S Re Vo ro E Figure 1: Diagram of the comet's trajectory with the positions rj, j = 0,...,4. 4. A comet with mass m move

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S Re Vo Ro E Figure 1 Diagram Of The Comet S Trajectory With The Positions Rj J 0 4 4 A Comet With Mass M Move 1 (43.37 KiB) Viewed 16 times

S Re Vo ro E Figure 1: Diagram of the comet's trajectory with the positions rj, j = 0,...,4. 4. A comet with mass m moves under the gravitational attraction of the sun, -(GM,m/r²). The comet can be observed from the Earth, which we assume to have a fixed position at distance R. from the centre of the Sun. See the diagram. The turning point of the comet (r₂ in the diagram), the centre of the Sun, and the centre of the Earth, all lie on the x-axis. (a) The trajectory of the comet is a parabola, which can be written explicitly as y²-2Rox = R₂. Let 0= arctan(y/x). Derive that the distance r(0) from the centre of the Sun can be expressed as Ro r(0) 1 - cos (0) (b) Determine the speed of the comet at ro and r2, and the magnitude of the angular momentum . (c) Recall Kepler's second law: dA dt. 2m Determine the time intervals T₁3 between the comet passing r₁ and 13, and To between the comet passing ro and r₁, in terms of Ro. R. and GM₂.