Suppose we assume orbits of earth and venus to be circular. Assume the radius of earth orbit as 1AU and that of venus as 0.75 AU. It takes 360 days for earth to complete its orbit and venus takes 225 days to complete this orbit.
How would you derive the parametric equations of :
1) orbit of venus as viewed from sun
2) orbit of earth as viewed from sun
3) orbit of venus as viewed from earth
For 1 and 2 will it be a circle? And what will happen for 3?
I also need to plot these orbits in geogebra. If i take parametric equations $r\cos(\theta)$ and $r\sin(\theta)$ for circular orbits, how should I go about? Should I also take into account the change of $\theta$ w.r.t time?
You want an expression like \begin{align*} x(t) &= r \cos(2 \pi t / T) \\ y(t)& = r \sin(2 \pi t / T) \end{align*} where $T$ is the period of the orbit and $r$ is the radius.