Question

Difficulty: MediumComparing and Contrasting Models

### The Formation of the Asteroid Belt

The asteroid belt, located between Mars and Jupiter, contains millions of rocky and metallic bodies. However, its total mass is only about 0.05%0.05\% of Earth's mass. Astronomers have proposed competing models to explain the origin and low mass of the asteroid belt.

#### Model 1 (The Grand Tack Model)
Model 1 proposes that the asteroid belt region initially contained a high density of planetesimals, totaling several Earth masses. Shortly after its formation, Jupiter migrated inward from its birth orbit toward the Sun, reaching a distance of 1.5 AU1.5\text{ AU} (near Mars's current orbit). As Jupiter migrated, its strong gravitational influence scattered approximately 99.9%99.9\% of the planetesimals out of the region. Jupiter then migrated back outward to its current orbit. The remaining 0.1%0.1\% of the original planetesimals, along with some outer solar system material swept up during Jupiter's return, formed the current asteroid belt.

#### Model 2 (The Low-Mass Disk Model)
Model 2 proposes that the region of the asteroid belt was initially almost empty, containing very little mass due to a physical gap in the early protoplanetary dust disk. As the terrestrial planets (such as Earth and Mars) and the giant planets (such as Jupiter and Saturn) grew, their gravitational interactions scattered nearby leftover planetesimals. Some planetesimals from the inner solar system (silicate-rich) and others from the outer solar system (carbon-rich) were thrown into the gap. These scattered bodies became gravitationally trapped in stable orbits, creating the modern asteroid belt. In Model 2, the giant planets did not undergo large-scale orbital migrations through the inner solar system.

According to the models, which of the following statements describes an assumption about the initial mass of the asteroid belt region that is made by Model 1 but NOT by Model 2?

  1. The region currently occupied by the asteroid belt originally contained several Earth masses of planetesimals.Answer
  2. B
    The region currently occupied by the asteroid belt was initially almost empty and gained mass only through the scattering of planetesimals by growing planets.
  3. C
    The region currently occupied by the asteroid belt was always dominated by carbon-rich planetesimals from the outer solar system.
  4. D
    The gravitational influence of growing planets was responsible for clearing out 99.9%99.9\% of the planetesimals from the region.

Answer

The correct answer is the statement that the region currently occupied by the asteroid belt originally contained several Earth masses of planetesimals.
The correct option is correct because Model 1 explicitly states that the asteroid belt region originally contained a high density of planetesimals totaling several Earth masses. In contrast, Model 2 proposes that the region was initially almost empty due to a physical gap in the disk, meaning the assumption of a high initial mass belongs only to Model 1.

Step-by-Step Solution

1
Identify the initial mass of the asteroid belt region according to Model 1.
Model 1 states that the region initially contained a high density of planetesimals, totaling several Earth masses.
Establishing the starting condition of Model 1 allows for comparison with Model 2.
2
Identify the initial mass of the asteroid belt region according to Model 2.
Model 2 states that the region was initially almost empty, containing very little mass due to a gap in the disk.
Establishing the starting condition of Model 2 allows us to determine what is unique to Model 1.
3
Compare the two starting conditions to identify the unique assumption of Model 1.
Model 1 assumes a high initial mass (several Earth masses), whereas Model 2 assumes a low initial mass (almost empty).
This direct comparison reveals that assuming the region originally had several Earth masses of material is unique to Model 1.

Key Concept

Comparing and Contrasting Models
Estimated Time:1m 30s
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