Orbital Simulation

by Noah Trupin '23 for SC535: Honors Physics

Note: leaving the page will cause the simulation to malfunction.

Contents: Introduction, Scenario, Hypothesis, Simulation, Observed Behavior, Conclusions, Physics Used, and References. You may have to scroll this panel.

Introduction
As provided by the equation v_(escape) = sqrt(2GM/r), Earth's moon has an escape velocity of 1440.12 m/s while in its typical orbit (3.84e+8 m from Earth with a mean eccentricity of 0.05). The Moon's mean orbital velocity, 1018.32 m/s, allows it to maintain its stable, slightly elliptical orbit
So, what happens if we accelerate the moon close to a velocity close to, but not equal to or greater than, 1440.12 m/s?

Scenario
An asteroid has struck the Moon with 5.62e+22 Newtons of force (enough to knock the Moon out of its traditional orbit while remaining under the influence of Earth's gravity and, most importantly, in my laptop's viewing window).

Hypothesis
Following a significant collision, the Moon will begin an elliptical orbit with a rotating apsides (perigee and apogee, or nearest and farthest orbital points) and a greater eccentricity (roundness) than its typical orbit. During this new orbit, the Moon's total energy will oscillate between the apogees of each cycle.

Simulation
The Moon maintains an approximately circular orbit (mean eccentricity 0.05) with Earth-relative velocity 1018.32 m/s for five seconds before the simulation applies 5.62e+22 Newtons of force in the negative x-direction and y-direction. The simulation then begins mapping the Moon's new orbit. The simulation consists of a kinematics engine written in vanilla JavaScript with p5.js as its renderer.

Observed Behavior
As charted in the simulation and observed in the statistics panel, the Moon's new elliptical orbit features rotating apogees and perigees and an oscillating total energy. The ΔTotal stat displays positive values as the Moon travels from its perigee to apogee and negative values while traveling back out to its perigee.

Conclusions
Due to variations in acceleration (due by a slingshot effect caused by Earth's gravity), the Moon cannot return to a stable elliptical orbit following a significant impact, instead maintaining a rotating elliptical orbit characterized by large, yet oscillating, variations in energy at its apogees and perigees.

Physics Used
The simulation relies on kinematics and universal gravitation to function. The statistics panel features information on the energy of the simulated system.

References

• Dr. Voss (assorted questions)

• JPL Horizons (positions, sizes, and velocities of orbital bodies)

• NASA Eclipse (Moon orbit and eccentricity data)

• p5.js (rendering)