Typically, asteroids are too small to have their own satellites. The gravitational force exerted by an asteroid is too minor to hold on to any object larger than a boulder if that object passes close by. The object are moving faster than the escape velocity of the asteroid. However, there are exceptions. The prime example is the dual system of Ida and Dactyl.
243 Ida was the 243rd asteroid discovered in the Asteroid Belt. It was originally discovered by Austrian astronomer Johann Palisa in 1884. Based on the spectroscopy, Ida is an S-type asteroid with an albedo of 0.2383. It has a semi-major axis of 2.862 AU, taking 4.84 Earth years to orbit the Sun. It has an average diameter 31.4 km across which is kinda weird to use since it is longer than it is wide.
In 1993, the space probe Galileo visited Ida on its way to explore Jupiter. It was in this visit where Dactyl was discovered. Dactyl is only 1/20th the size of Ida, only about 1.4 km in diameter. It is difficult to determine Dactyl's orbital characteristics without much more observation, but because it is so small in relation to Ida, to determine how it orbits Ida, Dactyl and Ida will have to be visited. Constraints to its orbit did allow a density to be roughly detemined and Dactyl is lacking metallic minerals. Ida and Dactyl share similar characteristics, so it is possible that they formed at the same time.
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