From an Earth-Centered to a Sun-Centered Sky

On the celestial sphere the stars keep their places, but five bright "wanderers" (the Greek word is planetes) drift slowly among them: Mercury, Venus, Mars, Jupiter and Saturn. Usually they creep eastward from night to night. Every so often one stops, moves backward (westward) for weeks, stops again and resumes its eastward path. This retrograde motion was the great puzzle of ancient astronomy.

Ptolemy's Earth-centered model (about AD 150) explained the loops with circles on circles, called epicycles. In 1543 Copernicus proposed something simpler: the Sun is at the center, Earth is one planet among the others, and the loops are an effect of our own motion.

Why it works

In a Sun-centered system every planet always moves forward around the Sun, and the inner ones move faster. Earth, on the inside track, regularly catches up with Mars, Jupiter and Saturn. While we pass, our line of sight to the outer planet swings backward against the distant stars, just as a slower car seems to drift backward against far-off hills when you pass it on the highway. Nothing actually reverses. And the loops come exactly when Earth passes the planet, when it is opposite the Sun in our sky and at its brightest, which is what the model predicts.

Key idea

In the Sun-centered (heliocentric) model, retrograde loops are an illusion caused by Earth overtaking a slower outer planet (or a faster inner planet overtaking us). Galileo's observation that Venus shows a full set of phases, large as a crescent and small when nearly full, settled the case against Ptolemy's model.

Earth (inner) passing Mars (outer). Each line of sight lands on the strip of distant stars; while Earth overtakes Mars, the lines swing backward and Mars appears to loop.

Galileo's evidence

In 1610 Galileo turned a telescope on Venus. In Ptolemy's model Venus always stays between Earth and the Sun, so it could only ever show crescent phases. Galileo saw it go through all the phases, from a big thin crescent to a small, nearly full disk. A nearly full Venus has to be on the far side of the Sun from us, which only a Sun-centered orbit allows. He also found four moons circling Jupiter, proof that not everything goes around Earth.

Worked example

Worked example: Venus near and far

Venus orbits the Sun at $0.72$ AU and Earth at $1$ AU. How many times larger does Venus look at its closest than at its farthest?

Closest, between us and the Sun: $1 - 0.72 = 0.28$ AU. Farthest, beyond the Sun: $1 + 0.72 = 1.72$ AU.
Apparent size is inversely proportional to distance: $\frac{1.72}{0.28} \approx 6.1$.
The crescent phase comes when Venus is close, and the full phase when it is far: big crescents and small full disks, as Galileo saw.

Answer: About 6 times larger.

Common mistake

A retrograde planet does not really loop backward in space, any more than a car you pass on the highway really drives backward. Check: if the loops were real motion, they would happen at random places in the orbit. Instead each one comes exactly when Earth passes the planet, when it is opposite the Sun and brightest.

Watch Mars loop backward in the Sky and Solar System lab.

From an Earth-Centered to a Sun-Centered Sky

Galileo's evidence

Worked example

Practice

Builds on

Leads to

Sources and further reading