Sputnik chandeliers don't belong to the Art Deco period, but they are an iconic part of American design. They belong in the period known as Mid-Century Modern. The name is derived from the first satellite launched into space in 1957 by the Soviet Union. That event ushered in the Space Race and a whole flurry of new design ideas.
Sputnik chandeliers are known by their very distinct arms. From a small ceiling fixture, a long arm drops down to hold a central element. From that central point, arms with lights at the end of them stick out in all directions. The size, materials, and symmetry of these pieces can vary quite a lot. Some have short arms and other are long. Metallic finishes are the rule but you can find many examples in bronze or silver. The arms radiating from a spherical center are reminiscent of the shape of the original Sputnik satellite.
For a person of the era, this design would have been seen as very futuristic, a further example of the celebration of progress that kicked off during the Art Deco period. These days, we may be more inclined to see them as simulating a starry night or as a figure of whimsy. There are modern variants such as the bubble chandelier, which uses strong symmetry and blown glass elements on the ends of the arms.
Unlike a lot of design from this period, sputnik chandeliers are unique enough that they don't seem kitschy or old-fashioned. It is important to choose the right size for the room though. A lamp that is out of proportion won't look good. Experiment by using foam balls and armature wire with clay on the tips to see how a piece might look in your room.
Here is an example of a sputnik chandelier. Note the large round center with the radiating arms. Some designs will only have a ring of lights parallel to the ceiling. This design has glass enclosures around the bulbs with chrome reflectors. The light from a sputnik chandelier can be quite unpredictable, but most are very bright!
Lest you think that this was only used in homes, here is an example of a sputnik chandelier used at the Metropolitan Opera House in New York. It is a gigantic piece with many different armature elements but still retaining the classic sputnik design. If you are ever at the Met, a good seat in the cheap section could net you a chance to study these chandeliers in detail.