The theory supporting this applet is presented in the paper [i]Cassini Ovals in Harmonic Motion Orbits[/i], Journal of Geometry and Symmetry in Physics, JGSP 47 (2018) 1–9.The initial position [math]x_{0}[/math]is chosen on the horizontal axis and the initial velocity is a vector [math]\bar{v}_{0} =\; (v_{0} \cos \alpha ,\; \, v_{0} \sin \alpha )[/math], cutting angle [math]\alpha[/math]with the [math]x[/math]-axis. For fixed [math]x_{0}[/math]and [math] v_{0}[/math]we change the angle [math]\alpha[/math]from [math]0[/math]to [math]\pi[/math]in order to generate a family of ellipses. The enveloping curve for this family is also an ellipse (ellipse of safety) with center [math](0,0) [/math]and foci at [math](-x_{0} ,0)[/math]and [math](x_{0} ,0). [/math]Its axes are [math]a=\sqrt{\, x_{0}^{2} +\frac{v_{0}^{2} }{\omega ^{2} } }[/math]and [math] p=\frac{v_{0} }{\omega }[/math]. Very interesting is the locus of the foci of the changing ellipses (when [math]\alpha [/math]changes): this locus is a Cassini oval. When [math] x_{0} =v_{0}[/math]this oval is the Lemniscate of Bernoulli.[br]See an applet for [url=https://ggbm.at/eb3gTYnm]Rotating the Lemniscate of Bernoulli [/url]