Orbital Trajectory Numerical Propagator
Solves two-body equations of motion using 8th-order Dormand-Prince numerical integration.
Aerospace & Aeronautical Engineering / Keplerian Orbit Mechanics
FREE TO EXPLORELABORATORY 41 · AEROSPACE & AERONAUTICAL ENGINEERING
Keplerian Two-Body Orbit Determination and Vis-Viva Velocity
Determine spacecraft orbital velocity v(r) and specific mechanical energy epsilon from geocentric radius r using Kepler's laws and the Vis-Viva energy equation. Explore interactive wind tunnel simulation, flight dynamics, and aerospace engineering telemetry.
AERODYNAMICS · PROPULSION · FLIGHT DYNAMICS
Your virtual aerospace engineering laboratory.
ORBITAL VELOCITY SQUARED—
FLIGHT & TEST CELL TELEMETRY
Ready to sample with (1/r)x10^7 = 1.25 m^-1.
Adjust (1/r)x10^7, then execute aerospace trial.
Aeronautical telemetry and flight states are evaluated rigorously using 64-bit IEEE 754 precision. Residuals reflect ordinary least-squares regression across successive observations. Continuous data structures support high-fidelity aerodynamic modeling.
Aeronautical assumptions and boundary condition limits
Pure Keplerian two-body formulation neglects non-spherical Earth gravity harmonics (J2, J3, J4). Linear regression of orbital velocity squared against inverse radius yields a slope 2*mu = 7.9720 x 10^14 m^3/s^2 corresponding to Earth mu = 3.9860 x 10^14 m^3/s^2 with R^2 > 0.999999.
Aeronautical apparatus & wind tunnel sensors.
Deep Space Network (DSN) Telemetry Simulator
Simulates 2-way coherent Doppler range-rate velocity measurements and range time delays.
Keplerian Orbital Element Converter
Transforms Cartesian state vectors (r, v) into classical orbital elements (a, e, i, Omega, omega, nu).
Geocentric Coordinate Reference Frame
Earth-Centered Inertial (ECI J2000) frame tracking satellite state vectors.
Orbital Energy & Angular Momentum Monitor
Verifies conservation of specific mechanical energy epsilon and angular momentum h.
Satellite Ground Track Visualizer
Plots 2D Mercator ground tracks with ascending node regression and orbit footprints.
FOLLOW THE METHOD
A reason behind every step.
Determine spacecraft orbital velocity v(r) and specific mechanical energy epsilon from geocentric radius r using Kepler's laws and the Vis-Viva energy equation. Standardized parameter settings: 1.05, 1.14, 1.22, 1.31, 1.4, 1.48 m^-1.
01
Orbit Definition and Initialization
Initialize an eccentric Earth orbit with perigee altitude h_p = 400 km and apogee altitude h_a = 10,842 km (semi-major axis a = 12,000 km, e = 0.435).
02
Gravitational Parameter Datum
Confirm Earth gravitational parameter mu = 3.986004 x 10^14 m^3/s^2 and Earth mean radius R_E = 6378.137 km.
03
Telemetry State Vector Sampling
Track the satellite through true anomaly positions corresponding to inverse radius (1/r) x 10^7 = 1.05, 1.14, 1.22, 1.31, 1.40, and 1.48 m^-1.
04
Orbital Velocity Acquisition
Record instantaneous inertial velocity magnitude v at each radial station using simulated Doppler telemetry.
05
Specific Energy Verification
Calculate specific orbital energy epsilon = 0.5 * v^2 - mu / r, confirming constancy across all observation points.
06
Vis-Viva Linear Regression
Plot (v^2) x 10^-7 versus (1/r) x 10^7, perform linear regression to determine slope 2*mu x 10^-14, and compute semi-major axis from the intercept.
YOUR NOTEBOOK · 0 OBSERVATIONS
Turn measurements into aerodynamic insight.
Points are your recorded observations. The solid regression line validates Keplerian Orbit Mechanics mathematical scaling.
LINEAR REGRESSION FIT · y = mx + b
v^2 = 2\mu \left(\frac{1}{r}\right) - \frac{\mu}{a} \implies \left(v^2 \times 10^{-7}\right) = m \cdot \left(\frac{1}{r} \times 10^7\right) + b
| # | Inverse Radius Parameter (m^-1) | Orbital Velocity Squared (m^2/s^2 x 10^-7) | Inverse Orbital Radius (1 / r) x 10^7 (m^-1) | Orbital Velocity Squared (v^2) x 10^-7 (m^2/s^2) | Remove |
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