We begin by observing that we may draw parametric curves as follows:

ParametricPlot[{Cos[12*t]+5Cos[t],Sin[12*t]+5*Sin[t]},{t,0,2*Pi}]

Assume that Earth is 1 astronomical unit from the sun and that Jupiter is 5 astronomical units from the sun.

 If it takes about 12 years for Jupiter to orbit the sun, animate a discription of Jupiter’s orbit with respect to the Earth.
 The solution is given below.

Animate[ParametricPlot[{Cos[12*t]+5Cos[t],Sin[12*t]+5*Sin[t]},{t,0,s},PlotRange->6],{s,0,2*Pi},AnimationRate->0.1]

Assume that Earth is 1 astronomical unit from the sun and that Saturn is 10 astronomical units from the sun.

 If it takes about 30 years for Saturn to orbit the sun, animate a discription of Saturn’s orbit with respect to the Earth.
 
 Start by coping the above Parametric plot inside the brackets.  Make sure that it works and then edit the code to obtain an animation for Saturn.

Animate[]

Find the corresponding values for the planet Mars using Wolfram Alpha  and animate the orbit wrt Earth using 2 significant digit values.  Let s goe from 0 to 12*Pi

Animate[]

The values for Venus are  disance from sun =0.72 au and 224/365=0.61, and so we have

Animate[ParametricPlot[{Cos[0.61*t]+0.72*Cos[t],Sin[0.61*t]+0.72*Sin[t]},{t,0,s},PlotRange->2],{s,0,36*Pi},AnimationRate->0.1]

Determine the values for Mercury and animate the orbit wrt to Earth.

Animate[]