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 = 4.4 (radians). 9 r 0.87 1.08 1.45 1.77 2.12 3.56 3.03 1.97 1.03 0.65 The comet has orbit. When 9 = 4.4 (radians), the comet will be at r = (Round to two decimal places as needed.)

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 39E
Question
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 = 4.4 (radians).
90.87
3.56
r
The comet has
1.08 1.45 1.77 2.12
3.03 1.97 1.03 0.65
orbit.
When 9 = 4.4 (radians), the comet will be at r =
(Round to two decimal places as needed.)
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 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 = 4.4 (radians). 90.87 3.56 r The comet has 1.08 1.45 1.77 2.12 3.03 1.97 1.03 0.65 orbit. When 9 = 4.4 (radians), the comet will be at r = (Round to two decimal places as needed.)
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