Topic 8 is the physics that makes the solar system tick: Kepler's three laws (ellipses, equal areas, T² ∝ r³) and Newton's law of gravitation with its inverse-square behaviour — plus how the two fit together.
Work through each screen, answer the questions as you go (some are wordy, some are calculations) and collect ⭐ stars. Press Start when you're ready.
Planetary motion · Kepler 1 & 2
Kepler's first and second laws
Kepler's first law: the orbit of each planet is an ellipse with the Sun at one focus. The other focus is empty. How squashed the ellipse is, is measured by its eccentricity (0 = a perfect circle; the planets are all fairly close to circular, but comets are extreme).
Perihelion — the point closest to the Sun.
Aphelion — the point furthest from the Sun.
Kepler's second law: a line joining the Sun to a planet sweeps out equal areas in equal times. Because the planet is closer at perihelion, that line is short — so to sweep the same area the planet must move faster.
fastest at perihelion · slowest at aphelionthis is why a comet whips round the Sun and then crawls through the outer solar system
The Earth is at perihelion (147 million km) in early January and aphelion (152 million km) in early July — proof that distance is not what causes the seasons.
Quick check
Where is the Sun?
?According to Kepler's first law, where is the Sun in a planet's elliptical orbit?
Planetary motion · Kepler 3
Kepler's third law
Kepler's third law ties a planet's period to its distance: the square of the orbital period is proportional to the cube of the mean orbital radius.
T² ∝ r³use YEARS and AU and the constant becomes 1, so simply: T² = r³
Worked example — Saturn, r = 9.5 AU
T² = 9.5³ = 857.4
T = √857.4 = 29.3 years — and Saturn really does take about 29.5 years.
Both ways round: given a period, find the distance instead. A comet with T = 64 years has r³ = 64² = 4096, so r = ∛4096 = 16 AU.
Calculate
Your turn — a comet's orbit
1A comet has an orbital period of 64 years. Use T² = r³ (years, AU) to find its mean orbital radius r in AU.
AU
Hint: r³ = T² = 64² = 4096. Then r = the cube root of 4096.
Calculate
Your turn — a dwarf planet
2A dwarf planet orbits at r = 4.0 AU. Use T² = r³ to calculate its orbital period T in years (1 decimal place).
years
Hint: T² = 4.0³ = 64, so T = √64.
Planetary motion · gravity
Newton: why the planets obey Kepler
Kepler described the motion. Newton (1687) explained it. He realised that the force pulling an apple to the ground is the same force that holds the Moon in orbit — gravity is universal.
F = G M m ÷ r²F = force · G = gravitational constant · M, m = the two masses · r = separation of centres
Gravity is always attractive, acts between any two masses, and never truly reaches zero.
It obeys an inverse square law: double the distance → the force falls to ¼. Triple it → ⅑.
Gravity provides the centripetal force that keeps a planet curving into orbit instead of flying off in a straight line. Newton pictured it as a cannonball fired so fast it keeps falling round the Earth.
Why Newton is the better theory: he could derive Kepler's three laws from F = GMm/r², apply them to moons, comets and binary stars, and predict new results — Halley's comet returning, and the existence of Neptune from Uranus's wobbles.
Calculate
Your turn — inverse square law
3The gravitational force on a probe is 180 N when it is a distance r from a planet. The probe moves out to 3r. Calculate the new gravitational force in N.
N
Hint: Force ∝ 1/r². Three times the distance → 3² = 9 times weaker: 180 ÷ 9.
Quick check
Twice as far
?A satellite is moved from a distance r from a planet's centre to a distance 2r. What happens to the gravitational force on it?
Quick check
What keeps a planet in orbit?
?Which statement best describes why a planet stays in orbit rather than flying off in a straight line?
Sort it
Which of Kepler's laws?
Tap a statement, then tap the law it belongs to.
1️⃣ First law
2️⃣ Second law
3️⃣ Third law
Match it
Match the description to the term
Tap a description on the left, then its matching term on the right.
Description
Term
Quick check
Kepler or Newton?
?What did Newton add that Kepler's laws did not provide?
Planetary motion · comets
Kepler's laws applied to a comet
Comets are the most extreme test of Kepler's laws, because their orbits are so eccentric.
Kepler 1 — a comet's orbit is a long, thin ellipse with the Sun at one focus, so its distance from the Sun changes enormously.
Kepler 2 — it therefore sweeps past perihelion at enormous speed in a matter of weeks, and then crawls through the outer solar system for decades. Halley's Comet has a period of about 76 years, yet is only bright for a few months of it.
Kepler 3 — T² = r³ still works: for Halley, T = 76 years, so r³ = 76² = 5776 and r = 17.9 AU — a mean distance out beyond Saturn (its aphelion carries it past Neptune).
Halley's triumph: using Newton's gravity, Edmond Halley predicted the comet's return for 1758 — decades after his own death. Its reappearance, on cue, was one of the great confirmations of the theory.
Quick check
Fastest where?
?Where in its orbit is a comet moving fastest, and which law tells you?
Recap
The big ideas to know
Kepler 1: every orbit is an ELLIPSE with the Sun at ONE FOCUS (the other focus is empty)
Kepler 2: a line from the Sun to a planet sweeps equal areas in equal times → fastest at perihelion, slowest at aphelion
Kepler 3: T² ∝ r³. In years and AU: T² = r³
Newton: F = GMm/r² — gravity is universal, attractive, and obeys an inverse-square law
Inverse square: double the distance → a QUARTER of the force; triple it → a NINTH
Orbits: gravity supplies the centripetal force; closer orbits need higher speeds
Newton beats Kepler: Kepler DESCRIBED the motion; Newton EXPLAINED it, and predicted new bodies
That is Planetary Motion & Gravity covered for Edexcel GCSE Astronomy. Press Finish to see your score.
🏆
Mini-lesson complete!
⭐⭐⭐
You have worked through Planetary Motion & Gravity for Edexcel GCSE Astronomy. 🎉
Your stars: 0 / 0
Next: test yourself in the Evaluate stage Confidence Quiz, then lock it in with Verify.
📣 Smashed it? Share your score
Challenge a mate to beat your stars, or show a parent how you got on.