 
Summary: Problem Set 1 (due 17th September)
(1) A planet of radius Rp orbits a star of radius R in a circular orbit at radius a. If
the orbit plane is randomly distributed relative to the observer's line of sight, show
that the probability that transits will be observed is,
ptrans =
R + Rp
a
.
If the orbital period of the planet is P, show that for a system viewed at an incli
nation angle i the duration of the transit is,
ttrans
P
R
a
2
 cos2 i.
[Note that i = 90
corresponds to a perfectly edgeon system.]
(2) Suppose that the planet, of mass Mp, orbital radius ap, and orbital period P, is
