What to try
1. Kick with the Mars preset, then switch the world to Earth: same boot, much shorter flight. 2. Add sidespin and watch the plan view curve (stronger on Earth, where the air is 60 times denser). 3. In the range graph find the best angle: exactly 45° in vacuum, lower with air drag. 4. Choose the Moon: no air, no curve, a perfect parabola.
The science
Equation of motion. m dv/dt = m g + F_drag + F_Magnus with F_drag = -½ ρ C_d A |v| v (C_d = 0.25) and a Magnus force perpendicular to v and the spin axis, F_M = ½ ρ A C_L |v|², C_L = min(1.2 ωr/|v|, 0.32) (a simple saturating model, not a measured ball curve). Ball: 0.43 kg, radius 0.22 m. Gravity 3.721 m/s² on Mars, 9.807 on Earth, 1.62 on the Moon; Mars surface air density about 0.020 kg/m³ versus 1.225 on Earth.
Vacuum limit. Without air: range R = v² sin(2θ)/g, apex H = v² sin²θ / (2g), flight time T = 2 v sinθ / g. Range scales as 1/g, so the same kick goes about 2.6 times farther at Mars gravity.
Simplifications. Flat ground, constant air density, no wind, no bounce or roll, constant spin rate, a one-parameter lift model. Integrated with fourth-order Runge-Kutta; the 3D page uses a simpler fixed step and agrees within a few percent.