(Part a) Consider the double asteroid system Diomorphos and Didymos, which undergoes uniform circular motion about the center of mass of the system such that the asteroids are always a fixed distance s = 1180 m apart (rotating counterclockwise in the figure, which exaggerates the relative radii of each circular orbit). The mass of Diomorphos is m = 4.84 × 10^3 kg. The mass of Didymos is m = 5.23 × 10^1 kg.
What is the period T of the orbit?
Express your answer in units of hr.
T
What is the speed of Diomorphos about the center of mass?
Express your answer in units of m/s.
m/s
(Part b) The DART spacecraft of mass m = 570 kg crashed head-on with Diomorphos. The velocity of DART before the collision was v = 6.310 m/s.
What is the speed of Diomorphos and DART after the collision? For the moment, assume the collision was completely inelastic.
Express your answer in m/s.
m/s