Explanations of what the sky is doing and why - when things happen, and how to see them for yourself. Most lessons come with a diagram you can work through; the numbers in them are computed from orbital elements on the spot, not typed in.
Start with changes you can observe: why planets move backwards, when they stay visible all night, and why Mercury and Venus never stray far from the Sun.
Scrub through time and draw the loop Mars traces backwards across the stars yourself.
No planet has ever actually moved backwards. Retrograde motion is a line-of-sight effect: Earth and the planet travel the same direction on different orbits at different angular speeds, and when Earth overtakes on the inside, the planet appears to slip backwards against the background stars. Drag the timeline below and draw that loop yourself.
Use elongation to tell when a planet is visible all night or close to the Sun, and compare different Mars oppositions.
Elongation is the angle between the Sun and the planet as seen from here. Drag through a full cycle and watch it go from zero, when the planet is lost in the Sun, out to 180 degrees, when it is up all night.
Why the two inner planets are always twilight objects, and why Venus is brightest as a crescent.
Mercury and Venus orbit inside ours, so neither can ever appear more than a limited angle from the Sun. Drag through an apparition and watch the planet swing out, turn round, and come back.
Move into the ecliptic plane to understand the Solar System's disk, the motion of all eight planets, and the geocentric and heliocentric points of view.
All eight planets on the ecliptic plane at true scale and true period, with free zoom and a speed ladder.
A top-down view of the ecliptic plane that moves. Every position is solved live from Keplerian orbital elements, and the scale is genuinely linear — the inner planets are not enlarged to make the picture nicer. Pull back to watch Neptune complete a lap, or zoom in to see how visibly off-centre Mercury's ellipse really is.
The solar system is a disc. Seen from the side it is a line, which is why the diagram has to say how much it is exaggerating.
The Sun and the planets formed out of one rotating cloud, and a rotating cloud collapses into a disc. Everything that followed inherited that plane, which is why the planets are always found along one line in the sky.
One geometry, two choices of origin. Move the origin and the epicycles appear on their own.
Drag the slider and the origin moves from the Sun to the Earth. Nothing is recalculated: every planet stays exactly where it was, and the loops that appear are what subtracting Earth's own motion looks like.
Stretch the timescale to see how planetary orbits slowly change, and how tiny differences can become clues to new physics.
The orbit itself turns. Watch the long axis sweep a few degrees over six thousand years, and meet Mercury's extra 43 arcseconds.
The previous lesson argued that retrograde motion is a trick of the line of sight and that the orbit itself does not change. This one is about the way the orbit does change, only far more slowly. The long axis of the ellipse — the line from aphelion through the Sun to perihelion — rotates, so a planet never quite returns to where it started.
| Learning units | Astronomy Classroom | Open lesson |
|---|---|---|
| Planets in the sky | Why planets appear to move backwards | Scrub through time and draw the loop Mars traces backwards across the stars yourself. |
| Planets in the sky | Opposition and conjunction | Use elongation to tell when a planet is visible all night or close to the Sun, and compare different Mars oppositions. |
| Planets in the sky | Greatest elongation | Why the two inner planets are always twilight objects, and why Venus is brightest as a crescent. |
| The shape and models of the Solar System | Solar System Orrery | All eight planets on the ecliptic plane at true scale and true period, with free zoom and a speed ladder. |
| The shape and models of the Solar System | The ecliptic plane | The solar system is a disc. Seen from the side it is a line, which is why the diagram has to say how much it is exaggerating. |
| The shape and models of the Solar System | Ptolemaic and heliocentric | One geometry, two choices of origin. Move the origin and the epicycles appear on their own. |
| Long-term orbital change | Perihelion precession | The orbit itself turns. Watch the long axis sweep a few degrees over six thousand years, and meet Mercury's extra 43 arcseconds. |
Orbital elements from NASA/JPL, "Keplerian Elements for Approximate Positions of the Major Planets" (Standish & Williams, 1992), valid 1800–2050. Positions are geometric — no light-time or aberration — because this is a diagram of the ecliptic plane, not a simulation of a telescope view.
Interactive retrograde teaching tools have a long history: Nebraska (NAAP), Foothill AstroSims, the University of New Mexico, SimuFísica, NoA at the University of Fukui, Marble Cafe, and jsOrrery. None of their code is used here; the calculation and drawing are our own.
Scrub through time and draw the loop Mars traces backwards across the stars yourself. No planet has ever actually moved backwards. Retrograde motion is a line-of-sight effect: Earth and the planet travel the same direction on different orbits at different angular speeds, and when Earth overtakes on the inside, the planet appears to slip backwards against the background stars. Drag the timeline below and draw that loop yourself.
Explanations of what the sky is doing and why - when things happen, and how to see them for yourself. Most lessons come with a diagram you can work through; the numbers in them are computed from orbital elements on the spot, not typed in.
Orbital elements from NASA/JPL, "Keplerian Elements for Approximate Positions of the Major Planets" (Standish & Williams, 1992), valid 1800–2050. Positions are geometric — no light-time or aberration — because this is a diagram of the ecliptic plane, not a simulation of a telescope view.
Related tools: Live Sky Map · Astro Events · Moon Phases