Halley's Comet spends most of its 76-year orbit crawling through the outer solar system, then whips around the Sun in a matter of weeks before slowing down again on the way back out. Nothing is pushing or pulling it to speed up on a schedule — it's obeying a rule Johannes Kepler worked out from raw observational data in 1609, decades before anyone knew gravity was the reason behind it.
The rule: equal areas, equal times
Draw a line from the Sun to an orbiting body — a planet, a comet, a satellite — and let that line sweep around as the body moves. Kepler's second law says that line sweeps out equal areas in equal intervals of time, no matter where in the orbit you measure it. Near the Sun, where the line is short, it has to sweep through a wide angle quickly to cover the same area a longer line covers slowly far away. The only way for a short line to keep up is for the object to move fast — so close-in motion is fast, and far-out motion is slow, purely as a geometric consequence of that one rule.
A thin, fast sector near the Sun and a wide, slow sector far from it — swept in the same amount of time, with equal area. Watch the dot: it visibly speeds up and slows down around a single orbit.
Why it happens: angular momentum, not magic
Kepler had no explanation for his own law — he found the pattern in Tycho Brahe's planetary data before Newton existed to explain it. The modern explanation is conservation of angular momentum: with no sideways force acting on an orbiting body (gravity always points straight at the Sun, never sideways), its angular momentum stays constant throughout the orbit. Angular momentum depends on both distance from the Sun and speed, so as distance shrinks near perihelion, speed has to grow to keep the product constant — and that exact trade-off is what produces equal areas in equal times.
Exam-style question
A comet at perihelion is 0.5 AU from the Sun, moving at 60 km/s. At aphelion it is 30 AU from the Sun. Use conservation of angular momentum to find its speed at aphelion. [3 marks]
Show model answer and mark breakdown
- Angular momentum is conserved: m v₁ r₁ = m v₂ r₂ (the mass cancels from both sides) (1 mark)
- v₂ = v₁ × r₁ / r₂ = 60 × 0.5 / 30 (1 mark)
- v₂ = 1 km/s (1 mark)
Examiner focus: write the conservation equation in full first (with the mass included) so it's clear why the mass cancels, rather than jumping straight to the ratio.
Common mistake: inverting the ratio (multiplying by r₂/r₁ instead of r₁/r₂), which would predict the comet speeding up at aphelion — the opposite of what equal-areas-in-equal-time actually requires.
Try it yourself
Drag the eccentricity slider below from a perfect circle out to a stretched ellipse, and watch two things happen together: the orbit itself changes shape, and the speed readout swings harder between fast (near the Sun) and slow (far away) the more stretched it gets. At eccentricity zero it barely moves at all — exactly the constant speed a circular orbit already has, with nothing left for the law to say.
Eccentricity e = 0.50
A real solution of Kepler's equation, not just an animated approximation — equal areas really are swept in equal time here. Drag the slider to see how eccentricity controls the size of the speed swing.
A real engineering use, not just a planet fact
Satellite designers exploit this rule deliberately. A Molniya orbit — used for decades by Russian communications satellites to cover high-latitude regions poorly served by geostationary satellites — is a deliberately stretched ellipse. Its whole point is Kepler's second law: the satellite moves slowly while far from Earth at apogee, over the region it's meant to serve, giving hours of useful coverage from a single satellite, then swings quickly through the close, less useful part of the orbit to get back out again. The elongated shape isn't an accident of the orbit — it's chosen specifically because of how Kepler's second law makes an object behave on it. If orbital mechanics, angular momentum or any other A-Level physics topic needs explaining with the actual reasoning rather than a formula to memorise, that's exactly what our A-Level physics and maths tutoring is for — see the full learning pathway here.
Frequently asked questions
Does Kepler's second law mean orbits are unstable or changing shape?
No — the ellipse itself stays fixed (that's Kepler's first law). The second law only describes how fast the planet moves along that fixed ellipse at different points, not any change to the shape or size of the orbit itself. Speed changes; the path doesn't.
Is this the same reason Earth's seasons aren't exactly equal length?
Yes, indirectly. Earth reaches perihelion (closest to the Sun) in early January and moves fastest around then, which is a real, measurable reason astronomical winter in the Northern Hemisphere is very slightly shorter than astronomical summer — a genuine, if small, consequence of Kepler's second law playing out in a calendar you actually use.
Do satellites in circular orbits obey Kepler's second law too?
Technically yes, but it's not interesting to look at — a perfect circle has a constant radius, so equal areas swept in equal time just means constant speed, which is what a circular orbit already has by definition. The law only becomes visually and practically dramatic for orbits with real eccentricity, like Molniya orbits or comets.
Reader ratings & reviews
Rate this article across a few different things — your rating helps other readers, and helps us improve.
Was this article helpful?
Tell us what you think — a correction, a question it left unanswered, or a topic you'd like covered next.
Prefer To Talk? Book a free video call at a time that suits you: 15 minutes for a quick question, 30 for anything else. Times show in your own time zone.
About the author
Sudershan Soni
Founder & Lead Tutor at Mostak Services — an MSc-qualified Mathematics, Science, Computer Science & STEM tutor with 20+ years of professional experience, teaching students from 11+ and GCSE to A-Level and beyond, online worldwide.
Read full profile