For two thousand years, astronomers drew the planets' paths as perfect circles — to them, the circle was the perfect heavenly shape.
Then Johannes Kepler put the circle to the test. He worked through decades of careful measurements of Mars's position in the sky. The circles never quite fit: Mars's measured positions kept missing the drawn circle by small, stubborn amounts.
But if a circle never fits, what shape does?
Well, the answer starts from a squashed circle. Squashing keeps the curve closed — it still joins up with itself — but stretches it, longer one way than the other. A stretched, closed curve like this is called an ellipse.
An ellipse can be drawn exactly, with no guesswork. Two pins hold a loop of string against a board. A pencil point pulls the string tight and moves around the pins, keeping it tight all the way. The pencil traces an ellipse.
The two pin points anchor the whole curve: every point of the ellipse keeps the same total string length to the pair of pins. Each anchor point is called a focus, and the two together are called the foci. The foci sit inside the ellipse, off-center along its long axis.
Kepler tried an ellipse on the Mars measurements, with the Sun placed at one focus. The measured positions sat on the ellipse — not roughly, but exactly.
The Sun sits at one focus, not at the center. So the planet's distance from the Sun changes as it goes around — shortest at the orbit's nearest point, longest at its farthest point.
Mars's orbit is an ellipse with the Sun at one focus. What follows about Mars's distance from the Sun?
The Sun sits at one focus, off the ellipse's center.
So the distance from the Sun to Mars changes as Mars moves around its orbit.
Mars is sometimes nearer the Sun and sometimes farther.
Lena says Mars is nearer the Sun at some points of its orbit than at others. Is she correct?
Lena is correct. Mars's orbit is an ellipse with the Sun at one focus, off the center. So Mars is nearer the Sun at some points of its orbit and farther at others.
For Earth, the stretch is slight. Earth's orbit is very nearly a circle, so its distance from the Sun varies by only about 3% over a year. Earth is nearest the Sun in early January, at about 147 million kilometers, and farthest in early July, at about 152 million kilometers.
How does Earth's distance from the Sun behave over one year?
Earth's distance from the Sun changes, but only slightly — by about 3% — because Earth's ellipse is nearly circular.
For comets, the stretch is extreme. A comet's ellipse can be long and thin, swinging from close past the Sun to far beyond the planets.
Mars's orbit, Earth's orbit, and the comets' orbits all follow one pattern.
A moon or a comet follows the same shape. Circle-shaped orbits are the special case; ellipses are the rule.
Where does the Sun sit in a comet's long, stretched orbit?
Kepler's first law covers every body orbiting the Sun, comets included.
In a long, thin ellipse, the foci sit far from the center, near the ends of the long axis.
The Sun sits at one focus of the comet's ellipse — near one end of the long orbit.
A planet's orbit is a slightly stretched, closed curve. What is this shape called?
A slightly squashed circle — a stretched, closed curve — is an ellipse. And each planet's orbit is an ellipse with the Sun at one focus: sometimes nearer, sometimes farther, all the way around.