Edexcel IGCSE Physics 8(b) Motion in the Universe — Notes
Written for Pearson Edexcel International GCSE Physics (4PH1), Science Double Award (4SD0) and Science Single Award (4SS0), linear and modular. This page also covers the 8(a) units for Topic 8.
Which parts do I need?
Single Award candidates can skip every section tagged Double · Physics. On this page that is only the orbital speed equation \(v=\dfrac{2\pi r}{T}\) and the calculations that use it. Nothing on this page is Physics-only.
What this page covers
| Spec | Modular no. | You need to be able to… | Route |
|---|---|---|---|
| 8.1 | 9.1 | work in kg, m, m/s, m/s², N, s and N/kg | Single · Double · Physics |
| 8.2 | 9.2 | state how stars, galaxies, the Milky Way and the universe are related | Single · Double · Physics |
| 8.3 | 9.3 | explain why g is not the same everywhere, and that it has different values on the Moon and other planets | Single · Double · Physics |
| 8.4 | 9.4 | explain that gravity is the force that keeps moons, planets, satellites and comets in orbit | Single · Double · Physics |
| 8.5 | 9.5 | compare the orbits of comets, moons and planets | Single · Double · Physics |
| 8.6 | 9.6 | calculate with orbital speed = 2π × orbital radius ÷ time period | Double · Physics |
Modular candidates: Astrophysics is topic 9 in the modular specifications — these are statements 9.1–9.6 of 4XPH1 Unit 2 (4WPH2) and 4XSD1 Physics Unit 6 (4WSD6).
In one minute
- The universe is a huge collection of billions of galaxies; each galaxy is a collection of billions of stars. Our solar system is in the Milky Way galaxy.
- Gravitational field strength, g, depends on the mass of the planet or moon and on how far you are from its centre, so it is different on the Moon (about 1.6 N/kg) and on other planets.
- Gravitational force keeps moons in orbit around planets, planets and comets in orbit around the Sun, and artificial satellites in orbit around the Earth. The force always pulls towards the body being orbited.
- Planets and moons have nearly circular orbits; comets have very elongated (elliptical) orbits and move fastest when closest to the Sun.
- Orbital speed: \(v=\dfrac{2\pi r}{T}\), where \(r\) is the orbital radius and \(T\) the time for one orbit. Double · Physics
Which units do I need for Topic 8? Single · Double · Physics
Astrophysics uses the same units as forces and motion. Astronomical numbers are very large, so be ready to write them in standard form, for example 384 000 km = 3.84 × 108 m.
| Quantity | Unit | Symbol |
|---|---|---|
| mass | kilogram | kg |
| distance, orbital radius | metre | m |
| time, time period | second | s |
| speed, orbital speed | metre/second | m/s |
| acceleration | metre/second² | m/s² |
| force, weight | newton | N |
| gravitational field strength | newton/kilogram | N/kg |
- Convert before you substitute. km to m (× 1000), minutes to s (× 60), hours to s (× 3600), days to s (× 86 400).
- Examples: 7.5 km/s = 7500 m/s; 90 minutes = 5400 s; 1 day = 24 × 3600 = 86 400 s.
- Orbital periods are often given in days or years. If the question asks for the speed in m/s, the period must be in seconds.
How are stars, galaxies and the universe related? Single · Double · Physics
You need to know three facts, and the order of size they put things in.
- Our solar system is the Sun and everything that orbits it: planets and their moons, dwarf planets, asteroids and comets.
- The Sun is one star among billions in the Milky Way. The stars you see at night are all in the Milky Way.
- Order of size, smallest first: planet → solar system → galaxy → universe.
- Do not mix up “solar system” and “galaxy”. A solar system has one star; a galaxy has billions.
Why is gravitational field strength different on the Moon and other planets? Single · Double · Physics
From 1(c) you know that weight = mass × gravitational field strength, \(W=m\times g\). On Earth, Pearson papers say “assume g = 10 N/kg”; the more precise value 9.8 N/kg is also accepted. The value of g depends on two things:
- The mass of the planet or moon. A body with more mass pulls harder on each kilogram near it, so g is larger.
- The distance from its centre. The further you are from the centre, the weaker the pull, so g is smaller. A planet with a large radius has its surface far from its centre, which reduces g at the surface.
So g is about 1.6 N/kg on the Moon, which has a much smaller mass than the Earth. Jupiter has about 318 times the Earth's mass, but its radius is about 11 times larger, so its g is only about 2.5 times the Earth's.
- Mass does not change from place to place — it is the amount of matter. Weight changes, because g changes.
- A smaller g means a smaller weight: an astronaut on the Moon can jump higher and lift heavier objects than on Earth.
Beyond the specification — not examined
g also gets smaller as you go higher above the Earth, but only slowly: at the height of a typical space station (about 400 km) it is still about 8.7 N/kg, roughly 90 % of its surface value. So astronauts in orbit do not float because “there is no gravity in space” — gravity is what keeps them and their spacecraft in orbit; they are falling around the Earth together. You will not be asked for values of g at a height.
An astronaut has a mass of 75 kg. Calculate her weight (a) on Earth, (b) on the Moon, where g = 1.6 N/kg, and (c) on Mars, where g = 3.7 N/kg. (d) State her mass on Mars.
(a) \(W=m\times g=75\times10=\) 750 N
(b) \(W=75\times1.6=\) 120 N
(c) \(W=75\times3.7=277.5=\) 280 N (2 significant figures, like the data)
(d) 75 kg — mass is the same everywhere.
What keeps moons, planets, satellites and comets in orbit? Single · Double · Physics
An orbit is the curved path of one body around another. Every orbit in the specification is caused by the same force: gravitational attraction between the two bodies.
| Orbiting body | Orbits around | Force that keeps it in orbit |
|---|---|---|
| moon (for example, the Moon) | a planet (the Earth) | gravitational force of the planet on the moon |
| planet | the Sun | gravitational force of the Sun on the planet |
| artificial satellite | the Earth | gravitational force of the Earth on the satellite |
| comet | the Sun | gravitational force of the Sun on the comet |
- Without gravity, the satellite would carry on in a straight line at constant speed (Newton's first law).
- The gravitational force acts towards the centre of the body being orbited. It keeps pulling the satellite off its straight-line path, so the path curves into an orbit.
- The velocity keeps changing direction, so a body in a circular orbit is accelerating even though its speed is constant. That is why there must be a resultant force on it.
- The force is attractive and acts on both bodies: the Earth pulls the Moon, and the Moon pulls the Earth with an equal and opposite force.
How are the orbits of comets, moons and planets different? Single · Double · Physics
| Planets | Moons | Comets | |
|---|---|---|---|
| Orbit around | the Sun | a planet | the Sun |
| Shape of orbit | nearly circular (slightly elliptical) | nearly circular | highly elliptical — very elongated |
| Position of the Sun (or planet) | close to the centre of the orbit | planet close to the centre | Sun near one end, not at the centre |
| Speed during the orbit | nearly constant | nearly constant | changes a lot: fastest near the Sun, slowest far away |
| Time period | from about 88 days to about 165 years | the Moon: about 27 days | from a few years to thousands of years |
- The orbits of the planets lie roughly in the same plane. Many comet orbits are tilted at large angles to this plane.
Describe two differences between the orbit of a comet and the orbit of a planet around the Sun. (2 marks)
Any two of:
- a comet's orbit is highly elliptical / elongated, but a planet's orbit is nearly circular;
- a comet's speed changes greatly — fastest when it is closest to the Sun — but a planet's speed is nearly constant;
- the Sun is near one end of a comet's orbit, but near the centre of a planet's orbit;
- a comet's orbit is often in a different plane from the planets' orbits.
“A comet goes round the Sun and so does a planet” is a similarity, not a difference — it scores nothing.
How do you calculate orbital speed? Double · Physics
Not required for Single Award (4SS0).
In one orbit, a body travels once around a circle. The distance is the circumference, \(2\pi r\), and the time is the time period, \(T\). Speed = distance ÷ time, so:
\[ \text{orbital speed}=\frac{2\times\pi\times\text{orbital radius}}{\text{time period}}\qquad v=\frac{2\times\pi\times r}{T} \]- \(v\) = orbital speed (m/s), \(r\) = orbital radius (m), \(T\) = time period, the time for one complete orbit (s).
- The orbital radius is measured from the centre of the body being orbited. If a question gives the height of a satellite above the surface, add the radius of the planet.
- The equation assumes a circular orbit at constant speed, so it works well for planets, moons and satellites but not for comets.
- Rearranged: \(T=\dfrac{2\pi r}{v}\) and \(r=\dfrac{vT}{2\pi}\).
The Earth orbits the Sun once every 365 days at an orbital radius of 1.50 × 1011 m. Calculate the orbital speed of the Earth.
Convert the period: \(T=365\times86\,400=3.15\times10^{7}\ \text{s}\) (31 536 000 s).
\(v=\dfrac{2\pi r}{T}=\dfrac{2\times\pi\times1.50\times10^{11}}{31\,536\,000}=29\,886\ \text{m/s}=\) 29 900 m/s (about 30 km/s)
Leaving the period in days gives 2.58 × 109 “m/s” — faster than light, which is a clear sign of a missing conversion.
A weather satellite orbits at a height of 850 km above the Earth's surface. It takes 102 minutes to complete one orbit. The radius of the Earth is 6370 km. Calculate the orbital speed of the satellite.
Orbital radius from the centre of the Earth: \(r=6370+850=7220\ \text{km}=7.22\times10^{6}\ \text{m}\).
Period: \(T=102\times60=6120\ \text{s}\).
\(v=\dfrac{2\times\pi\times7.22\times10^{6}}{6120}=7412\ \text{m/s}=\) 7410 m/s (7.41 km/s)
Using r = 850 km (the height only) gives 873 m/s — the most common error in this type of question.
A communications satellite moves at a constant speed of 3.07 km/s and completes one orbit every 24.0 hours. (a) Calculate its orbital radius. (b) The radius of the Earth is 6.37 × 106 m. Calculate the height of the satellite above the Earth's surface.
(a) \(v=3070\ \text{m/s}\); \(T=24.0\times3600=86\,400\ \text{s}\).
\(r=\dfrac{vT}{2\pi}=\dfrac{3070\times86\,400}{2\times\pi}=4.2216\times10^{7}\ \text{m}=\) 4.22 × 107 m
(b) height = \(4.22\times10^{7}-6.37\times10^{6}=3.583\times10^{7}\ \text{m}=\) 3.58 × 107 m (about 35 800 km)
Exam tips for 8(b)
When asked which force keeps a body in orbit, write “gravitational force” or “gravity”, and say what it pulls towards (“towards the Sun”). “Centrifugal force”, “a forward force” or “magnetism” score nothing.
To explain why g is different on another planet, refer to both its mass and its radius (distance from its centre). “The Moon is smaller” is too vague: say it has a smaller mass.
In a “describe the differences” question, make each point a comparison: “a comet's orbit is very elliptical but a planet's is nearly circular”. A statement about only one of the bodies may not be credited.
In \(v=\dfrac{2\pi r}{T}\), r is measured from the centre of the planet. Add the planet's radius to any height above the surface before substituting.
Satellites close to the Earth move at about 7–8 km/s; the Moon at about 1 km/s; the Earth around the Sun at about 30 km/s. An answer wildly different from these usually means a unit conversion has been missed.
Common misconceptions
| Misconception | Why it is wrong | Correct idea |
|---|---|---|
| Your mass is smaller on the Moon. | Mass is the amount of matter and does not depend on location. | Your weight is smaller on the Moon because g is smaller; your mass is unchanged. |
| A body moving in a circle at constant speed has no resultant force on it. | Its direction, and so its velocity, is always changing. | There is a resultant force (gravity) towards the centre of the orbit. |
| The galaxy and the solar system are the same thing. | The solar system has one star; a galaxy has billions. | Our solar system is a tiny part of the Milky Way galaxy. |
| A comet moves at a steady speed like a planet. | Its distance from the Sun changes greatly around its elliptical orbit. | A comet is fastest closest to the Sun and slowest furthest away. |
Key equations
| Equation | Use it to find | Route | On the Equation List? |
|---|---|---|---|
| weight = mass × gravitational field strength, \(W=m\times g\) | weight on another planet or the Moon (from 1(c)) | All | yes — all papers |
| orbital speed = \(\dfrac{2\times\pi\times\text{orbital radius}}{\text{time period}}\), \(v=\dfrac{2\times\pi\times r}{T}\) | orbital speed, radius or period | Double · Physics | yes — all papers |
The Equation List is printed with the question papers, but you still have to choose the right equation, convert units and rearrange it yourself.
Check your understanding
1. Put these in order of size, smallest first: galaxy, planet, universe, solar system. All
planet → solar system → galaxy → universe. Our solar system is in the Milky Way galaxy.
2. A student has a mass of 60 kg. Calculate her weight on the Moon, where g = 1.6 N/kg. All
\(W=m\times g=60\times1.6=\) 96 N. Her mass is still 60 kg.
3. A space probe weighs 2400 N on Earth. Calculate its weight on Mars, where g = 3.7 N/kg. (g on Earth = 10 N/kg) All
mass = 2400 ÷ 10 = 240 kg (1 mark); weight on Mars = 240 × 3.7 = 888 N = 890 N (1 mark).
4. Explain why the gravitational field strength on the surface of the Moon is less than on the surface of the Earth. All
g depends on the mass of the body (and on the distance from its centre) (1 mark); the Moon has a much smaller mass than the Earth, so its gravitational pull on each kilogram at its surface is smaller (1 mark).
5. Explain why the Moon moves in a curved path around the Earth instead of in a straight line. All
The Earth exerts a gravitational force on the Moon (1 mark), directed towards the centre of the Earth (1 mark). This force continually changes the direction of the Moon's motion, so its path curves into an orbit (1 mark).
6. The Moon orbits the Earth at a radius of 3.84 × 108 m with a period of 27.3 days. Calculate its orbital speed. Double · Physics
\(T=27.3\times86\,400=2\,358\,720\ \text{s}\); \(v=\dfrac{2\pi\times3.84\times10^{8}}{2\,358\,720}=1023=\) 1020 m/s (about 1.0 km/s).
7. Mars orbits the Sun at a radius of 2.28 × 1011 m with an orbital speed of 24.1 km/s. Calculate its time period in seconds and in days. Double · Physics
\(T=\dfrac{2\pi r}{v}=\dfrac{2\pi\times2.28\times10^{11}}{24\,100}=\) 5.94 × 107 s; ÷ 86 400 = 688 days.
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