(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 > 0 and β, γ ∈ (−π, π],
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
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(a) Determine the position (xP (t), yP (t)) of the planet, t years after midnight March 1 2021.
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(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].
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(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 > 0 and β, γ ∈ (−π, π], leave your answers in exact form.
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