Orbits

What this lesson covers in the specification

Incandio is aligned to this specification. It is not published by, endorsed by or affiliated with Pearson, and it reproduces none of Pearson's wording — the statement numbers are given so you can check every lesson against your own copy.

• 8.4 — Gravitational force causes moons, planets, satellites and comets to orbit
• 8.5 — The differences in the orbits of comets, moons and planets
• 8.6 — Use orbital speed = 2πr ÷ T

1 · Understand it

No exam language yet. The only question this section answers is: do I actually understand what is happening?

An object moving in a circle is CHANGING DIRECTION all the time. Changing direction is a change of velocity, and a change of velocity is an acceleration — even if the speed never varies at all. An acceleration requires a force. So anything in orbit must have a force acting on it, and that force is GRAVITY, acting towards the centre of the orbit.

This is the whole of statement 8.4, and it is worth reading twice because it inverts the intuitive picture. An orbiting satellite is not sitting still in space with gravity switched off; it is being pulled towards the Earth constantly, and is constantly falling. What stops it landing is that it is also moving sideways fast enough that the ground curves away beneath it just as fast as it falls.

Think of it like a cannonball fired harder and harder from a mountain

Fire a cannonball horizontally from a mountain top and it curves down and lands some distance away. Fire it harder and it lands further off. Keep increasing the speed and eventually you reach a point where the curve of its fall exactly matches the curve of the Earth — it falls, and falls, and never gets any closer to the ground, because the ground keeps dropping away underneath it at the same rate. It is now in orbit. Nothing about gravity changed at any point in that sequence; the only thing that changed was the sideways speed. This is why an astronaut floats: not because gravity has stopped, but because they and their spacecraft are falling together.

Why a comet speeds up and slows down — statement 8.5

1. A comet's orbit is very elongated, so its distance from the Sun changes enormously — from inside the orbit of the Earth out beyond the outer planets.
2. Gravity is stronger when the comet is CLOSER to the Sun and much weaker when it is far away.
3. As the comet falls inwards it is pulled by an increasingly strong force in roughly the direction it is travelling, so it SPEEDS UP, moving fastest at its closest approach.
4. As it swings away again the force acts against its motion, so it SLOWS DOWN, moving slowest at its most distant point.
5. A planet's orbit is nearly circular, so its distance from the Sun barely changes and its speed is very nearly constant.
6. This is why a comet is visible for only a short period out of an orbit lasting decades or centuries: it spends almost all of its time in the slow, distant part.

So the three kinds of orbit named by the specification differ mainly in SHAPE. A MOON orbits a planet, in a roughly circular orbit. A PLANET orbits a star, also in a roughly circular orbit — slightly elliptical, but close enough to circular that the speed hardly varies. A COMET orbits a star in a highly elliptical orbit, with a period that can be decades or thousands of years, and a speed that varies dramatically. Artificial SATELLITES orbit the Earth, in whatever orbit they are put into for the job they do.

The orbital speed comes from a simple observation: in one complete orbit the object travels once around the circle, and the distance around a circle of radius r is 2πr. If the time for one orbit — the ORBITAL PERIOD, T — is known, then the speed is that distance divided by that time. ORBITAL SPEED = 2πr ÷ T.

An orbital speed, with the unit conversion that decides it

A satellite orbits at a radius of 7000 km from the Earth's centre, taking 97 minutes to complete one orbit. Calculate its orbital speed in m/s.

1. Convert the radius to metres: 7000 km = 7 000 000 m.
2. Convert the period to seconds: 97 minutes = 97 × 60 = 5820 s.
3. Circumference = 2πr = 2 × π × 7 000 000 = 43 980 000 m.
4. Orbital speed = 43 980 000 ÷ 5820 = 7557 m/s, about 7600 m/s.
5. That is roughly 27 000 km per hour, which is what it takes to keep falling and keep missing.

Answer: About 7600 m/s — and both conversions had to be done before the division.

Both conversions in that example are where marks are lost. The radius is almost always quoted in kilometres and the period in hours, minutes or days, so both must be converted before dividing if the answer is wanted in metres per second. It is also worth noticing that r is measured from the CENTRE of the body being orbited, not from its surface — a satellite 600 km above the Earth has an orbital radius of about 7000 km, because the Earth's radius of 6400 km has to be added.

One last relationship worth carrying. The further out an orbit is, the SLOWER the orbiting body moves and the LONGER its period. Mercury takes 88 days to go round the Sun and Neptune takes 165 years, and that is not only because Neptune's path is longer — it is genuinely travelling more slowly, because gravity is weaker that far out and less speed is needed to stay in orbit.

2 · Grade 9 Notes

A different job from the section above. You have already understood it; this is the precise set of things to LEARN — definitions to reproduce word for word, processes in order, equations with units, and the answers that score full marks.

orbital speed = 2πr ÷ T

orbital speed in metres per second (m/s), r is the orbital radius in metres (m) measured from the CENTRE of the body being orbited, T is the orbital period in seconds (s)

Units: m/s, m, s. 2πr is the circumference of the orbit — the distance travelled in one complete revolution.

Learn this definition · Orbital period

The time taken for one complete orbit. It must be converted into seconds before being used in the orbital-speed equation.

Calculating an orbital speed

1. Convert the orbital radius to metres — it is usually given in kilometres.
2. If the height above a surface is given, ADD the radius of the body to get the orbital radius from its centre.
3. Convert the period to seconds — it is usually given in hours, minutes or days.
4. Work out the circumference, 2πr.
5. Divide the circumference by the period.

The vocabulary of an orbit

Orbital radius

The distance from the CENTRE of the body being orbited. Add the body's radius to any height given above its surface.

Satellite

Any body in orbit around another. A moon is a natural satellite; the rest are artificial.

Comet

A body orbiting a star on a highly elliptical path, so its distance and speed vary enormously during one orbit.

Statement 8.5 — how the orbits differ

Why anything orbits at all — statement 8.4

• Moving in a circle means CONSTANTLY CHANGING DIRECTION, which is an acceleration even at constant speed
• An acceleration requires a force, and that force is GRAVITY, acting towards the centre of the orbit
• An orbiting body is therefore FALLING, but moving sideways fast enough that the surface curves away as fast as it falls
• Astronauts float because they are falling with their spacecraft, NOT because gravity is absent
• The further out the orbit, the SLOWER the speed and the LONGER the period

Model answer [4 marks]

A moon orbits a planet at a radius of 400 000 km with a period of 27 days. Calculate its orbital speed in m/s. [4]

Convert the radius: 400 000 km = 400 000 000 m. Convert the period: 27 days = 27 × 24 × 60 × 60 = 2 332 800 s. The circumference is 2πr = 2 × π × 400 000 000 = 2 513 000 000 m. The orbital speed is 2 513 000 000 ÷ 2 332 800 = 1077 m/s, or about 1100 m/s.

Model answer [4 marks]

Explain why a comet travels much faster when it is close to the Sun than when it is far away. [4]

A comet's orbit is highly elliptical, so its distance from the Sun changes enormously during one orbit. The gravitational force on the comet is much stronger when it is close to the Sun and much weaker when it is far away. As the comet moves inwards towards the Sun, the gravitational force acts broadly in the direction it is travelling, so the comet accelerates and reaches its greatest speed at its closest approach. As it moves outwards again the force acts against its motion, so it decelerates and is slowest at its most distant point.

Not this: There is no gravity in space, which is why astronauts float.

This: Gravity is precisely what keeps them in orbit — without it they would fly off in a straight line. They float because they and their spacecraft are FALLING TOGETHER, moving sideways fast enough that the Earth curves away beneath them as fast as they fall.

Mark-losing trap. Orbital radius is measured from the CENTRE of the body, so add its radius to any height given.

Mark-losing trap. Convert BOTH: kilometres to metres and the period to seconds, before dividing.

Mark-losing trap. An orbiting body accelerates even at constant speed, because its DIRECTION is always changing.

Mark-losing trap. Further out means SLOWER and a LONGER period — not faster.

3 · Prove it — the five questions

The five questions climb Grade 6 → Grade 7 → Grade 8 → Grade 9 → Grade 9 challenge, and are marked inside Incandio on your own device, by rule, with an authored diagnosis of the mistake you actually made. The mark schemes stay in the app so that the practice is worth doing; the questions themselves are here.

1. Grade 6 · State [1 mark] — What provides the force that keeps a planet in orbit around the Sun?
2. Grade 7 · Explain [3 marks] — A satellite moves around the Earth at a constant speed. Explain why it is nevertheless accelerating.
3. Grade 8 · Calculate [4 marks] — A satellite orbits at a radius of 8000 km with a period of 2.0 hours. Calculate its orbital speed in m/s.
4. Grade 9 · Explain [6 marks] — Select every statement that belongs in a full-mark explanation of why a comet's speed varies so much during its orbit while a planet's barely changes.
5. 9+ · Analyse [6 marks] — A student proposes that a satellite could be made to orbit closer to the Earth without changing its speed, simply by firing a small thruster continuously towards the Earth to 'hold it down' at the lower altitude. Select every statement that belongs in a full-mark analysis.

The people behind this science

Two ways into the same idea — the one who gave up the circle after eight years of arithmetic, and the one who explained why Kepler's rules had to be true. Inside Incandio each of them answers knowing exactly which lesson you have just finished.

Johannes Kepler — the one who gave up the circle after eight years of arithmetic

Statement 8.5 depends on orbits being ellipses rather than circles, and that took Kepler about eight years of calculation on Tycho Brahe's observations of Mars to accept. He began convinced, as everyone was, that heavenly motion must be built from perfect circles, and his best circular model fitted the data to within eight minutes of arc — an error most astronomers would have shrugged off. He refused to, on the grounds that Tycho's measurements were better than that, and followed the discrepancy until it destroyed the assumption he had started with. He is the right person to ask what it costs to trust a small disagreement.

• “Why did you give up on circular orbits?”
• “What was the eight minutes of arc that would not go away?”
• “Why does a planet move faster when it is nearer the Sun?”
• “How long did the calculations actually take?”
• “What did Tycho Brahe's observations give you?”

Isaac Newton — the one who explained why Kepler's rules had to be true

Kepler found the shapes of the orbits; Newton showed WHY they had to be those shapes, deriving them from one law of gravitation together with his laws of motion. The cannonball picture in this lesson is his own, from a thought experiment he published to explain that an orbit is nothing but a projectile falling and continually missing. He is the right second figure here because the analogy on this page is his, and because the move he made — deriving a set of observed rules from a deeper principle — is what changed the subject.

• “How is an orbit the same thing as falling?”
• “What happens if the cannonball is fired even faster?”
• “How did you get Kepler's rules out of your law of gravity?”
• “Why does an object in orbit accelerate when its speed is constant?”
• “What would happen to the Moon if gravity stopped?”

Then defend it

On Incandio a lesson is not finished when the questions come out right. You teach the idea back to Ember, an AI apprentice who asks the awkward question, and then you argue it against Johannes Kepler in a structured debate marked against descriptors you can read before you enter. Learn it, teach it, then defend it — all three happen on this page once the app loads.

Carry on through the course

• Previous lesson: The Universe and Gravity
• Next lesson: Star Colour and Temperature
• The Universe and Gravity — From a moon to the whole universe in five steps, and why your weight would change on the way.
• Star Colour and Temperature — Why blue stars are the hot ones, and how a colour tells you a temperature across the whole galaxy.
• The Life Cycle of Stars — Two endings from one beginning — and the mass a star is born with decides which it gets.
• The Hertzsprung–Russell Diagram — Plot every star by colour and true brightness and they do not scatter — they fall into groups.
• The Big Bang and its Evidence — Two observations that between them decided how the universe began.
• All of Physics · Incandio Science