Know that, in comparison to each other, the four planets nearest the Sun are rocky and small and the four planets furthest from the Sun are gaseous and large, and explain this difference by referring to an accretion model for Solar System formation,

6.1.2 The Solar System

Learning Objective

Know that, in comparison to each other, the four planets nearest the Sun are rocky and small and the four planets furthest from the Sun are gaseous and large, and explain this difference by referring to an accretion model for Solar System formation, including:

1. The model’s dependence on gravity.
2. The presence of many elements in interstellar clouds of gas and dust.
3. The rotation of material in the cloud and the formation of an accretion disc.

1. Comparison of Inner and Outer Planets

2. The Accretion Model for Solar System Formation

The accretion model explains how a rotating cloud of interstellar gas and dust (a nebula) collapsed under its own gravity to form the Sun and the planets. The key steps are outlined below.

2.1 Dependence on Gravity

Gravity is the driving force that causes the nebula to contract. As the cloud collapses, the gravitational potential energy is converted into kinetic energy, heating the centre of the cloud. When the central temperature becomes high enough, nuclear fusion ignites, forming the Sun.

Mathematically, the collapse condition can be expressed by the Jeans criterion:

\$ M > MJ = \left(\frac{5kB T}{G \mu m_H}\right)^{3/2} \left(\frac{3}{4\pi\rho}\right)^{1/2} \$

where \$MJ\$ is the Jeans mass, \$T\$ the temperature, \$\rho\$ the density, \$\mu\$ the mean molecular weight, \$kB\$ Boltzmann’s constant, \$G\$ the gravitational constant and \$m_H\$ the mass of a hydrogen atom.

2.2 Presence of Many Elements in the Nebula

The interstellar cloud contains:

• Hydrogen and helium – the most abundant elements, making up \overline{98}% of the mass.
• Heavier elements (often called “metals” in astronomy) such as carbon, oxygen, silicon, iron, etc., locked in dust grains.

These heavier elements are crucial for forming solid particles that can stick together (coagulate) to become planetesimals.

2.3 Rotation and Formation of an Accretion Disc

Even a slight initial rotation of the nebula is conserved as the cloud contracts (conservation of angular momentum). As the radius decreases, the rotation speed increases, flattening the collapsing material into a rotating disc – the accretion disc.

The disc provides a plane in which material can orbit the proto‑Sun and collide gently, allowing growth from dust grains to kilometre‑size planetesimals and eventually to full‑size planets.

2.4 How the Model Explains the Inner–Outer Planet Differences

1. Temperature Gradient: Near the proto‑Sun the disc is hot; volatile gases (hydrogen, helium) cannot condense, leaving only refractory materials (silicates, metals) to form solid bodies. These become the small, rocky inner planets.
2. Mass Accretion: Beyond the “frost line” (≈ 3–4 AU) the disc is cool enough for ices (water, methane, ammonia) to freeze, dramatically increasing the amount of solid material available. Larger planetesimals form quickly and can gravitationally attract surrounding hydrogen and helium, growing into massive gaseous planets.
3. Timescales: The inner region loses gas to the Sun faster, limiting the time available for gas capture. The outer region retains gas longer, allowing the giant planets to accrete massive envelopes.

3. Summary Points

• The four inner planets are small and rocky because they formed in the hot inner disc where only refractory materials could condense.
• The four outer planets are large and gaseous because they formed beyond the frost line where ices and abundant hydrogen/helium could be incorporated.
• Gravity drives the collapse of the interstellar cloud, while the conservation of angular momentum creates a rotating accretion disc.
• The mixture of gases and dust in the nebula provides the raw material for both rocky and gaseous planets.