to be about 2 inches, which is much larger than the numbers on a license plate.  Even if it could resolve that small, the viewing angle would make it difficult to see the plate.\n\nAnyway, spy satellites circle the Earth at altitudes of about 150-200 miles, they aren't in geostationary orbit, which is around 22,000 miles.  At that distance, they'd be lucky to distinguish large buildings.\n\nEdit: A Guy, the GPS satellites are not in geostationary orbit.  They orbit at around 12,000 miles, which is about half geostationary distance.  The orbits are designed such that there are almost always 4 satellites in view from any point on the surface, since you need 4 for complete 3-D positioning.\n\nGeostationary orbit is used mostly for communications satellites, and some large-area weather overview satellites.  We do have some military satellites up there that watch for missile launches and any other large heat events, because they can be seen from that distance.  At that height, they can cover a good chunk of a hemisphere.\n\nHaysoos, stop being so paranoid.  They can't read your paper.
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Most modern satellites have similar basic parts and most have extra parts for their special needs. They have generally three basic parts. They are a radar system which is used to measure the height from the earths surface, receivers and transmitters to receive and send out signals, usually radio or micro waves, they also have small altitude control nozzles that squirt out puffs of gas to tilt the satellite to change it’s altitude or direction. These are also known as thrusters or sometimes ‘puffers'. Most satellites have special equipment for their special needs. For example Research satellites may have telescopes and antennae that they point into space to receive rays from deep in space, Survsat (survey satellites) have telescopes, cameras and other sensors to view the earth’s surface and Comsat (communications satellites) have various antennae and thousands of transponders (automatic devices used to receive and send radio signals) each one dealing with a radio or telephone signal, or dealing with part of a Television channel. All of the equipment is built by electronics experts and aerospace engineers who give satellite makers a range that they can choose from. Some satellite makers sell their satellites commercially and their satellites can cost you in excess of US$15million and can take up to two years to build. Custom satellites can also be made for individual needs but these can take double the time and can cost up to five times as much. It can be seen that the satellite business is a very costly one.\n\nSatellites electronics have to be powered and are usually sone so with the help of the sun. Satellites have large panels, which fold out and contain many solar cells. Although this is the case for half of the satellites orbit it is in total darkness and therefore it needs to have a battery to power it, which most satellites do. These batteries as recharged by the solar panels and then continue to power the satellite during the time of darkness.
710254
I think the St. Louis Arch is a partial parabola. Or how about a satellite dish?\n\nHere's another interesting phenomenon. Some museums set up devices that look like satellite dishes so you can try out a similar effect:\n\nWhispering Gallery in NYC\nTalk into one corner of this room and your friend in the other corner will hear it.\nSounds do interesting things in round shapes, parabolas will bounce sound from a large area into one spot, or from that one spot to a large area and are used extensively in theaters. Another interesting phonomenon is a Whisper Gallery where you can stand along one wall and sound bounces along the sphere, travelling straight and then bouncing off the wall until it hits the wall again, continuing around the inner surface of the circle.\n\nWell, I just learned that there's one in Grand Central Station.\n\nIn the arched hallway outside the entrance, check out the engineering magic of the "whispering corners." When you and a companion stand in opposite corners and whisper, you can hear each other as well as if you were standing a foot apart.\n - http://www.newyorkmetro.com/pages/details/4218.htm
433311
I really like the parabola, but the ellipse is pretty cool too.
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It's a parabola. I believe the astronomer Roger Angell proposed a parabolic reflector using mercury in a spinning container. The paraboloid is the natural equilibrium shape of minimum potential energy. The liquid assumes a level consistent with the local acceleration, which is the sum of gravity and radial acceleration given by w^2*r, where w is the rotational rate in rad/sec and r is the radius. The resulting paraboloid surface is perpendicular to the acceleration at all points.
582411
2 paralel lines that are not perpendicular to the object they measure