Astronomy — The Moving Sky

Accessibility: This is the accessible version of the lab, built following WCAG 2.1 AA guidelines. It adds screen-reader support, full keyboard navigation, and text descriptions of the interactive diagrams. If you encounter any barrier, please let us know through e2innovations.ai so we can address it.

Theory — The Moving Sky

To describe where things are and how they move, astronomers imagine the sky as a giant celestial sphere surrounding the Earth. Directions on it are given by two angles, much like latitude and longitude on the Earth. The sphere appears to turn once a day because the Earth rotates; the daily circles that stars trace are called their diurnal motion.

1. The celestial sphere

Key reference points: the celestial poles lie above the Earth’s poles, the celestial equator is the projection of the Earth’s equator, and the ecliptic is the Sun’s yearly path, tilted about 23.5 degrees to the equator. Your local horizon and meridian (the north–south line through the zenith) fix what is up at any moment. The seasons arise from that 23.5 degree tilt, not from any change in the Earth–Sun distance.

2. Kepler’s laws

First law: each planet moves on an ellipse with the Sun at one focus. Second law: a line from the Sun to the planet sweeps out equal areas in equal times, so a planet moves faster when it is closer to the Sun. Third law links period and size of the orbit:

Kepler’s third law P² = a³ (P in years, a in astronomical units)
So P = √(a³) and a = P^(2/3)

Newton later showed this law follows from gravity, and in its full form it also depends on the mass of the central body, which is how the mass of a planet or star is measured from the orbit of a companion.

3. Phases of the Moon

The Moon shines by reflected sunlight, so exactly half of it is always lit. Which part of the lit half we see depends on the angle between the Sun, Earth, and Moon as the Moon orbits us once a month. When the Moon is between us and the Sun we see the unlit side (new Moon); when the Earth is between the Sun and Moon we see the fully lit side (full Moon); in between we see crescents, quarters, and gibbous phases.

4. Why eclipses are rare

If the Moon’s orbit lay exactly in the plane of the Earth’s orbit, we would get a solar eclipse at every new Moon and a lunar eclipse at every full Moon. But the Moon’s orbit is tilted about 5 degrees, so its shadow usually misses. Eclipses happen only when a new or full Moon occurs near a node, where the two orbit planes cross.

Apparatus

Positional astronomy uses instruments for modelling the sphere, tracking orbital motion, and reading the Sun and Moon. In the simulation these are modelled, but the readings match what each instrument would give.

Celestial globe

A star globe showing the celestial poles, equator, and constellations for reading positions on the sphere.

Armillary sphere

A ring model of the sky used to demonstrate the equator, ecliptic, and the daily rotation.

Orrery

A mechanical model of the Sun and planets that shows their relative orbits and periods.

Gnomon / sundial

A vertical style casting a shadow; its direction and length track the Sun through the day and year.

Moon-phase dial

A rotating dial that shows the lit fraction of the Moon at each point in its monthly cycle.

Refracting telescope

Used to observe the phases of the Moon and the positions of the planets against the stars.

Instructions

Work through both tabs. Record your values, and for each task calculate first by hand, then use the button to compare with the simulation.

Part A — Kepler’s third law

Choose a planet and read its semi-major axis a in AU.
Using P = √(a³), calculate the orbital period in years by hand.
Enter your period and press Check. The simulation compares it with the accepted value within 3 percent.
Repeat for a second planet, then solve one reverse case: given a period, find the semi-major axis.

Part B — Moon phases and eclipses

Move the Moon around its orbit and watch the lit fraction change in the geometry view.
Predict the phase name and whether an eclipse is possible at that position (near a node), then press Check.

Simulation

Planet

Your period P (years)

Moon position (degrees)

Predicted phase

Eclipse possible?

Team Questions

1. A planet orbits at a = 4 AU. By Kepler’s third law its period is:

2 years 4 years 8 years 16 years

2. We see a full Moon when:

The Moon is between the Earth and the Sun The Earth is between the Sun and the Moon The Moon is at a node The Moon is closest to the Earth

3. Eclipses do not occur every month mainly because:

The Moon is too small The Moon’s distance changes The Moon’s orbit is tilted about 5 degrees, so its shadow usually misses Clouds block the view

Example Report

Worked example: the period of Mars

Mars has a semi-major axis of a = 1.524 AU. Apply Kepler’s third law:

P = √(a³) = √(1.524³) = √(3.54) ≈ 1.88 years.

The accepted orbital period of Mars is 1.88 years, so the calculated and accepted values agree. Reading the semi-major axis from the orbit and predicting the period this way is the calculate-then-compare core of the lab.

The Moving Sky