Propagate a spacecraft orbit from classical orbital elements, visualize the 3D trajectory,
inspect the ground track, and check specific mechanical energy. This tool connects the COE converter
to real orbital motion and introduces the difference between ideal two-body motion and J2-perturbed motion.
What this tool computes
This module starts from classical orbital elements and converts them into an inertial position-velocity state.
It then numerically propagates the orbit forward in time and draws the resulting trajectory.
Initial ECI state vector from COEs
3D inertial orbit trajectory
Latitude-longitude ground track
Specific mechanical energy history
Optional J2 perturbation effect on RAAN and argument of perigee
Core orbital model
In the two-body model, spacecraft acceleration depends only on the central body's gravity:
\[
\ddot{\mathbf r} = -\frac{\mu}{r^3}\mathbf r
\]
The propagated state is checked using specific mechanical energy:
\[
\varepsilon = \frac{v^2}{2} - \frac{\mu}{r}
\]
For ideal two-body motion, this energy should remain nearly constant. If numerical step size is too large,
the orbit may appear to gain or lose energy even when the physical model says it should not.
J2 perturbation option
The optional J2 mode adds the leading oblateness perturbation of the central body. This is useful for seeing
how real Earth orbits slowly rotate in space rather than repeating perfectly.
\[
J_2 \rightarrow \dot{\Omega},\ \dot{\omega}
\]
RAAN drift shows nodal precession.
Argument of perigee drift shows rotation of the line of apsides.
Ground tracks shift because Earth rotates under the inertial orbit.
Learning note
This is still an educational propagator. It is not a replacement for STK, Orekit, GMAT, or flight-dynamics validation tools.
How to read the plots
3D orbit: shows the inertial trajectory around Earth.
Ground track: shows where the spacecraft passes over the rotating Earth.
Energy plot: checks whether the numerical integration is physically consistent.
RAAN / argument drift: becomes meaningful when J2 is enabled.
Interactive propagator
Use presets for fast demonstrations, then adjust the inputs manually.
Results
Orbital period
—
Perigee / Apogee altitude
—
Initial speed
—
Energy drift
—
RAAN change
—
Argument change
—
Interpretation
Run the propagator to generate the 3D orbit, ground track, and energy check.
3D orbit in ECI frame
Ground track
Longitude wraps at ±180°. Sharp jumps usually indicate dateline crossing, not a physical jump.
Specific mechanical energy history
Assumptions and limitations
This tool assumes:
Earth-centered inertial propagation
RK4 numerical integration
Two-body gravity, with optional J2
No atmospheric drag, SRP, third-body gravity, thrust, or maneuvers
Simplified Earth rotation for ground-track visualization