About

This is not a simple parabola plotter. This is a numerical integration engine that solves the equations of motion accounting for aerodynamic drag, which varies dynamically with altitude. On Earth, air density decreases exponentially as you ascend (Barometric Formula), meaning a projectile experiences less drag at the top of its arc than at sea level. This simulator models that reality.

It calculates flight paths for Earth, Mars, and the Moon, adjusting both gravitational acceleration (g) and atmospheric density profile (ρ). It allows users to visualize "Terminal Velocity" limits and the transition from atmospheric flight to near-vacuum conditions.

Formulas

The simulation runs a time-stepped loop solving forces. Drag F_d is calculated at every frame using instantaneous velocity v and altitude y:

F_d = 12 ρ(y) v² C_d A

Where density ρ scales barometrically:

ρ(y) = ρ₀ exp(−yH)

Reference Data

Variable	Earth Surface	Mars Surface	Effect on Flight
Gravity g	9.81 m/s²	3.71 m/s²	Determines arc height & flight time
Density ρ₀	1.225 kg/m³	0.020 kg/m³	Base drag force magnitude
Scale Height H	8,500 m	11,100 m	How fast air thins out with altitude

Frequently Asked Questions

Scale Height (H) is the vertical distance over which atmospheric density drops by a factor of "e" (approx 2.718). On Earth, it's about 8.5km. This means at 8.5km altitude, air is ~37% as thick as sea level.

In a vacuum, trajectories are perfect parabolas. With air resistance, the projectile loses energy constantly. It rises steeply but falls more vertically as it slows down, creating a "ballistic" curve rather than a geometric parabola.