Sir Isaac Newton first described how any two objects, no matter what size or how far apart they are from each other, exert an attractive force upon one another. Since gravity is, relatively, a very weak force (compared to electricity and magnetism, with which we have familiar experiences), we don't recognize that tables, baseballs, buildings, and even people all gravitationally attract each other. These forces are fantastically small, but it is interesting to note that the gravitational attraction between a parent holding a child is stronger than that of any one of the planets (except Earth!) on that child. In other words, even an object with little mass can exert a greater force than another much more massive object, if the smaller object is much closer than the larger one. In mathematical terms, the force of gravity falls off as the inverse of the distance squared. So, if the distance between two objects is doubled, the attractive force is one-quarter the value.
Similarly, Ida and its moon attract each other. Because they are far from other bodies compared to their mutual separation, they influence each other very strongly. Any two bodies under the right circumstances will orbit each other, even if they also orbit about a third body, such as the Sun. (The Sun, of course, is in orbit about the Galaxy, which in turn is in orbit about other galaxies, and so on.) Bodies actually orbit about their mutual center of mass, called the barycenter, which is located along a line connecting their centers, and at a distance from either center inversely proportional to the mass of that object. Calculations have shown that asteroids like Ida can have satellites in stable orbits out to about 100 to 200 times their radius, so Ida could have satellites out to several thousand kilometers. However, only the one moon, 1993 (243) 1, has been seen as yet.
Any two objects, even if small and distant, will orbit one another if they are far from other objects.
If a planet or asteroid is orbiting the Sun, the planet or asteroid can have a satellite if the satellite is close enough that the planet's or asteroid's gravity influences it more than the Sun's gravity.
-- Jan Ludwinski, Mission Design Team Chief
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