The Universe and Gravity

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.

• 8.1 — Use the units kg, m, m/s, m/s², N, s and N/kg
• 8.2 — The universe, galaxies and the place of the solar system in the Milky Way
• 8.3 — Why gravitational field strength varies, and that it differs on other planets and the Moon

1 · Understand it

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

The universe is organised in a hierarchy, and knowing the order is worth more marks than knowing any single fact in it. A MOON orbits a PLANET. Planets, together with dwarf planets, asteroids and comets, orbit a STAR — and a star with everything orbiting it is a SOLAR SYSTEM. Enormous numbers of stars are held together by gravity in a GALAXY. And the UNIVERSE is everything: all the galaxies, and all the space between them.

Our star is the Sun, and our galaxy is the MILKY WAY, which contains something in the region of a hundred thousand million stars. The solar system is not at the centre of it; we are roughly two thirds of the way out along one of the spiral arms. The Milky Way is one galaxy among perhaps two thousand million in the observable universe.

Think of it like grains of sand on a beach

If the Sun were a single grain of sand, the Milky Way would be a beach a few kilometres long — and then you would need thousands of such beaches to account for the galaxies. The numbers are past imagining, so the useful thing to take from them is not the size but the ORDER, because that is what questions test: moon inside planet, planet inside solar system, solar system inside galaxy, galaxy inside universe. Get the order secure and the scale can look after itself.

Now gravity, which is what holds every level of that structure together. GRAVITATIONAL FIELD STRENGTH, g, is the force acting on each kilogram of mass, measured in NEWTONS PER KILOGRAM. On the Earth's surface it is about 10 N/kg, which means every kilogram is pulled down with a force of about 10 newtons. Weight is therefore mass multiplied by g.

What decides the gravitational field strength at a place

1. THE MASS of the body producing the field. A more massive planet pulls harder, so g is greater at its surface.
2. THE DISTANCE from its centre. The further away you are, the weaker the field — which is why g is slightly smaller at the top of a mountain than at sea level.
3. So a large but very spread-out planet can have a surface g no larger than a small dense one, because you are further from the centre when you stand on it.
4. This is why the values differ so much: about 10 N/kg on Earth, about 1.6 N/kg on the Moon, about 3.7 N/kg on Mars, and about 25 N/kg on Jupiter.
5. Your MASS is the same everywhere — it is the amount of matter in you. Only your WEIGHT changes, because weight is a force and depends on g.

That last distinction is examined constantly and is worth stating as plainly as possible. MASS is measured in kilograms, is a measure of how much matter something contains, and does not change when you go to the Moon. WEIGHT is measured in newtons, is the gravitational force acting on that mass, and changes with g. An astronaut with a mass of 80 kg weighs about 800 N on Earth and about 128 N on the Moon, and is exactly as much of a person in both places.

The same astronaut in three places

An astronaut has a mass of 75 kg. Find their weight (a) on Earth where g = 10 N/kg, (b) on the Moon where g = 1.6 N/kg, and (c) on Jupiter where g = 25 N/kg.

1. Weight = mass × gravitational field strength.
2. (a) On Earth: 75 × 10 = 750 N.
3. (b) On the Moon: 75 × 1.6 = 120 N — about a sixth of their Earth weight.
4. (c) On Jupiter: 75 × 25 = 1875 N, two and a half times their Earth weight.
5. In all three cases the MASS is 75 kg. Only the weight has changed, because only g has changed.

Answer: 750 N, 120 N and 1875 N — with the mass unchanged at 75 kg throughout.

Finally the units, statement 8.1, all of which have appeared before and are collected here because astrophysics questions use them together. Mass in KILOGRAMS; distance in METRES; speed in METRES PER SECOND; acceleration in METRES PER SECOND SQUARED; force in NEWTONS; time in SECONDS; and gravitational field strength in NEWTONS PER KILOGRAM. The last one repays reading as an instruction, exactly as kg/m³ did for density: newtons per kilogram means the force per kilogram of mass, which is the definition said aloud.

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.

Statement 8.2 — the hierarchy, in order

Moon

A natural satellite orbiting a planet.

Planet

A large body orbiting a star. Also orbiting the Sun: dwarf planets, asteroids and comets.

Solar system

A star together with everything orbiting it.

Galaxy

An enormous collection of stars held together by gravity. Ours is the Milky Way, with about 100 000 million stars.

Universe

All of the galaxies and all the space between them — perhaps 2000 million galaxies are observable.

weight = mass × gravitational field strength

weight in newtons (N), mass in kilograms (kg), gravitational field strength g in newtons per kilogram (N/kg)

Units: N, kg, N/kg. On Earth g ≈ 10 N/kg, on the Moon ≈ 1.6 N/kg, on Mars ≈ 3.7 N/kg, on Jupiter ≈ 25 N/kg.

Learn this definition · Gravitational field strength

The gravitational force acting on each kilogram of mass at a point, measured in newtons per kilogram. It depends on the mass of the body producing the field and on the distance from its centre.

Mass against weight

A. MASS is the amount of matter in an object, measured in kilograms. It is the same everywhere in the universe.

B. WEIGHT is the gravitational force on that mass, measured in newtons. It changes with g, so it differs on the Moon.

Statement 8.3 — why g varies

• A more MASSIVE body produces a stronger field, so g is greater at its surface
• The greater the DISTANCE from the body's centre, the weaker the field
• So g is slightly smaller at the top of a mountain than at sea level
• Approximate values: Earth 10 N/kg · Moon 1.6 N/kg · Mars 3.7 N/kg · Jupiter 25 N/kg
• Mass never changes with location; only weight does

Statement 8.1 — the units of this topic

kg

Mass — the amount of matter, unchanged by location.

N

Force, including weight.

N/kg

Gravitational field strength — the force acting per kilogram of mass.

m, s, m/s, m/s²

Distance, time, speed and acceleration.

Model answer [3 marks]

An astronaut has a mass of 68 kg. Calculate their weight on Mars, where g = 3.7 N/kg, and state what their mass is on Mars. [3]

Weight = mass × gravitational field strength = 68 × 3.7 = 251.6 N, which is about 252 N. Their mass on Mars is still 68 kg, because mass is the amount of matter in an object and does not depend on where the object is.

Model answer [3 marks]

Explain why the gravitational field strength on the Moon is much smaller than on Earth. [3]

Gravitational field strength depends on the mass of the body producing the field and on the distance from its centre. The Moon has a much smaller mass than the Earth, so it produces a much weaker gravitational field. Although its radius is also smaller, which brings the surface closer to its centre, the difference in mass is far greater in its effect, so the field strength at the Moon's surface is about 1.6 N/kg compared with about 10 N/kg on Earth.

Not this: An astronaut in space has no mass because there is no gravity there.

This: Their MASS is unchanged — it is the matter they are made of. Gravity does not run out either: it is what holds them in orbit. They float because they are falling freely around the Earth, not because gravity is absent.

Mark-losing trap. MASS in kilograms never changes. WEIGHT in newtons changes with g.

Mark-losing trap. g depends on the body's MASS and your DISTANCE from its centre — both, not just mass.

Mark-losing trap. N/kg means newtons of force PER KILOGRAM of mass, which is the definition said aloud.

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 · Calculate [2 marks] — An object has a mass of 40 kg. Calculate its weight on the Moon, where the gravitational field strength is 1.6 N/kg.
2. Grade 7 · State [2 marks] — Place these in order of increasing size: galaxy, moon, universe, solar system, planet.
3. Grade 8 · Explain [3 marks] — A student says that a 70 kg astronaut 'loses most of their mass' when they land on the Moon, because they can jump six times higher. Explain what is wrong.
4. Grade 9 · Explain [6 marks] — Two planets have the same mass, but planet A has twice the radius of planet B. Select every statement that belongs in a full-mark explanation of how the gravitational field strength at their surfaces compares.
5. 9+ · Analyse [6 marks] — A student reads that Jupiter is about 320 times the mass of the Earth and concludes that they would weigh about 320 times as much standing on Jupiter. In fact they would weigh about two and a half times as much. Select every statement that belongs in a full-mark analysis.

The people behind this science

Two ways into the same idea — the one who claimed the same force works everywhere, and the one who replaced the force with a shape. Inside Incandio each of them answers knowing exactly which lesson you have just finished.

Isaac Newton — the one who claimed the same force works everywhere

Statement 8.3 rests on Newton's most audacious claim: that the force pulling an apple to the ground is the SAME force holding the Moon in its orbit. Nobody had suggested that the heavens and the Earth ran on one set of rules — the ancient view, which had stood for two thousand years, was that celestial bodies were made of a different substance obeying different laws. Newton's test was quantitative: he calculated how much weaker gravity should be at the Moon's distance and checked it against how fast the Moon actually curves. It agreed. He is the right person to ask what it takes to propose that two entirely separate subjects are one.

• “Why should an apple and the Moon obey the same rule?”
• “How did you test whether gravity reaches the Moon?”
• “Why is gravity weaker further from a planet?”
• “What did people believe about the heavens before this?”
• “What convinced you the calculation had worked?”

Albert Einstein — the one who replaced the force with a shape

Newton's law says with great precision how strong gravity is and never says what it IS — Newton himself declined to speculate on how one body could pull another across empty space. Einstein's answer in 1915 was that gravity is not a force at all but the curvature of space and time by mass, so an orbiting planet is not being pulled off a straight line but is travelling the straightest available path through curved space. He is the right second figure because a learner has just been asked to accept an invisible pull acting across millions of kilometres, and it is worth knowing that this bothered the best physicists too.

• “What is gravity actually, if it is not a pull?”
• “How can space itself be bent?”
• “Was Newton wrong, or just incomplete?”
• “Why does everything fall at the same rate?”
• “How was your theory first tested?”

Carry on through the course

• Previous lesson: Nuclear Fusion
• Next lesson: Orbits
• Orbits — Why anything in orbit is falling, why comets speed up as they arrive, and how to find an orbital speed.
• 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 · Physics key terms · required practicals · equations · Incandio Science · The 4PH1 specification