Lesson 5.5 • Interactive LaboratoryInteractive Simulation

Orbital Mechanics & Escape Velocity Simulation Lab

Interactive 60fps canvas simulation: Real-time orbital propagation, LEO/MEO/GEO altitude presets, orbital velocity, period, Kepler’s law verification, escape velocity trajectory, and energy telemetry.

Marking a lesson complete represents finishing your study of the topic; it does not denote tested mastery.

Learning Objectives

Interactively explore how orbital speed and period change with altitude from Low Earth Orbit (ISS) up to Geostationary Orbit.
Observe the transition from circular orbit to elliptical orbit and parabolic escape trajectory when launch velocity reaches v_e.
Inspect live telemetry of kinetic, potential, and total mechanical energy balance across varying orbital radii.

Syllabus Topic Outline

Interactive Laboratory

1Low Earth Orbit (LEO) dynamics and ISS orbital parameters
2Medium Earth Orbit (MEO) navigation satellite constellations
3Geostationary Orbit (GEO) equilibrium and 24-hour synchronization
4Escape Velocity simulation and hyperbolic trajectory transition

Interactive Orbital Mechanics & Satellite Trajectories Laboratory

Explore circular satellite orbits, Keplerian periods, geostationary synchronization, and hyperbolic escape velocities around Earth.

Orbital Altitude h above Earth (km):400 km (r = 6,771 km)

Real-Time Orbital Physics Telemetry (m = 1,000 kg)

Orbital Speed (v_o = √(GM/r)):

7.67 km/s

Orbital Period (T = 2π√(r³/GM)):

1.54 hrs

Field Intensity (g_h = GM/r²):

8.694 m/s²

Gravitational Potential (V = -GM/r):

-58.87 MJ/kg

Total Mechanical Energy (E = -GMm/2r):

-29.43 GJ

Earth Escape Velocity (v_e = √(2GM/R)):

11.19 km/s

Orbital Mechanics & Governing Physical Laws

• Newton’s Universal Gravitation: F = G · M · m / r² • Centripetal Force Balance: m · v_o² / r = G · M · m / r² ⟹ v_o = √(G · M / r) • Kepler’s Third Law: T² = (4π² / GM) · r³ • Geostationary Orbit: T = 24.0 hours (86,400 s) in the equatorial plane, yielding r ≈ 42,164 km and altitude h ≈ 35,786 km • Escape Velocity: v_e = √(2 · G · M / R) = √(2 · g₀ · R) ≈ 11.2 km/s for Earth • Mechanical Energy: E = KE + PE = (1/2)m v_o² - GMm/r = - GMm / (2r) (Bound negative state)