Questions: Satellite Formation and Orbital Mechanics

Question 1

A newly discovered moon of a giant planet orbits at very large distance from the planet, on a highly eccentric, retrograde path inclined steeply to the planet's equatorial plane. Which formation mechanism does this orbital signature most strongly suggest?

• A. Giant-impact accretion — the impactor delivered angular momentum in the wrong direction
• B. Co-formation in a circumplanetary disk — the disk was disrupted early in the planet's history
• C. Gravitational capture of a small body originally orbiting the Sun
• D. Tidal migration from a closer prograde orbit over billions of years

Answer: (C)

Retrograde, distant, eccentric, and highly inclined orbits are the diagnostic fingerprints of captured moons. Bodies that form in a circumplanetary disk (like the Galilean moons) are nearly circular, prograde, and close to the planet's equatorial plane — because the disk itself rotates that way. Giant impacts produce large moons near the equatorial plane with low inclination. Tidal forces circularize and can migrate orbits, but cannot reverse the direction of orbital motion. The irregular orbital properties uniquely point to capture of a formerly free-orbiting body.

Question 2

The Laplace resonance among Io, Europa, and Ganymede (orbital period ratios of 1:2:4) makes Io the most volcanically active body in the solar system because the resonance...

• A. Keeps Io's orbit perfectly circular, maximizing the constant tidal force from Jupiter
• B. Prevents Io's orbit from circularizing, continuously pumping its eccentricity and driving cyclic tidal deformation
• C. Traps heat from Jupiter's magnetosphere inside Io's mantle
• D. Causes Io to orbit at the minimum distance from Jupiter where tidal forces are strongest

Answer: (B)

If Io orbited alone, tidal friction would quickly circularize its orbit, and tidal heating would cease. The resonance with Europa and Ganymede continuously re-excites Io's orbital eccentricity: every orbit, the periodic gravitational kicks from Europa keep the orbit from becoming circular. An eccentric orbit means Io's distance from Jupiter changes each orbit, so tidal deformation cycles up and down, generating enormous internal heat by friction. The resonance does not create a circular orbit — it prevents one, which is the key misconception to avoid.

Question 3

The Galilean moons' nearly circular, prograde, equatorial orbits are evidence that they formed within Jupiter's circumplanetary disk rather than by capture.

• T. True
• F. False

Answer: True

A circumplanetary disk rotates in the same direction as the planet and lies near its equatorial plane. Moons that condense within such a disk inherit these properties — circular orbits (circularized by disk drag), prograde motion (same as disk rotation), and equatorial alignment. Captured bodies, by contrast, arrive from arbitrary directions and retain eccentric, inclined, and often retrograde orbits. The ordered properties of the Galilean moons are thus strong evidence for disk formation.

Question 4

Earth's Moon formed through the same process as Jupiter's Galilean moons — gradual accumulation of material within a circumplanetary disk that surrounded the proto-Earth.

• T. True
• F. False

Answer: False

Earth's Moon formed through a giant-impact event: a Mars-sized body struck the proto-Earth ~4.5 billion years ago, ejecting a disk of vaporized and molten rock that coalesced into the Moon. This is very different from the gradual disk-accretion that produced the Galilean moons. The evidence includes the Moon's composition matching Earth's mantle, its depletion in volatiles (expelled by the impact's heat), and its relatively large size compared to Earth. The Moon's single, large size and compositional similarity to Earth's mantle are not what you'd expect from slow disk accretion.

Question 5

The giant-impact model explains why the Moon's bulk composition is so similar to Earth's mantle. Why does the impact model produce this compositional match?

Model answer: The giant-impact model explains this because the impactor struck the proto-Earth at an angle, ejecting material primarily from the outer layers of both bodies — which in a differentiated planet means mantle rock, not core material. The Moon formed from this ejected mantle debris, so its composition reflects Earth's mantle chemistry rather than the whole Earth (which would include the iron-rich core). The Moon's depletion in iron relative to the whole Earth and its match with Earth's mantle silicates are the key compositional signatures the impact model explains.

A competing model — co-accretion — would produce a Moon with a more 'cosmic' composition averaging Earth and the surrounding nebula, not specifically matching Earth's mantle. The impact geometry (grazing strike, debris from upper mantle layers) is what produces the mantle-composition fingerprint. This is why compositional matching is considered one of the strongest lines of evidence for the giant-impact hypothesis.