Gravity and the Solar System

Weight is the force of gravity on an object, and it is calculated from the mass and the gravitational field strength where the object is:

weight (N) = mass (kg) × gravitational field strength (N/kg)

Mass is a property of the object and never changes. Gravitational field strength depends entirely on where you are, so weight changes with it. An astronaut of mass 75 kg has a mass of 75 kg on the Moon as well — what changes is that they weigh about a sixth as much.

The value of g at the surface of a body depends on two things: the mass of that body and its radius. A more massive body pulls harder, and a larger radius puts the surface further from the centre, which weakens the pull. That is why Mars, which is smaller and less massive than Earth, has a surface g of about 3.7 N/kg, and why Jupiter's is around 25 N/kg.

The value also falls with height above a surface, because the distance from the centre of the body is what matters. At the height of a low orbit the change is small — which is worth knowing, because astronauts on a space station are not weightless because gravity has stopped; they are in free fall around the Earth along with their spacecraft.

Within our solar system there is one star, the Sun, plus the eight planets and the dwarf planets that orbit around the Sun. Natural satellites — the moons that orbit planets — are also part of the solar system.

Our solar system is a small part of the Milky Way galaxy.

The Sun was formed from a cloud of dust and gas, a nebula, pulled together by gravitational attraction.

You should be able to explain how, at the start of a star's life cycle, the dust and gas drawn together by gravity causes fusion reactions.

As gravity pulls the nebula together, the material becomes more and more tightly packed. That compression raises the temperature and the pressure at the centre enormously. Eventually they become high enough for hydrogen nuclei to fuse together, and the star begins to shine.

You should also be able to explain that fusion reactions lead to an equilibrium between the gravitational collapse of a star and the expansion of a star due to fusion energy.

That equilibrium is what makes a star stable for billions of years. Gravity pulls everything inwards, and the energy released by fusion pushes outwards. While the two are balanced the star neither collapses nor expands — and it is when the fuel for fusion runs low that the balance is lost and the star changes.

Gravity provides the force that allows planets and satellites, both natural and artificial, to maintain their circular orbits.

You should be able to describe the similarities and distinctions between the planets, their moons, and artificial satellites.

Higher tier students should be able to explain qualitatively how, for circular orbits, the force of gravity can lead to changing velocity but unchanged speed, and how, for a stable orbit, the radius must change if the speed changes.

Changing velocity at constant speed: gravity acts towards the centre of the orbit, which is at right angles to the direction the satellite is travelling. A force at right angles to the motion changes the direction of travel but not how fast the object is going. Since velocity includes direction, the velocity is changing continuously even though the speed is constant — and a changing velocity means the satellite is accelerating, which is exactly what a resultant force must produce. This is the circular motion idea applied to orbits.

Why the radius must change if the speed changes: for a stable orbit the gravitational force must exactly match what is needed to keep the satellite turning in that circle. If the satellite moves faster, gravity at that radius is no longer enough to hold it in, so it moves outwards — but gravity is weaker further away, so a stable orbit at a higher speed is impossible at a larger radius. Working it through the other way gives the rule to remember: a satellite in a smaller orbit must travel faster, and one in a larger orbit travels more slowly.

That is why a low-orbit satellite circles the Earth in about ninety minutes, while the Moon, far further out, takes about a month.