(b) Motion in the universe
- Syllabus
- 2024
- Topic
- —
- Level
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Learning objectives
8.2Universe, galaxies and solar systemKnow that:• the universe is a large collection of billions of galaxies• a galaxy is a large collection of billions of stars• our solar system is in the Milky Way galaxy8.3Gravitational field strengthUnderstand why gravitational field strength, g, varies and know that it is different on other planets and the Moon from that on the Earth8.4Gravity and orbitsExplain that gravitational force:• causes moons to orbit planets• causes the planets to orbit the Sun• causes artificial satellites to orbit the Earth• causes comets to orbit the Sun8.5Orbits of comets, moons and planetsDescribe the differences in the orbits of comets, moons and planets8.6Orbital speed equationUse orbital speed = 2π × orbital radius ÷ time period, v = 2πr/T.
Place the Solar System in the universe
The universe is the largest structure in this hierarchy: it contains billions of galaxies. Each galaxy is itself a collection of billions of stars.
| Structure | What it contains or where it belongs |
|---|---|
| universe | billions of galaxies |
| galaxy | billions of stars |
| Milky Way galaxy | the galaxy that contains our Solar System |
| Solar System | the Sun together with the objects that orbit it, including planets and their moons |
Read the containment chain from small to large: Earth is a planet in the Solar System; the Solar System is in the Milky Way galaxy; the Milky Way is one of the billions of galaxies in the universe.
The Solar System is not a galaxy, and the Milky Way is not the universe. A galaxy contains billions of stars, whereas the Solar System is organised around one star—the Sun.
Explain why gravitational field strength varies
Gravitational field strength, g, is the gravitational force acting per kilogram of mass at a position. It is measured in N/kg and is not the same everywhere.
A more massive planet produces a stronger gravitational field, while the field becomes weaker farther from the planet's centre. Surface gravitational field strength therefore depends on both the planet's mass and the distance from its centre to its surface. Different planets and moons have different masses and sizes, so their surface values of g differ.
At Earth's surface, g is about 10 N/kg; at the Moon's surface it is about 1.7 N/kg. The Moon's much smaller mass is the main reason its surface gravitational field is weaker.
A body's atmosphere or its distance from the Sun does not by itself set its surface g. Also distinguish field strength from force: g describes force per kilogram at a position, while the force on a particular object also depends on that object's mass.
Explain how gravity keeps objects in orbit
An orbit needs a force directed inward towards the object being orbited. In astronomical orbits, gravity supplies this inward force.
An orbiting object is moving forwards, but gravity continually changes the direction of its velocity towards the central body. The combination produces a curved path around that body. Without the inward gravitational force, the object would continue along a straight-line path rather than remain in orbit.
| Orbiting object | Central body attracting it |
|---|---|
| moon | planet |
| planet | Sun |
| artificial satellite | Earth |
| comet | Sun |
Gravity does not push an object forwards around its orbit; it pulls inward and changes the direction of motion. ‘Gravitational field strength’ describes a field at a position, whereas ‘gravitational force’ is the force that acts on the orbiting object.
Compare the orbits of moons, planets and comets
Moons, planets and comets all follow gravitational orbits, but they differ in what they orbit and in the shape and motion of their paths.
| Object | Usually orbits | Typical path | Distance and speed during one orbit |
|---|---|---|---|
| moon | a planet | nearly circular | distance from the planet and speed are approximately constant |
| planet | the Sun | nearly circular | orbital radius and speed are approximately constant |
| comet | the Sun | much more elliptical | distance and speed vary; it moves fastest when closest to the Sun |
A comet's strongly elliptical path takes it through a wide range of distances from the Sun. Its speed changes along the path, unlike the approximately steady speed of a moon or planet in a nearly circular orbit.
‘Elliptical’ does not mean that only comets have ellipses: circles are a special case of ellipses, and real planetary and lunar orbits are slightly elliptical. The useful comparison is that comet orbits are usually far more elongated.
Calculate orbital speed, radius or period
For an approximately circular orbit, mean orbital speed equals the circumference of the orbit divided by the time for one complete orbit.
v=\frac{2\pi r}{T}
v is orbital speed, r is orbital radius measured from the centre of the orbit, and T is the time period for one orbit. Rearrangements are T=2πr/v and r=vT/(2π). Use compatible units: metres with m/s, kilometres with km/s, and convert the period to seconds when speed is per second.
Example: a satellite has orbital radius 7100 km and period 5800 s. v=(2π×7100)/5800=7.69 km/s, so its orbital speed is about 7.7 km/s.
Use orbital radius, not height above a planet's surface and not the diameter. The equation uses the length 2πr of one circular orbit; it gives a mean speed and does not describe the changing instantaneous speed of a comet on a strongly elliptical path.