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In: Advanced Math

According to​ Kepler's first​ law, a comet should have an​ elliptic, parabolic, or hyperbolic orbit​ (with...

According to​ Kepler's first​ law, a comet should have an​ elliptic, parabolic, or hyperbolic orbit​ (with gravitational attractions from the planets​ ignored). In suitable polar​ coordinates, the position left parenthesis r comma script theta right parenthesis of a comet satisfies an equation of the form r = betaplus​e(r*cosine script theta​), where beta is a constant and e is the eccentricity of the​ orbit, with 0less than or equals less than1 for an​ ellipse, e equals1 for a​ parabola, and e greater than1 for a hyperbola. Suppose observations of a newly discovered comet provide the data below. Determine the type of​ orbit, and predict where the comet will be when script theta equals 4.1 left parenthesis radians right parenthesis. script theta 0.88 1.14 1.48 1.72 2.17 r 3.68 3.08 2.08 1.06 0.54 The comet has either a. hyperbolic b parabolic c elliptic  orbit. When script thetaequals4.1 ​(radians), the comet will be at requals nothing.

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Colby Messinger answered 1 year ago
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