orbital mechanics

ORBITAL MECHANICS

QUESTION: Explain how Saturn and Jupiter’s rapid rotation increases their moons orbital velocity and orbital distance?

ChatGPT: The rapid rotation of Jupiter and Saturn increases their moons’ orbital momentum through tidal torque which transfers angular momentum from the planet’s spin to the moon’s orbit. Both planets rotate much faster than their major moons orbit. For example, Jupiter rotates in about 10 hours while Io takes 1.77 days to orbit, and Saturn rotates in about 10.7 hours while Titan takes nearly 16 days. Because these planets are fluid and deformable, each moon’s gravity raises a tidal bulge in the planet. If the planet were not rotating, that bulge would point directly at the moon. But because the planet rotates faster than the moon orbits, the bulge is carried slightly ahead of the moon’s position.

That forward-shifted bulge exerts a gravitational pull on the moon with a forward component along its direction of motion. This forward pull acts like a continuous thrust. It increases the moon’s orbital velocity and, more importantly, its orbital angular momentum (L=mvr). As angular momentum increases, the only stable outcome is for the moon to move into a higher orbit, where orbital speed is lower but the larger radius more than compensates, so total angular momentum increases.

At the same time, the tidal bulge is constantly dragged across the planet’s interior, where friction dissipates energy as heat. This dissipation is what allows the torque to exist; without internal friction, the bulge would align exactly with the moon and no net momentum transfer would occur. Over millions of years, this process causes moons outside the synchronous orbit to spiral outward. Titan, for example, is moving away from Saturn by several centimeters per year, and Io, Europa, and Ganymede are also slowly migrating outward from Jupiter.

In short, the rapid rotation of Jupiter and Saturn continually pulls their tidal bulges ahead of their moons, and the gravity of those offset bulges transfers angular momentum from the planet’s spin into the moons’ orbital motion, causing their orbital momentum and orbital radius to increase over time.

The three Galilean satellites are involved in orbital resonance, in which the orbital periods of Ganymede, Europa and Io are in a near 1:2:4 ratio and the mutual conjunctions of the Io–Europa pair and of the Europa–Ganymede pair precess around Jupiter at precisely the same rate.

Io and Ganymede are embedded in the high velocity ring current, and block and slow the current which pushes the moons, increasing their velocity, orbital momentum, and radius of their orbits. Io is increasing in mass the fastest of the 3 Galilean moon. One model suggests this resonance was progressively achieved after Io moved outward into a near 2:1 resonance with Europa, and then the Io–Europa pair moved outward until Ganymede was captured into its own near 2:1 resonance with Europa.

The six planets of HD110067 form successive pairs of 3:2, 3:2, 3:2, 4:3, and 4:3 resonances, resulting in the closest planet completing six orbits while the outer-most planet does one.

Scientists thought they knew the rate at which Titan is moving away from Saturn, but they recently made a surprising discovery: Using data from NASA’s Cassini spacecraft, they found Titan drifting a hundred times faster than previously understood — about 4 inches/year.

The ionized rotating cores of stars and planets transform the momentum of moving charges into dipole moments and the sum of moments is captured by their field which increases the momentum of orbiting ions in the direction of core rotation. Dipole moments induced by Jupiter’s rotating core, captured by Jupiters field, powers the high velocity ring current of heavy ions ejected from Io’s volcanoes around Io’s orbital path.

The magnetosphere of Jupiter sweeps up ionized gases and dust from Io’s thin atmosphere at a rate of 1 tonne per second. This material is mostly ionized sulfur, oxygen, chlorine and sodium chloride dust. Io orbits Jupiter with a velocity of 17 km/sec. The Io plasma torus rotates with a velocity of about 74 km/sec. Since Io is embedded in the Io plasma torus, the torus plasma flows past Io with a relative velocity of 57 km/sec.

Juneau dedects massive magma lake near Io’s South Pole larger than Earth’s Lake Superior and belches out eruptions six times the total energy of all the world’s power plants. Io’s volcanism has led to formation of hundreds of volcanic centers. Lava flows tens or hundreds of kilometers long have primarily basaltic composition similar to lavas seen on Earth at shield volcanoes such as Kilauea in Hawaii.