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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 (r, 9) of a comet satisfies an equation of the form r=ß+e(r cos 9), where ß is a constant and e is the eccentricity of the orbit, with 0≤e<1 for an ellipse, e = 1 for a parabola, and e> 1 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 9 = 4.1 (radians). 9 r 0.87 1.11 1.48 1.79 3.64 3.19 2.04 1.04 The comet has a hyperbolic orbit. When 9 = 4.1 (radians), the comet will be at r = (Round to two decimal places as needed.) 2.17 0.69

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 (r, 9) of a comet satisfies an equation of the form r=ß+e(r cos 9), where ß is a constant and e is the eccentricity of the orbit, with 0≤e<1 for an ellipse, e = 1 for a parabola, and e> 1 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 9 = 4.1 (radians). 9 r 0.87 1.11 1.48 1.79 3.64 3.19 2.04 1.04 The comet has a hyperbolic orbit. When 9 = 4.1 (radians), the comet will be at r = (Round to two decimal places as needed.) 2.17 0.69

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.6: Polar Equations Of Conics
Problem 40E
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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 (r, 9) of a comet satisfies an equation of the form = ß+e(r• cos 9), where ß is a constant and e is the eccentricity of the orbit, with 0≤e < 1 for an ellipse, e = 1 for a parabola, and e> 1 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 9 = 4.1 (radians). r= d r 0.87 1.11 1.48 1.79 3.64 3.19 2.04 1.04 The comet has a hyperbolic orbit. When 9 = 4.1 (radians), the comet will be at r = (Round to two decimal places as needed.) 2.17 0.69
Transcribed Image Text: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 (r, 9) of a comet satisfies an equation of the form = ß+e(r• cos 9), where ß is a constant and e is the eccentricity of the orbit, with 0≤e < 1 for an ellipse, e = 1 for a parabola, and e> 1 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 9 = 4.1 (radians). r= d r 0.87 1.11 1.48 1.79 3.64 3.19 2.04 1.04 The comet has a hyperbolic orbit. When 9 = 4.1 (radians), the comet will be at r = (Round to two decimal places as needed.) 2.17 0.69
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