Orbital Mechanics Principles

🛰️ Gravity Gradient Torque — The Silent Stabilizer in Space In this simulation, I modeled how Earth’s gravitational field induces natural torques on a satellite, known as Gravity Gradient Torque. It’s a purely physical phenomenon that arises because Earth’s gravity acts more strongly on the part of the satellite closer to it, creating a restoring torque that tends to align the satellite’s long axis toward the planet’s center. Here is what I Simulated: 👉Two CubeSats in a 7000 km circular orbit, each with different mass distributions and inertia properties. 👉Full attitude propagation using quaternion-based rotational dynamics. 👉Numerical integration with a 4th-order Runge–Kutta solver for angular velocity and attitude. 👉Real-time visualization combining 3D CubeSat motion with angular velocity evolution. What the Simulation Shows: 👉The CubeSat with higher inertia asymmetry aligns faster toward Earth due to stronger gravity gradient effects. 👉A more symmetric satellite maintains slow oscillations — demonstrating passive attitude stability. 👉Varying orbital velocity modulates the torque magnitude, visible in angular velocity plots. Why It Matters? 👉Gravity gradient torque is one of the simplest yet most elegant concepts in orbital mechanics. 👉It forms the foundation for passive attitude stabilization, allowing small satellites to orient themselves without active control — a principle still used in low-cost CubeSat missions and Earth-observation payloads. #OrbitalMechanics #AerospaceEngineering #CubeSat #AttitudeControl #Dynamics #Simulation #Physics #Research #SpaceTechnology #Satellites

A video series on mathematical and computational techniques to design trajectories in the 3-body problem. Space missions going to the Moon, cislunar space, the asteroids, or the moons of Jupiter are complex and challenging to design, requiring new and unusual kinds of orbits to meet their goals, orbits that cannot be found by classical 2-body approaches. In addition, Lagrange point orbits are seeing greater use, such as the James Webb Space Telescope on a Sun-Earth L2 halo orbit. This series can serve as a valuable resource for graduate students and advanced undergraduates in aerospace engineering, as well as a manual for practitioners who work on Lagrange point and deep space missions in industry and at government laboratories. MATLAB code is provided as well. https://lnkd.in/eNCtdeGd And Happy Perihelion Day, 2025! #space #engineering #aerospace #orbitalmechanics #LagrangePoint #mathematics #SpaceManifolds #JamesWebb #NonlinearDynamics #gravity #SpaceTravel #SpaceManifold #DynamicalSystems #perihelion #JamesWebbSpaceTelescope #solarSystem #NASA #dynamics #InterplanetarySuperhighway

⚛️ It's #Physics Time: Planetary Orbit - Newton's Ingeneous Insight ⚛️ 💡 #Newton was definitely one of the greatest geniuses who ever lived. His basic laws of classical #mechanics are still taught in #schools and #universities around the world. And even today, we still steer space probes unerringly through our #solar #system according to his law of #gravity, although a more comprehensive theory of gravity was developed with #Einstein's general theory of relativity (Newton is sufficiently accurate for interplanetary space flights!). 🌍 And not only that: he even created his own mathematical formalism (differential calculus) for his calculations himself and independently of Wilhelm #Leibniz. One of his greatest #achievements was the very precise calculation of planetary and cometary orbits. Thus, based on his theory, he was able to mathematically prove Kepler's laws, which had previously been established by the German astronomer Johannes #Kepler and which already represented a paradigm shift in the description of planetary orbits (he introduced ellipses instead of circles as planetary orbits, a revolution in his days!). 🔄 Using #conservation of #energy and angular #momentum, the possible planetary orbits can be calculated very easily (see photo). The result: the solution describes a so-called conic section. In a conic section, a plane is intersected with a double cone and, depending on the relative geometric position, different intersection curves result. There are four fundamentally different types of planetary orbits that depend on the parameter Epsilon (the #eccentricity): 1️⃣ Epsilon = 0: circular orbit 2️⃣ 1 > Epsilon > 0: Ellipse 3️⃣ Epsilon = 1: parabola 4️⃣ Epsilon > 1: Hyperbola ℹ The orbital curves (1) and (2) are closed, i.e. the two bodies are gravitationally bound to each other, while the orbital curves (3) and (4) are open orbital curves (the bodies are not gravitationally bound and the distance increases with time). The exact shape of the curve is determined by the constants of motion, energy E and angular momentum L. 📣 Next time, you will hear more about those different kind of orbital motions!