|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)