Needing to find the X(t) and Y(t) in the equation. This involves Calculus and the hint was Recall the parametric representation of the unit circle as (cost,sin

Question

While a planet P rotates in a circle about its sun, a moon M rotates in a circle about the planet, and both motions are counterclockwise in the same plane. Let's call the distance between M and P one lunar unit. Suppose the distance of P from the sun is 9.8×103 lunar units; the planet makes one revolution about the sun every 4 years, and the moon makes one rotation about the planet every 1/3 years. Choose coordinates centered at the sun, so that, at time t=0 the planet is at (9.8×103,0), and the moon is at (9.8×103,1). With these choices, the location of the moon at time t, where t is measured in years, is (x(t),y(t)).

Answer 1

The location of the moon (WRT the sun) is the vector sum of the position vectors of the planet WRT the sun (r_sp) plus the moon WRT the planet (r_pm).

r_sp=<Rcos(ω_pt),Rsin(ω_pt)> and r_pm=<rcos(ω_mt),rsin(ω_mt)>

so R_sm=<Rcos(ω_pt)+rcos(ω_mt),Rsin(ω_pt)+rsin(ω_mt)>

R=9.8kLU, r=1LU  and  ω_p=2π/(4yr), ω_m=2π/(1/3)yr