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3. Earth's orbit. The Earth, with mass m and angular momentum L, moves around the Sun in arn elli...

3. Earths orbit. The Earth, with mass m and angular momentum L, moves around the Sun in arn elliptic orbit of eccentricity e


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3. Earth's orbit. The Earth, with mass m and angular momentum L, moves around the Sun in arn elliptic orbit of eccentricity e. The equation of trajectory is given by, r=p1+ecoso 1+e where p is the distance of the closest approach to the Sun (perihelion) (a) Find the two components of the velocity as functions ofQie, v,(9) and vo(9). (8 marks) (b) Prove that the angle α between the velocity v and displacement r of the Earth is described by, esin 1+e2 + 2e cos θ cos α = (8 marks)
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3) ma 树 cl ol t (ft b) Itcroso teloso

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