CALCULUS,EARLY TRANSCENDENTALS-ACCESS
9th Edition
ISBN: 9780357128947
Author: Stewart
Publisher: CENGAGE L
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In 1992,a NASA team began a project called Spaceguard Survey, calling for an international watch for comets that might collide with Earth. Why is it more difficult to detect a possible “doomsday comet” with a hyperbolic orbit than one with an elliptical orbit?
The distance from the planet Pluto to the sun is $4.43 \times 10^{9} km$ at perihelion and $7.37 \times 10^{9} km$ at aphelion. Use Exercise 24 to find the eccentricity of Pluto's orbit.
In a distance star system a planet is 9 AU (astronomical unit) away from the sun, and has a circular orbit with period 12 earth years. The planet has a moon distanced 0.5 AU away, which circles the planet in a circular orbit also with period 12 earth years. Suppose the orbital planes of the planet around the sun and the moon around the planet coincide, and their motions are both counterclockwise. At midnight March 1 2021, the positions of the sun, planet, and moon are observed to be (0, 0), (9, 0), (9, 0.5) on their common orbital plane.
(a) Determine the position (xP (t), yP (t)) of the planet, t years after midnight March 1 2021.
(b) Determine the position (xM (t), yM (t)) of the moon, t years after midnight March 1 2021. Express your
answer in the form
xM (t) = A cos(kt + α) + xP (t) yM (t) = A sin(kt + α) + yP (t)
where A,k > 0 and α ∈ (−π,π].
(c) Simplify your expressions for xM (t) and yM (t) to the form
xM (t) = B cos(kt + β) yM (t) = C sin(kt + γ)
where B, C, k >…
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