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Orbits are ellipses
Every planet follows an elliptical orbit with the Sun located at one focus — not at the centre of the ellipse.
Astronomy Lab · Orbital mechanics
Why Don't Planets Move at Constant Speed?
A planet does not simply travel around the Sun at one fixed speed. Its orbit is an ellipse, its distance from the Sun changes, and so does its orbital velocity. Johannes Kepler found the mathematical pattern behind that motion more than four centuries ago.
The key idea:
a planet moves fastest when it is closest to the Sun and slowest when
it is farthest away. Kepler's laws describe this motion; Newton's law
of gravity later explained why it happens.
From circles to ellipses
Three astronomers changed our view of planetary motion
Copernicus placed the planets in orbit around the Sun. Tycho Brahe then accumulated exceptionally precise observations of planetary positions. Johannes Kepler used those observations — especially of Mars — to discover that planetary orbits are not perfect circles.
1543
Copernicus
The heliocentric model places Earth and the other planets in motion around the Sun.
1609
Kepler's first two laws
In Astronomia Nova, Kepler describes elliptical orbits and the equal-area rule.
1619
Kepler's third law
Kepler reveals the mathematical relationship between orbital period and orbital size.
Kepler's three laws
The rules behind planetary orbits
2
Equal areas in equal times
A line from the Sun to the planet sweeps equal areas during equal intervals of time. The planet therefore moves faster near perihelion and slower near aphelion.
3
P² is proportional to a³
The farther a planet is from the Sun, the longer it takes to complete its orbit according to a precise mathematical relation.
Interactive experiment
Watch Kepler's second law in action
Move the planet around an exaggerated elliptical orbit. The orbit is deliberately more eccentric than Earth's so that the speed change is easy to see.
Move around the orbit
Position
Perihelion
Relative speed
Fastest
The Sun is at a focus of the ellipse. When the planet is close to the Sun it must cover a greater length of orbit in a given time to sweep the same area.
Kepler's third law
Measure distance from orbital period
For planets orbiting the Sun, if the orbital period P is measured in Earth years and the semi-major axis a in astronomical units, Kepler's third law becomes particularly simple.
P² = a³
P = orbital period in years · a = semi-major axis in AU
This means we can estimate a planet's orbital size from nothing more than its period:
a = ∛(P²)
Example · Jupiter
How far is Jupiter from the Sun?
Jupiter takes about 11.86 Earth years to complete one orbit. Kepler's third law therefore gives:
a = ∛(11.86²) ≈ 5.20 AU
11.86 yr
Orbital period
One Jovian year.
≈5.20 AU
Semi-major axis
About 5.2 times Earth's orbital scale.
≈778 million km
Mean orbital scale
Approximately the Sun–Jupiter semi-major axis expressed in kilometres.
Try it yourself
Turn an orbital period into a distance
Enter an orbital period in Earth days. The calculator converts the period to years and applies Kepler's third law.
Orbital period
0.615 yr
Compared with Earth
0.62×
Semi-major axis
0.723 AU · ≈ 108 million km
Venus completes an orbit in about 224.7 days,
giving a semi-major axis of about 0.723 AU.
Orbit size is drawn relative to Earth's 1 AU orbit. The drawing is schematic, not a full orbital simulation.
Orbital period vs synodic period
Why does Jupiter return to opposition every 399 days if its orbit takes nearly 12 years?
The orbital period measures one complete revolution around the Sun. The synodic period measures the time between repeated configurations as seen from Earth — for example, one opposition of Jupiter to the next.
Because Earth is moving too, we do not wait an entire Jovian year for Earth to catch Jupiter again. For an outer planet the relation is:
1 / S = 1 / PEarth − 1 / Pplanet
For Jupiter this gives a synodic period of roughly 399 days. For an inner planet such as Venus, the corresponding relationship uses the difference between the inner planet's faster orbital frequency and Earth's.
Kepler described it. Newton explained it.
Gravity provides the missing physics
Kepler's laws were empirical: they described planetary motion with remarkable accuracy without identifying the underlying force. Decades later, Isaac Newton showed that the same gravitational attraction that makes objects fall on Earth can account for planetary orbits.
That connection transformed celestial mechanics. The motions of planets, moons, comets and spacecraft could now be understood using the same physical principles.
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