Two space colonies of equal mass orbit a star (Figure). The Yangs in m₁ move in a circular orbit of radius 10¹¹ m with a period of 2 y. The Yins in m₂ move in an elliptical orbit with a closest distance r₁ = 10¹¹ m and a farthest distance r₂ = 1.8 x 10¹¹ m.

(a) Using the fact that the mean radius of an elliptical orbit is the length of the semimajor axis, find the length of the Yin year.

(b) What is the mass of the star?

(c) Which colony moves faster at point P in Figure?

(d) Which colony has the greater total energy?

(e) How does the speed of the Y ins at point P compare with their speed at point A?

Transcribed Image Text:

Star P.