(6) Consider a comet that moves in an elliptical orbit around the Sun located at
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(6) Consider a comet that moves in an elliptical orbit around the Sun located at an ellipse focus. In the following give your answers in terms of the eccentricity, e, the semi-major axis, a, a momentum per unit mass, L/m. (a) What is the condition for the existence of a radial turning point in the comet's motion'? b) Show that the comet has two turning points. What are the plane polar coordinates (r, ) of the turning points as measured from the Sun's location? (c) What are the plane polar coordinates of the position in the comet's orbit that coincides with semi-minor axis, b, as measured in a Cartesian coordinate system? (d) the What is the comet's speed when it is at the point in the orbit computed in part (b)?Explanation / Answer
a) As governed by the laws of relative motion in the celestial mechanics, when one body is in motion relative to another. For bound orbits, in a spherical potential, when the apocenter distance is closer to the pericenter distance, the orbit will have low eccentricity.
Like all bodies orbiting the Sun, closer the comet is to the Sun, faster it moves.The condition of a radial turning point in the comet's motion is to have Radial Velocity of Zero. At the turning point, the Angular Velocity component is maximum.
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