Astronomy Quiz: Planetesimals And Planetary Formation
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Planetesimals And Planetary FormationQuestion 1 of 20

The nebular gas in a protoplanetary disk has a complex and seemingly contradictory role in planetesimal formation. Which statement best captures this complexity?

The gas provides gravitational shielding, allowing planetesimals to grow in gravitationally stable pockets of the disk.
Gas drag causes solids to lose orbital energy and spiral inward, yet it also damps their random velocities, facilitating gentle, constructive collisions.
The gas heats the planetesimals through friction, which helps them stick together more effectively during collisions.
Gas pressure pushes outward against the star's gravity, slowing the orbits of solids and causing them to collide from behind.
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Astronomy Quiz

Astronomy Quiz: Planetesimals And Planetary Formation

Practice Planetesimals And Planetary Formation in Astronomy with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Planetesimals And Planetary Formation, giving you a quick way to practice the rules, question types, and explanations that matter most for Astronomy.

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Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

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Question 1

The nebular gas in a protoplanetary disk has a complex and seemingly contradictory role in planetesimal formation. Which statement best captures this complexity?

  1. The gas provides gravitational shielding, allowing planetesimals to grow in gravitationally stable pockets of the disk.
  2. Gas drag causes solids to lose orbital energy and spiral inward, yet it also damps their random velocities, facilitating gentle, constructive collisions. (correct answer)
  3. The gas heats the planetesimals through friction, which helps them stick together more effectively during collisions.
  4. Gas pressure pushes outward against the star's gravity, slowing the orbits of solids and causing them to collide from behind.
Explanation: When you encounter questions about protoplanetary disks and planetesimal formation, focus on how gas affects solid particles in seemingly opposite ways simultaneously. The nebular gas creates a complex environment where multiple physical processes operate at once. Gas drag is the key mechanism here. As solid particles orbit within the gas disk, they experience drag forces that cause two important effects. First, the drag removes orbital energy from the particles, causing them to spiral inward toward the star over time. This might seem destructive to planet formation. However, the same drag forces also damp the random velocities of particles, reducing their relative speeds when they encounter each other. This velocity damping is crucial because it allows particles to collide gently rather than destructively, promoting sticking and growth into larger planetesimals. Answer B correctly captures this dual nature—inward migration paired with constructive collision facilitation. Answer A incorrectly suggests gravitational shielding, but gas doesn't provide gravitational protection in disk regions. Answer C mischaracterizes frictional heating as helpful for sticking, when excessive heating typically makes collisions more destructive rather than constructive. Answer D confuses the mechanism—while gas pressure does create headwind effects that slow particles, the described "collision from behind" scenario oversimplifies the complex orbital dynamics involved. Remember that protoplanetary disk physics often involves competing processes. When studying planet formation, look for how the same physical mechanism can have both beneficial and detrimental effects on planetesimal growth, rather than assuming simple one-way relationships.

Question 2

Imagine two large planetesimals that form in the same protoplanetary disk. Planetesimal R forms at 1 AU from the star, and Planetesimal I forms at 5 AU. Both grow to a few hundred kilometers in diameter but do not become full planets. Which statement most accurately contrasts their likely bulk composition?

  1. Planetesimal R would be composed mostly of rock and metal, while Planetesimal I would be composed primarily of rock, metal, and significant amounts of water ice. (correct answer)
  2. Planetesimal R would contain more volatile organic compounds than Planetesimal I, as the higher temperature at 1 AU would drive more complex chemistry.
  3. Both planetesimals would have nearly identical compositions, as the protoplanetary disk is well-mixed, but Planetesimal I would have a thicker crust.
  4. Planetesimal R would be a mix of rock and ice, while Planetesimal I, forming in the colder outer region, would be composed almost purely of various ices.
Explanation: The key factor is the 'frost line' (or snow line), which in our solar system is located between the orbits of Mars and Jupiter. Inside the frost line (like at 1 AU), temperatures are too high for volatile compounds like water, ammonia, and methane to condense into solid ice. Therefore, planetesimals forming there are made of refractory materials: rock (silicates) and metal. Outside the frost line (like at 5 AU), it is cold enough for these ices to form. This means there is much more solid material available for accretion, and the resulting planetesimals are a mixture of rock, metal, and a large fraction of ice. (B) is incorrect; lower temperatures are better for preserving volatile organics. (C) is incorrect because the temperature gradient creates a strong compositional gradient. (D) is incorrect because even in the outer system, rock and metal are present and form a substantial part of planetesimals.

Question 3

According to the giant-impact hypothesis, the Moon formed from the debris of a collision between the proto-Earth and a Mars-sized object. Assuming both bodies had already differentiated, what does this imply about the Moon's expected interior structure and composition?

  1. The Moon should have a very large iron core, formed from the merged cores of both the proto-Earth and the impactor.
  2. The Moon should be largely depleted in iron and other siderophile elements relative to Earth, and have a very small core. (correct answer)
  3. The Moon should be compositionally identical to Earth's mantle, as the impactor was completely vaporized in the collision.
  4. The Moon should show no signs of differentiation itself, being a homogeneous mixture of material from both bodies' crusts.
Explanation: When you encounter questions about planetary formation, focus on how physical processes during collisions affect the distribution of different types of materials, especially metals versus silicates. The giant-impact hypothesis explains that a Mars-sized object called Theia collided with the early Earth. Since both bodies had differentiated, their dense iron cores had already settled to their centers, while lighter silicate materials formed their mantles and crusts. During this catastrophic collision, the cores of both bodies would have merged and remained with Earth due to their high density and the planet's strong gravitational pull. Meanwhile, the impact ejected primarily mantle material—lighter silicate rocks—into orbit around Earth, and this debris eventually coalesced to form the Moon. This process means the Moon formed predominantly from silicate-rich mantle material rather than iron-rich core material. Therefore, option B is correct: the Moon should be depleted in iron and siderophile (iron-loving) elements compared to Earth and have only a very small core. Option A incorrectly assumes the cores would be ejected and incorporated into the Moon, but dense iron would fall back to Earth. Option C is wrong because the Moon isn't identical to Earth's mantle—it also contains some material from Theia's mantle. Option D misunderstands the process: the Moon did differentiate after formation, developing its own small core, mantle, and crust structure. Remember: in planetary collision scenarios, dense materials (like iron) tend to stay with the larger body, while lighter materials (like silicates) are more easily ejected.

Question 4

The transition from gentle sticking of dust grains via electrostatic forces to gravity-dominated accretion of planetesimals is a key step in planet formation. At roughly what size does an object's self-gravity begin to significantly enhance its growth rate by gravitationally focusing other nearby particles?

  1. At the micrometer scale, as soon as dust grains form from the nebula.
  2. At the meter scale, where boulders are large enough to exert a noticeable pull on each other.
  3. At the kilometer scale, where the object can be formally classified as a planetesimal. (correct answer)
  4. At the 1000-kilometer scale, when the object is large enough to be considered a protoplanet.
Explanation: While gravity exists for all objects, it is an extremely weak force. For dust, pebbles, and even boulders, forces like gas drag and electrostatic attraction are much more important for their interactions. It is only when bodies grow to the kilometer scale—the size of planetesimals—that their self-gravity becomes strong enough to significantly perturb the trajectories of nearby objects. This effect, known as gravitational focusing, dramatically increases the planetesimal's effective collision cross-section, causing its growth rate to accelerate (the 'runaway growth' phase). By the protoplanet stage (D), this process is already well-established.

Question 5

An exoplanet orbiting a Sun-like star within its 'frost line' is found to have a mass of 0.8 Earth masses and a radius of 0.75 Earth radii, yielding an average density significantly higher than that of most silicate rocks. Which process is most essential to explain this observation?

  1. The capture of a dense metallic asteroid late in its formation, which settled on its surface.
  2. Intense atmospheric stripping by the host star's solar wind, which removed a low-density gaseous envelope.
  3. Rapid accretion of nebular gas, which gravitationally compressed the planet's rocky interior to a high density.
  4. Planetary differentiation, where gravitational settling formed a large, dense iron-nickel core and a less-dense silicate mantle. (correct answer)
Explanation: The high average density, especially for a planet less massive than Earth (implying less gravitational compression), strongly suggests a composition rich in heavy elements like iron and nickel. Planetary differentiation is the process by which these dense materials sink to form a large core, while lighter silicate materials form a mantle. This separation is the fundamental explanation for a terrestrial planet having a bulk density much higher than that of surface rocks. (A) is incorrect because a single asteroid would not significantly alter the bulk density of a planet. (B) is plausible for removing a gas envelope, but the resulting body's density is determined by its solid composition, which points back to differentiation. (C) is incorrect because accretion of gas would lead to a lower average density, as seen in gas giants.

Question 6

An astronomer analyzes two meteorites. Meteorite X is an achondrite, specifically an iron meteorite composed almost entirely of an iron-nickel alloy with a Widmanstätten pattern. Meteorite Y is a carbonaceous chondrite, containing a mix of silicates, complex organic compounds, and water-bearing clay minerals. What is the most likely conclusion about the parent bodies of these meteorites?

  1. The parent body of X accreted rapidly, trapping heat, while the parent body of Y accreted slowly, allowing heat to escape.
  2. The parent body of X was large enough to undergo differentiation before being shattered, while the parent body of Y was a primitive, unaltered planetesimal. (correct answer)
  3. Both parent bodies were fully differentiated, but Meteorite X originated from the core while Meteorite Y originated from the crust.
  4. The parent body of X formed close to the Sun where only metals could condense, while the parent body of Y formed in the outer solar system from a mix of materials.
Explanation: Iron meteorites are fragments of the cores of larger planetesimals or asteroids that were massive enough to generate sufficient heat to melt, differentiate (heavy metals sinking to the core), and then cool slowly (creating the Widmanstätten pattern). Carbonaceous chondrites are among the most primitive objects in the solar system, representing unaltered material from the solar nebula that never underwent differentiation. Therefore, Meteorite X comes from a shattered differentiated body, and Meteorite Y comes from a primitive, undifferentiated body. (A) is a trap; rapid accretion causes differentiation, it doesn't prevent it. (C) is incorrect because a chondrite is by definition undifferentiated. (D) is partially correct about location but fails to identify the critical difference in the evolution (differentiation) of the parent bodies.

Question 7

In the early protoplanetary disk, the growth from meter-sized boulders to kilometer-sized planetesimals faces the 'meter-size barrier,' as gas drag causes these bodies to rapidly spiral into the star. Which of the following is a leading hypothesis for a mechanism that allows this barrier to be overcome?

  1. The development of strong magnetic fields within the boulders, allowing them to repel the nebular gas and slow their inward drift.
  2. The collective gravitational force of boulders becoming strong enough to capture nebular gas, forming a protective envelope.
  3. The concentration of vast numbers of pebble-sized particles in localized regions of high pressure, leading to rapid gravitational collapse into larger bodies. (correct answer)
  4. The melting and subsequent fusing of boulders due to intense radiation from the young central star, creating larger and more stable aggregates.
Explanation: The 'meter-size barrier' is a significant hurdle in accretion models. One of the leading solutions is the idea of particle concentration. Turbulent eddies or pressure bumps in the gas disk can trap vast quantities of smaller, pebble-sized particles. If the density in these traps becomes high enough, their collective gravity can cause them to collapse directly into large (10s to 100s of km) planetesimals, effectively skipping the problematic meter-size stage. (A) is incorrect as magnetic fields are not strong enough in this way. (B) is incorrect as boulders are not massive enough to capture significant gas. (D) is incorrect because stellar radiation would not be sufficient to melt rock at typical planet-forming distances, and this process would be too slow.

Question 8

During the 'oligarchic growth' stage of planet formation, a few large protoplanets dominate their respective regions of the protoplanetary disk. What is the primary dynamical effect of these oligarchs on the smaller, surrounding planetesimals?

  1. They create stable gravitational pockets that protect the smaller planetesimals from falling into the star.
  2. They gravitationally 'stir' the planetesimal swarm, increasing their random velocities and leading to either accretion or ejection. (correct answer)
  3. They slow down the orbits of nearby planetesimals through gas-dynamic friction, causing them to accumulate in dense rings.
  4. They transfer angular momentum to the planetesimals, causing them to migrate to the outer regions of the solar system.
Explanation: A key feature of the oligarchic growth phase is that the large protoplanets (oligarchs) are massive enough to significantly perturb the orbits of the remaining smaller planetesimals in their 'feeding zone'. This gravitational influence increases the eccentricities and inclinations of the smaller bodies, a process called 'stirring'. This has two main outcomes: some planetesimals are perturbed onto collision courses with the oligarch and are accreted, while others are accelerated to the point where they are ejected from the system entirely. (A) is incorrect; their influence is generally destabilizing. (C) incorrectly attributes the effect to gas friction. (D) is a possible outcome for some bodies but 'stirring' is the more general and primary effect that leads to accretion, ejection, or migration.

Question 9

Imagine a 400-km diameter, fully differentiated asteroid (with an iron core and silicate mantle) is shattered by a hypervelocity impact. Over millions of years, the fragments gravitationally re-accrete to form a new, 300-km body. Which of the following most likely describes the interior of this second-generation object?

  1. A 'brecciated' or 'megarubble' pile, with large, intact chunks of the original iron core and silicate mantle randomly mixed together. (correct answer)
  2. A homogeneous body where the original core and mantle materials have been evenly mixed down to a microscopic level.
  3. A perfectly re-differentiated body, as the fragments would sort by density during the gentle re-accretion process.
  4. An object composed entirely of silicate mantle fragments, as the denser core material would have been ejected at higher speeds.
Explanation: When you encounter questions about asteroid disruption and re-accretion, think about the physical processes involved and the energy scales at play. This tests your understanding of how gravitational differentiation works and under what conditions it can occur. The correct answer is A because re-accretion after catastrophic disruption creates a fundamentally different type of object than the original differentiated asteroid. When fragments slowly drift back together under weak gravitational attraction, they lack the energy needed to melt and re-differentiate. Instead, they simply stick together in whatever configuration they encounter each other, creating a "rubble pile" structure with large chunks of both iron core and silicate mantle material jumbled together throughout the interior. Option B is wrong because complete homogeneous mixing would require enormous energy to break down and redistribute materials at the microscopic level—far more than available during gentle re-accretion. Option C incorrectly assumes that low-velocity re-accretion provides enough gravitational energy to melt the materials and allow density sorting, but a 300-km body's gravity is far too weak for this. Option D misunderstands impact dynamics—while some core material might achieve higher ejection velocities, plenty would remain in the debris field to be incorporated into the new body. Remember that differentiation requires significant heat to melt materials, allowing them to separate by density. Small bodies like asteroids can only achieve this during their initial formation when radioactive heating was available, not during later cold re-accretion events.

Question 10

The planet Uranus has an obliquity (axial tilt) of approximately 98 degrees. Within the framework of planet formation via planetesimal accretion, what is the most plausible explanation for this extreme tilt?

  1. Uranus formed from an unusually turbulent eddy in the solar nebula that had a pre-existing vertical spin.
  2. A strong and prolonged magnetic interaction with Neptune during their formation torqued Uranus onto its side.
  3. The slow, orderly accretion of countless small planetesimals gradually and systematically built up the planet's angular momentum to this state.
  4. A catastrophic, off-center impact with a protoplanet-sized object during the late stages of its formation knocked it over. (correct answer)
Explanation: The default result of accretion from a flattened disk is a planet with a low obliquity, as the random spins of accreting bodies tend to average out, leaving the net angular momentum of the disk. An extreme tilt like that of Uranus is very difficult to explain through gradual processes. The leading hypothesis is that late in its formation, when Uranus was already nearly full-sized, it was struck by another massive object (perhaps Earth-sized or larger). An off-center collision of this magnitude could provide enough torque to drastically alter the planet's spin axis. (A) is unlikely as large-scale eddies are not expected to have such coherent vertical spin. (B) is not a known or plausible mechanism for such a large tilt. (C) is the opposite of what would happen; slow, orderly accretion would lead to a very low obliquity.

Question 11

The Hafnium-182 (¹⁸²Hf) to Tungsten-182 (¹⁸²W) isotopic system is used to date core formation. ¹⁸²Hf is lithophile (rock-loving) and decays to the siderophile (iron-loving) ¹⁸²W with a half-life of 9 million years. If a planetesimal differentiated very early (within a few million years of solar system formation), what isotopic signature would be expected in its mantle material today?

  1. A high abundance of ¹⁸²Hf compared to stable hafnium isotopes.
  2. A ratio of ¹⁸²W to other tungsten isotopes that is identical to that found in its iron core.
  3. A significant excess of ¹⁸²W relative to other tungsten isotopes, compared to undifferentiated meteorites. (correct answer)
  4. A significant deficit of ¹⁸²W relative to other tungsten isotopes, as the ¹⁸²W would have sunk to the core with iron.
Explanation: During differentiation, lithophile ¹⁸²Hf remains in the silicate mantle, while iron and siderophile elements (including stable tungsten) sink to the core. If this separation happens quickly, while ¹⁸²Hf is still abundant, the ¹⁸²Hf is isolated in the mantle. Over time, it decays into ¹⁸²W. This means the ¹⁸²W is formed in situ in the mantle. Consequently, the mantle will show an excess of ¹⁸²W compared to the tungsten isotopes that originally went to the core, and also an excess compared to primitive, undifferentiated material. (A) is incorrect because ¹⁸²Hf has a short half-life and would have completely decayed away. (B) is incorrect because the mantle is where the excess ¹⁸²W is produced. (D) is a classic trap; students might assume the daughter product ¹⁸²W sinks, but its final location is determined by its parent element's chemical affinity at the time of differentiation.

Question 12

During the 'oligarchic growth' stage of planet formation, a few large protoplanets dominate their respective regions of the protoplanetary disk. What is the primary dynamical effect of these oligarchs on the smaller, surrounding planetesimals?

  1. They create stable gravitational pockets that protect the smaller planetesimals from falling into the star.
  2. They gravitationally 'stir' the planetesimal swarm, increasing their random velocities and leading to either accretion or ejection. (correct answer)
  3. They slow down the orbits of nearby planetesimals through gas-dynamic friction, causing them to accumulate in dense rings.
  4. They transfer angular momentum to the planetesimals, causing them to migrate to the outer regions of the solar system.
Explanation: A key feature of the oligarchic growth phase is that the large protoplanets (oligarchs) are massive enough to significantly perturb the orbits of the remaining smaller planetesimals in their 'feeding zone'. This gravitational influence increases the eccentricities and inclinations of the smaller bodies, a process called 'stirring'. This has two main outcomes: some planetesimals are perturbed onto collision courses with the oligarch and are accreted, while others are accelerated to the point where they are ejected from the system entirely. (A) is incorrect; their influence is generally destabilizing. (C) incorrectly attributes the effect to gas friction. (D) is a possible outcome for some bodies but 'stirring' is the more general and primary effect that leads to accretion, ejection, or migration.

Question 13

In the early protoplanetary disk, the growth from meter-sized boulders to kilometer-sized planetesimals faces the 'meter-size barrier,' as gas drag causes these bodies to rapidly spiral into the star. Which of the following is a leading hypothesis for a mechanism that allows this barrier to be overcome?

  1. The development of strong magnetic fields within the boulders, allowing them to repel the nebular gas and slow their inward drift.
  2. The collective gravitational force of boulders becoming strong enough to capture nebular gas, forming a protective envelope.
  3. The concentration of vast numbers of pebble-sized particles in localized regions of high pressure, leading to rapid gravitational collapse into larger bodies. (correct answer)
  4. The melting and subsequent fusing of boulders due to intense radiation from the young central star, creating larger and more stable aggregates.
Explanation: The 'meter-size barrier' is a significant hurdle in accretion models. One of the leading solutions is the idea of particle concentration. Turbulent eddies or pressure bumps in the gas disk can trap vast quantities of smaller, pebble-sized particles. If the density in these traps becomes high enough, their collective gravity can cause them to collapse directly into large (10s to 100s of km) planetesimals, effectively skipping the problematic meter-size stage. (A) is incorrect as magnetic fields are not strong enough in this way. (B) is incorrect as boulders are not massive enough to capture significant gas. (D) is incorrect because stellar radiation would not be sufficient to melt rock at typical planet-forming distances, and this process would be too slow.

Question 14

The Hafnium-182 (¹⁸²Hf) to Tungsten-182 (¹⁸²W) isotopic system is used to date core formation. ¹⁸²Hf is lithophile (rock-loving) and decays to the siderophile (iron-loving) ¹⁸²W with a half-life of 9 million years. If a planetesimal differentiated very early (within a few million years of solar system formation), what isotopic signature would be expected in its mantle material today?

  1. A high abundance of ¹⁸²Hf compared to stable hafnium isotopes.
  2. A ratio of ¹⁸²W to other tungsten isotopes that is identical to that found in its iron core.
  3. A significant excess of ¹⁸²W relative to other tungsten isotopes, compared to undifferentiated meteorites. (correct answer)
  4. A significant deficit of ¹⁸²W relative to other tungsten isotopes, as the ¹⁸²W would have sunk to the core with iron.
Explanation: During differentiation, lithophile ¹⁸²Hf remains in the silicate mantle, while iron and siderophile elements (including stable tungsten) sink to the core. If this separation happens quickly, while ¹⁸²Hf is still abundant, the ¹⁸²Hf is isolated in the mantle. Over time, it decays into ¹⁸²W. This means the ¹⁸²W is formed in situ in the mantle. Consequently, the mantle will show an excess of ¹⁸²W compared to the tungsten isotopes that originally went to the core, and also an excess compared to primitive, undifferentiated material. (A) is incorrect because ¹⁸²Hf has a short half-life and would have completely decayed away. (B) is incorrect because the mantle is where the excess ¹⁸²W is produced. (D) is a classic trap; students might assume the daughter product ¹⁸²W sinks, but its final location is determined by its parent element's chemical affinity at the time of differentiation.

Question 15

According to the giant-impact hypothesis, the Moon formed from the debris of a collision between the proto-Earth and a Mars-sized object. Assuming both bodies had already differentiated, what does this imply about the Moon's expected interior structure and composition?

  1. The Moon should have a very large iron core, formed from the merged cores of both the proto-Earth and the impactor.
  2. The Moon should be largely depleted in iron and other siderophile elements relative to Earth, and have a very small core. (correct answer)
  3. The Moon should be compositionally identical to Earth's mantle, as the impactor was completely vaporized in the collision.
  4. The Moon should show no signs of differentiation itself, being a homogeneous mixture of material from both bodies' crusts.
Explanation: When you encounter questions about planetary formation, focus on how physical processes during collisions affect the distribution of different types of materials, especially metals versus silicates. The giant-impact hypothesis explains that a Mars-sized object called Theia collided with the early Earth. Since both bodies had differentiated, their dense iron cores had already settled to their centers, while lighter silicate materials formed their mantles and crusts. During this catastrophic collision, the cores of both bodies would have merged and remained with Earth due to their high density and the planet's strong gravitational pull. Meanwhile, the impact ejected primarily mantle material—lighter silicate rocks—into orbit around Earth, and this debris eventually coalesced to form the Moon. This process means the Moon formed predominantly from silicate-rich mantle material rather than iron-rich core material. Therefore, option B is correct: the Moon should be depleted in iron and siderophile (iron-loving) elements compared to Earth and have only a very small core. Option A incorrectly assumes the cores would be ejected and incorporated into the Moon, but dense iron would fall back to Earth. Option C is wrong because the Moon isn't identical to Earth's mantle—it also contains some material from Theia's mantle. Option D misunderstands the process: the Moon did differentiate after formation, developing its own small core, mantle, and crust structure. Remember: in planetary collision scenarios, dense materials (like iron) tend to stay with the larger body, while lighter materials (like silicates) are more easily ejected.

Question 16

Imagine a 400-km diameter, fully differentiated asteroid (with an iron core and silicate mantle) is shattered by a hypervelocity impact. Over millions of years, the fragments gravitationally re-accrete to form a new, 300-km body. Which of the following most likely describes the interior of this second-generation object?

  1. A 'brecciated' or 'megarubble' pile, with large, intact chunks of the original iron core and silicate mantle randomly mixed together. (correct answer)
  2. A homogeneous body where the original core and mantle materials have been evenly mixed down to a microscopic level.
  3. A perfectly re-differentiated body, as the fragments would sort by density during the gentle re-accretion process.
  4. An object composed entirely of silicate mantle fragments, as the denser core material would have been ejected at higher speeds.
Explanation: When you encounter questions about asteroid disruption and re-accretion, think about the physical processes involved and the energy scales at play. This tests your understanding of how gravitational differentiation works and under what conditions it can occur. The correct answer is A because re-accretion after catastrophic disruption creates a fundamentally different type of object than the original differentiated asteroid. When fragments slowly drift back together under weak gravitational attraction, they lack the energy needed to melt and re-differentiate. Instead, they simply stick together in whatever configuration they encounter each other, creating a "rubble pile" structure with large chunks of both iron core and silicate mantle material jumbled together throughout the interior. Option B is wrong because complete homogeneous mixing would require enormous energy to break down and redistribute materials at the microscopic level—far more than available during gentle re-accretion. Option C incorrectly assumes that low-velocity re-accretion provides enough gravitational energy to melt the materials and allow density sorting, but a 300-km body's gravity is far too weak for this. Option D misunderstands impact dynamics—while some core material might achieve higher ejection velocities, plenty would remain in the debris field to be incorporated into the new body. Remember that differentiation requires significant heat to melt materials, allowing them to separate by density. Small bodies like asteroids can only achieve this during their initial formation when radioactive heating was available, not during later cold re-accretion events.

Question 17

The transition from gentle sticking of dust grains via electrostatic forces to gravity-dominated accretion of planetesimals is a key step in planet formation. At roughly what size does an object's self-gravity begin to significantly enhance its growth rate by gravitationally focusing other nearby particles?

  1. At the micrometer scale, as soon as dust grains form from the nebula.
  2. At the meter scale, where boulders are large enough to exert a noticeable pull on each other.
  3. At the kilometer scale, where the object can be formally classified as a planetesimal. (correct answer)
  4. At the 1000-kilometer scale, when the object is large enough to be considered a protoplanet.
Explanation: While gravity exists for all objects, it is an extremely weak force. For dust, pebbles, and even boulders, forces like gas drag and electrostatic attraction are much more important for their interactions. It is only when bodies grow to the kilometer scale—the size of planetesimals—that their self-gravity becomes strong enough to significantly perturb the trajectories of nearby objects. This effect, known as gravitational focusing, dramatically increases the planetesimal's effective collision cross-section, causing its growth rate to accelerate (the 'runaway growth' phase). By the protoplanet stage (D), this process is already well-established.

Question 18

Which of the following best describes the key transition between the 'runaway' and 'oligarchic' phases of planetary accretion?

  1. In the runaway phase, accretion is driven by electrostatic forces, which gives way to gravity-dominated accretion in the oligarchic phase.
  2. Runaway growth ceases when the largest protoplanets become massive enough to start accreting large amounts of gas from the solar nebula.
  3. During runaway growth, the largest bodies grow exponentially faster than smaller ones, but this slows in the oligarchic phase as a few dominant bodies gravitationally stir up the remaining planetesimals. (correct answer)
  4. The runaway phase produces a large number of Moon-sized bodies, while the oligarchic phase involves these bodies merging to form the final planets.
Explanation: Runaway growth occurs when the largest planetesimals in a region grow much more rapidly than their smaller neighbors because their gravitational cross-section increases faster than their physical radius. This leads to a single dominant body. The transition to oligarchic growth occurs when a few such large bodies (protoplanets or 'oligarchs') emerge. Their gravity becomes so strong that they no longer just accrete nearby material but also gravitationally excite the remaining planetesimals, increasing their random velocities. This stirring effect slows down the oligarchs' own growth rate and makes it harder for other bodies to grow, ensuring their dominance. (A) is incorrect; gravity is the dominant force in both phases. (B) describes the transition to gas giant formation, which is a separate process. (D) is a reasonable description, but (C) more accurately captures the underlying physical mechanism of gravitational stirring that defines the transition.

Question 19

The presence of a global magnetic field generated by an internal dynamo is a key feature of Earth. The process of differentiation is a necessary, but not sufficient, condition for such a field to exist. Why is differentiation considered a prerequisite?

  1. Differentiation creates a solid, highly magnetic iron core that acts as a permanent bar magnet.
  2. The process of differentiation itself releases charged particles that create powerful, lasting electrical currents in the mantle.
  3. Only a differentiated planet can have a rotation rapid enough to power a magnetic dynamo.
  4. It produces a liquid, electrically conductive outer core where convection, driven by heat flow and influenced by rotation, can generate a magnetic field. (correct answer)
Explanation: A planetary magnetic dynamo requires three ingredients: a fluid (liquid) region, electrical conductivity, and a source of motion (convection and rotation). Differentiation is the process that creates this structure. It forms a dense iron-nickel core, the outer part of which is liquid in Earth's case. This metallic core is electrically conductive. Heat flowing from the solidifying inner core drives convection in the liquid outer core. This motion, coupled with the planet's rotation (Coriolis effect), generates the electrical currents that produce the global magnetic field. (A) is incorrect; the core is too hot to be a permanent magnet (above the Curie point), and the field is generated by moving charges, not static magnetism. (B) misidentifies the location and mechanism of current generation. (C) is incorrect because while rotation is necessary, differentiation is what provides the correct internal structure (the liquid conductive core) for the rotation to act upon.

Question 20

Imagine two large planetesimals that form in the same protoplanetary disk. Planetesimal R forms at 1 AU from the star, and Planetesimal I forms at 5 AU. Both grow to a few hundred kilometers in diameter but do not become full planets. Which statement most accurately contrasts their likely bulk composition?

  1. Planetesimal R would be composed mostly of rock and metal, while Planetesimal I would be composed primarily of rock, metal, and significant amounts of water ice. (correct answer)
  2. Planetesimal R would contain more volatile organic compounds than Planetesimal I, as the higher temperature at 1 AU would drive more complex chemistry.
  3. Both planetesimals would have nearly identical compositions, as the protoplanetary disk is well-mixed, but Planetesimal I would have a thicker crust.
  4. Planetesimal R would be a mix of rock and ice, while Planetesimal I, forming in the colder outer region, would be composed almost purely of various ices.
Explanation: The key factor is the 'frost line' (or snow line), which in our solar system is located between the orbits of Mars and Jupiter. Inside the frost line (like at 1 AU), temperatures are too high for volatile compounds like water, ammonia, and methane to condense into solid ice. Therefore, planetesimals forming there are made of refractory materials: rock (silicates) and metal. Outside the frost line (like at 5 AU), it is cold enough for these ices to form. This means there is much more solid material available for accretion, and the resulting planetesimals are a mixture of rock, metal, and a large fraction of ice. (B) is incorrect; lower temperatures are better for preserving volatile organics. (C) is incorrect because the temperature gradient creates a strong compositional gradient. (D) is incorrect because even in the outer system, rock and metal are present and form a substantial part of planetesimals.