In the book "Feynman's Lost Lecture" David Goodstein and Judith Goodstein tell the story of a lecture prepared and delivered
by Richard Feynman. They were able to rescue the audio and notes, so we can follow the math and logic to demonstrate that
planets orbit the Sun in elliptical orbits. This is a consequence of the inverse square law of gravitation.
The lecture used only geometry and the math known before calculus to show this.
Among the necessary concepts is the construction of an ellipse using its foci and the length of its major axis.
In the animation below, an ellipse is drawn using the procedure explained in the book.
Move the mouse to change the rays and click to change the length of the major axis.
One surprising thing to me is how far apart the foci are for narrow ellipses.
Try yourself clicking close to the left focus.