Accretion Model of Solar System Formation

The Solar System formed from a rotating interstellar cloud of gas and dust containing many elements. Gravity drew the material together. As the cloud contracted, the rotating material formed a flattened accretion disc around the developing Sun.

Within the disc, pieces of material came together and accumulated into progressively larger bodies. This growth by accumulation is called accretion. Some bodies eventually grew into planets.

Temperature and the planets

Conditions in the disc differed with distance from the developing Sun. The inner region was hotter: rocky materials could form solids there, while many volatile substances—materials that readily become gases—remained gaseous. The planets that formed nearest the Sun, Mercury, Venus, Earth and Mars, are comparatively small and rocky.

Farther from the Sun, the disc was cooler. More substances could form solids and accumulate, helping bodies grow larger. These larger bodies could retain substantial amounts of gas and other volatile substances. The outer planets, Jupiter, Saturn, Uranus and Neptune, are therefore comparatively large and rich in gaseous or volatile material.

Planetary Gravitational Field Strength

A planet creates a gravitational field around it. An object with mass placed in this field experiences an attractive force towards the planet.

The gravitational field strength at a position tells us how much gravitational force acts on each kilogram of mass placed there.

Here, $$g$$ is gravitational field strength in newtons per kilogram ($$\mathrm{N/kg}$$), $$F_g$$ is gravitational force in newtons ($$\mathrm{N}$$), and $$m$$ is the object's mass in kilograms ($$\mathrm{kg}$$). A stronger field exerts a greater force on an object of the same mass.

Field strength at a planet’s surface

A planet’s surface field strength depends on both its mass and its radius. If two planets have the same radius, the more massive planet has the stronger surface field. If two planets have the same mass, the one with the larger radius has a weaker surface field because its surface is farther from the planet’s centre.

Field strength with distance

Gravitational field strength decreases as distance from the planet increases. An object farther from the planet therefore experiences a smaller gravitational force than the same object closer to it.

Gravity in Solar Orbits

The Sun contains most of the mass of the Solar System. It exerts a gravitational attraction on planets and other bodies, pulling them towards it.

An orbiting body is also moving sideways relative to the Sun. Without the Sun’s gravity, it would continue in a straight line. Gravity continually pulls the body towards the Sun, changing the direction of its motion and bending its path around the Sun. This attraction provides the force that keeps the body in orbit.

The orbit is determined by both the body’s motion and the Sun’s gravitational attraction. For example, a change in the body’s speed or direction changes the path it follows under gravity.

Light-Travel Time

Light does not travel instantaneously: it takes time to move from one object to another because its speed is finite. The greater the distance light travels at a given speed, the longer its journey takes.

The light-travel time is the distance travelled divided by the speed of light:

Here, $$t$$ is the travel time, $$d$$ is the distance and $$c$$ is the speed of light. In a vacuum, $$c$$ is approximately $$3.0 \times 10^8,\text{m/s}$$.

Calculating light-travel time

Distance and speed must use consistent units. For example, if the speed is in metres per second, express the distance in metres. The calculated time will then be in seconds and can be converted to minutes or hours if that is more convenient.

Suppose light travels approximately $$1.5 \times 10^8,\text{km}$$ from the Sun to Earth. Converting the distance to metres gives $$1.5 \times 10^{11},\text{m}$$. Using the speed of light in a vacuum:

There are $$60$$ seconds in a minute, so $$500,\text{s}$$ is 8 minutes 20 seconds. This is the approximate time sunlight takes to reach Earth.

Elliptical Solar Orbits

Planets, minor planets and comets travel around the Sun in elliptical orbits. An ellipse is an oval shape with two special points inside it, called foci. The Sun lies at one focus, not at the centre of the ellipse. This means that the object's distance from the Sun changes as it travels around its orbit.

Some ellipses are close to circular. For an approximately circular orbit, the two foci are close together, so the Sun is approximately at the centre.

Speed and energy in an elliptical orbit

An orbiting object moves faster when it is closer to the Sun and slower when it is farther away. As the object approaches the Sun, gravity accelerates it: its gravitational potential energy decreases and its kinetic energy increases.

As the object moves away from the Sun, the reverse happens. It slows down, so its kinetic energy decreases while its gravitational potential energy increases. Energy is transferred between these two stores; the object's total energy remains conserved.

Planetary Orbital Speed and Distance

The Sun’s gravitational field is weaker at greater distances. This means that the Sun exerts less gravitational force on each kilogram of a planet farther away, giving it a smaller acceleration towards the Sun.

For a nearly circular orbit, the Sun’s gravity provides the inward acceleration that keeps a planet moving around it. Planets farther from the Sun move along their orbits at lower orbital speeds than planets nearer to it.

Orbital speed describes how fast a planet travels along its path. It is different from orbital period, which is the time taken to complete one orbit. A more distant planet has a larger orbit to travel around and moves more slowly, so it takes longer to complete an orbit.