Velocity Modification for Earth Capture of An Astronomical Body in the Solar System

In studying the possible capture of an astronomical body that is orbiting around the sun, two questions are encountered: How near must it approach the earth before it could be captured? How could we make it approach as near to the earth as required? This paper answers the first question by using the results of the restricted three-body problem, and partially answers the second question by estimating the order of magnitude of the velocity modification needed to change the orbit of the body and make capture possible.