For these problems, you will need to get information from the book's appendices, A (inside from cover), B (inside back cover), and C (page A-1).  You should get used to using these appendices if you need information that is not given in the problem.

Prob. 1: (a) From the information in the lecture and example 2.2.2 of the text, calculate the acceleration of gravity due to the Earth, at the height (405 km) of the orbit of the International Space Station (ISS). (b) What velocity must ISS have in order to remain in a circular orbit? [Hint: Be careful with height--the distance from the center of the Earth to height h is R_earth + h.]

Prob. 2: We noted in the lecture that in Kepler's third law, P² = ka³, k = 1 when the units of time are years, and distance is in AU.  (a) Show this directly by calculating k = 4pi²/GM in those units. (b) Calculate the value of k, in the same year and AU units, that would apply in the case of one of Jupiter's moons in orbit around Jupiter.  According to appendix C, Jupiter's mass is 317.83 earth masses, where M_Earth = 5.9736x10²⁴ kg.