We describe a method that could have been used by Kepler to determine the shape and dimensions of Mars’ orbit around the Sun, starting from observations of its path across the night sky. Though we use Kepler’s work as a motivation, our approach does not intend to suggest that this method was actually used by him. Rather, it is only intended to show beginning undergraduate students what may be discovered about the planets using basic observational data together with simple geometric methods. We employ publicly available Harvard sky patrol (HSP) photographs of Mars at different moments in the Earth’s year to get its ecliptic coordinates, locate them on a Sun-centered coordinate system, and finally plot them on a sheet of paper. From this orbital graph, we obtain the shape and dimensions of Mars’ orbit around the Sun, using the radius of the Earth’s orbit to set the scale. By generalizing this orbital shape to the other planets in the Solar System, students may be led to conclude Kepler’s first and second laws. Other features of the scaled-down Martian orbit may be directly measured from the paper orbit. To obtain the actual values for such features, we only need to scale them up. The quantities thus determined agree well (within a surprising 5%) with those reported by NASA.