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, 8) of a comet satisfies an equation of the form r=B+ e(r• cos 8), where B is a constant and e is the eccentricity of the orbit, with 0se<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 8 = 4.2 (radians). 8 0.86 1.14 1.42 1.72 2.16 2.92 2.31 1.72 1.81 0.93 The comet has an elliptic orbit. When 8 = 4.2 (radians), the comet will be at r= (Round to two decimal places as needed.)
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, 8) of a comet satisfies an equation of the form r=B+ e(r• cos 8), where B is a constant and e is the eccentricity of the orbit, with 0se<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 8 = 4.2 (radians). 8 0.86 1.14 1.42 1.72 2.16 2.92 2.31 1.72 1.81 0.93 The comet has an elliptic orbit. When 8 = 4.2 (radians), the comet will be at r= (Round to two decimal places as needed.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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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= B+ e(r• cos 9), where B is a constant and e is the eccentricity of the orbit, with 0se <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 = 4.2 (radians).
0.86
1.14
1.42
1.72
2.16
r
2.92
2.31
1.72
1.81
0.93
The comet has
an elliptic orbit.
When 9 = 4.2 (radians), the comet will be at r=
(Round to two decimal places as needed.)
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