Lofted vs. Minimum Energy (MET) Profiles
Ballistic missile flight tests (such as North Korean launches into the East Sea / Sea of Japan) frequently adopt lofted trajectories. By firing at an extremely steep angle ($>60^\circ$ pitch), the missile attains high altitudes ($>1,000$ to $6,000\text{ km}$) while deliberately restricting the ground footprint to avoid overflying neighboring sovereign airspace.
The equivalent Minimum Energy Trajectory range can be estimated from the conserved specific mechanical energy:
R_{\text{MET}} \approx 2 \cdot R_{\text{lofted}} \cdot \sqrt{h_{\text{max}} / R_{\text{lofted}}}
Radar Horizon & Curvature Mechanics
Due to the curvature of the Earth ($R_E \approx 6,371\text{ km}$), ground and naval radar systems (such as SPY-1 Aegis or AN/TPY-2) cannot acquire low-altitude booster flight until the missile clears the radar horizon:
d_{\text{LOS}} = \sqrt{2 R_E h_{\text{sensor}}} + \sqrt{2 R_E h_{\text{missile}}}
Lofted missiles break through the horizon within tens of seconds, offering generous tracking windows for telemetry reconstruction and mid-course interceptor solutions.
Kinematic Modeling Assumptions
This laboratory computes the suborbital arc using central-force Newtonian gravity $g(r) = \mu / r^2$ with geocentric radius $r = R_E + h$. Atmospheric drag is modeled below 80 km altitude, producing realistic terminal deceleration in the re-entry corridor.
Exports provide formatted state vectors suitable for ingestion into mission planning and GIS mapping software.