The first death star was 160 KM in diameter, so a radius of 80 KM. If you assume the same mass density as, say, an aircraft carrier or other military vessel (about 0.15 kg/m^3), you end up with a Death Star that masses about 3e14 KG. That's absurdly heavy to realistically have engines zipping it about, but it's not going to result in major and instantaneous disruptions of orbits. Even Mars' tiny moon Phobos has 100 times the mass. Although the Death Star II from RotJ was supposed to be 900KM across, so that would put it about even with the mass of Phobos. Put another way, the Earth masses 10,000,000,000 times as much (or only 100,000,000 for the Death Star II), so I don't see how the Death Star is going to be winning that gravitational tug-of-war. If you want to argue "Well maybe they have super cool tractor beams so they can amplify their gravitational pull and their massive engines can keep them stationary while they're doing it!" the obvious counter is "They don't, that's why they went with the laser, since they thought about it. Also big laser is more menacing in a platform which has the primary purpose of intimidation. Additionally the big laser doubles as a way to destroy enemy capital ships from well outside their own engagement radius".
Source: http://rss.slashdot.org/~r/Slashdot/slashdotScience/~3/lrTk3jlaqkM/is-pluto-a-binary-planet
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