Abstract: The distance between Earth and Mars is vast. While a probe could theoretically fly along any arbitrary path, the fuel consumption varies dramatically among different routes. This paper introduces the most economical route connecting Earth and Mars — the Hohmann transfer orbit. Proposed by German physicist Walter Hohmann in 1925, this orbit requires only two engine burns, with the probe coasting inertially with its engine off for the remainder of the journey, to transfer from Earth's orbit to Mars' orbit. It stands as the most classic energy-optimal path in deep space exploration. Starting from Newtonian mechanics and Kepler's laws, this paper demonstrates the calculation of the geometric parameters, velocity conditions, and launch windows of the Hohmann transfer orbit. The demonstration shows that for a seemingly simple elliptical orbit, the choice of its parameters is simultaneously constrained by geometry, energy, and time. Understanding the relationships among these constraints helps readers build a basic physical picture of interplanetary orbit design, and also provides a comprehensive case study closely tied to engineering practice for teaching Kepler's laws and energy conservation in mechanics courses.