Can an Astronaut Orbit the Space Shuttle?
By Mike Luciuk I saw this question on the Internet. The professional astronomer replied that the answer is no, because the Earths gravitational field overwhelms the attraction between the astronaut and the shuttle. She mentioned that the shuttles Hill sphere was too small for orbiting to occur. Id never heard of the Hill sphere, so a few hours on Google were utilized to investigate this concept. We all know that the famous gravitational three-body problem has no explicit solution. Of course there are ways of solving it to any desired level of accuracy with computer techniques. In fact, the Hill sphere is often used as an analytic way of dealing with some aspects of this issue. The Hill sphere is named for the nineteenth century American celestial mechanics expert, G. H. Hill (1838 1914). He developed a formulation to approximate the gravitational sphere of influence of a minor body orbiting a major body i.e. the shuttle orbiting the Earth or the Earth orbiting the Sun: where rH is the
