IV. The Lord of the Rings

  A. Sedna is one of the largest (roughly 1500 km diameter) and most distant planetoids yet discovered in the outermost Solar System. Its perihelion distance is about 75 AU, while its aphelion distance is about 900 AU. It was discovered by a survey that (1) has a limiting R magnitude of about 22, and (2) surveyed a swath of sky +/- 10 degrees away from the ecliptic plane. It is likely that Sedna is but one member of a whole class of Sedna-like objects on Sedna-like orbits. These orbits might be isotropically distributed (that is, spherically symmetric) about the Sun. How many Sednas are there in all, based on the discovery of 1?

  B. How long does it take for a typical particle in the middle of Saturn's B ring to wander to the edge of the B ring? The ring particle wanders by a collisional random walk. The time that you compute is of order the time it takes for the ring to spread and double its radial width.

  C. Pluto/Kuiper Express is a spacecraft mission to the Pluto/Charon binary. After passing by the Pluto/Charon system, the spacecraft will travel out of the Solar System---it does not have enough fuel to brake itself. Hopes are that the spacecraft can encounter a Kuiper belt object (KBO). What is the probability that the spacecraft will find, by sheer chance, a large KBO and come close enough to take pictures of it with an angular resolution of, say, 1 kilometer?

Students in this group: (I: Cassy, Chris, Omair: Yes)