Answer Happy

3. We approximate the trajectory of Halley's comet around the sun by an ellipse, with distance to the sun in the perihelion (the point of the ellipse closest to the sun) equal to r_=0.586 AU and distance to the sun in the aphelion (the point of the ellipse farthest away from the sun) equal to r+ = 35.1 AU. An Astronomical Unit (AU) is approximately 150x10m, which is roughly equal to the distance between the earth and the sun. The general equation of the ellipse is given by: r(0) То 1 - e cos (a) Determine the eccentricity e and the distance ro for the trajectory of Halley's comet. (b) Assume that: i. the orbit of the earth is a circle (€carth = 0). ii. the mass of the sun mg is much larger than the mass of Halley's comet my and the mass of the earth me, iii. and that the answer is ro = 1 AU for part a). = Express the speeds of Halley's comet in the perihelion and the aphelion, in terms of the speed ve of the earth and €. (c) With the same assumptions as above, express the ratio of the periods of revo- lution around the sun of Halley's comet Ty and the earth T. in terms of €.