Recently Asteroid Apophis was in the news when it passed by in January (it passes about once every 11 months). There is a near miss scheduled for April of 2029 when it will pass well within the moon’s orbit and even closer than some geosynchronous satellites. I’m not particularly worried about that, although it should be an interesting nighttime view object. Apophis’s mass is estimated to be about 1/10^14 of Earth’s so although it will definitely change course due to gravitational interaction from Earth, its own effect on Earth will probably not be detectable (?). My question is–how large a body would it take, passing by inside the moon’s orbit, to detectably affect Earth’s rotation and/or orbit? (and therefore our climate–think ice ages and precession). Back when I was in college physics I probably could have calculated this, but that was 50 years ago…anybody got a rough number?
I don’t know what the limit of detectability is using the most sensitive instruments we can make, but to be noticable (as in climate effects) it would have to be Really Damn Big. Possibly bigger than Ceres. (But according to this nice model–uh, this Nice Model–even small objects can move gas giants, given enough of them and enough time.)