A four-axis tellurion for children to learn astronomy from a God's-eye view

[Bilibili Demo Address] https://www.bilibili.com/video/BV1qsJN6FEAg/?share_source=copy_web&vd_source=e9d7023f315ed8892a18d0d2e265243e

Notes:

1. Feel free to choose the sunlight source based on the materials available to each person (pay attention to heat dissipation; high-power light sources should avoid touching the inner wall of the sun model, and drill holes for heat dissipation; the light source opening is reserved for 1cm)

2. The sun model's bracket holds down the Earth's orbit and is nested on the sun model's stand. If it's too tight, you can scale it up slightly during printing. To prevent poor fit, I used a drill bit to ream the holes and fixed it with glue

3. For a better demonstration effect, you can choose to replace the Earth globe (with a world map) and a more vivid moon model after scaling them proportionally, or print them with matte and highly reflective materials to perfectly simulate the phases of the moon

4. The content involved may contain errors, and we welcome everyone to point them out

Four-Axis Coupled Earth-Moon-Sun Astronomical Demonstration Triple-Sphere System (Orrery) User Manual

Product Name: Four-Axis Coupled Earth-Moon-Sun Astronomical Demonstration Triple-Sphere System
Core Structure: Four independent drive axes (Earth rotation axis, Earth's axial precession axis, Earth's revolution axis, Moon's revolution axis)
Applicable Scenarios: Professional astronomy education, middle and high school geography classroom demonstrations, astronomy popularization and research, hands-on learning of celestial motion principles

Core Feature Description:

• This device is a purely manual mechanical model with no motors or automatic control; all movements require manual operation.
• No independent lunar rotation axis, adheres to the principle of tidal locking - the Moon completes one revolution without relative rotation, always presenting the same face towards Earth.
• Features an Earth's axial precession axis (second axis), used for initial calibration or demonstrating Earth's long-term axial precession. During regular demonstrations of the four seasons, polar day/night, and day/night length, the Earth's axis direction should remain fixed, with all phenomena naturally presented through Earth's revolution alone.
• Accurately reproduces the obliquity of the ecliptic (23.5°) and the inclination of the lunar orbit (5°09′), allowing for demonstrations of the terminator, changes in day/night length, movement of the sun's direct rays, seasonal changes, polar day/night, lunar phases, solar and lunar eclipses, and other professional astronomical phenomena.

Table of Contents

1. Product Core Structure and Four-Axis Principle Explanation
2. Professional Orbits, Celestial Inclinations, and Model Physical Parameters (including scaling explanation)
3. Detailed Description of Complete Machine Components
4. First-Time Operation and Manual Astronomical Baseline Reset
5. Basic Celestial Motion Demonstrations (Terminator, Day/Night Length, Movement of Direct Rays)
6. Advanced Professional Astronomical Phenomena Demonstrations (Polar Day/Night)
7. Complete Demonstrations of Lunar Phases, Solar, and Lunar Eclipses (incorporating the inclination of the lunar orbit)
8. Standard Operating Precautions
9. Common Faults and Principle Q&A

1. Product Core Structure and Four-Axis Principle Explanation

1.1 Functions of the Four Core Axes

1.2 Principle of Lunar Tidal Locking (Design Basis)

The real Moon's rotation period is perfectly synchronized with its revolution period around Earth (27.3 days), so it always presents the same face towards Earth. This device does not have an independent lunar rotation axis; during revolution, the Moon's face is fixed pointing towards the Earth's center, accurately replicating the state of real celestial bodies.

2. Professional Orbits, Celestial Inclinations, and Model Physical Parameters

2.1 Core Angle Parameters

• Obliquity of the Ecliptic (Earth's Axial Tilt): 23.5°, fixed. This is the fundamental reason for the four seasons, polar day/night, and variations in day/night length.
• Inclination of the Lunar Orbit: The angle between the ecliptic plane (Earth's orbital plane) and the lunar orbital plane is 5°09′. This device mechanically achieves this angle through the inclined auxiliary arm for lunar revolution (or orbital support structure), irrespective of whether the Moon has a rotation axis.
• The Moon's axial tilt (approx. 1.5°) is not demonstrated as the device has no lunar rotation.

2.2 Two Major Orbital Planes

• Ecliptic Plane: Earth's orbital plane.
• Lunar Orbital Plane: The Moon's orbital plane, inclined at 5°09′ to the ecliptic plane.

2.3 Model Physical Dimensions and Spacing (Differentiated Scaling for Desktop Adaptation)

Scaling Explanation:
The real Sun-Earth diameter ratio is approximately 109:1, and the distance ratio is approximately 11700:1. If both diameter and distance ratios were faithfully maintained in a desktop model, the model would be too large for teaching purposes. Therefore, this device uses scientific differentiated scaling:

• The sun model has a smaller diameter (36mm) to avoid obstructing the light source and ensure uniform illumination;
• The Earth model is appropriately enlarged (80mm) to clearly display surface markings (equator, tropics, polar circles, etc.);
• The Earth's axial tilt, inclination of the lunar orbit, illumination geometry, and relative motion relationships of revolution and rotation are strictly maintained, and the demonstration principles of all astronomical phenomena (seasons, polar day/night, lunar phases, solar and lunar eclipses) are completely unaffected.

✅ This scaling method is a conventional design for professional astronomical teaching models, not a scientific error

3. Detailed Description of Complete Machine Components

4. First-Time Operation and Manual Astronomical Baseline Reset

This device is a purely manual model with no automatic operation functions. All position adjustments require manual operation.

Purpose of Baseline Reset: To set a unified initial state and ensure subsequent demonstrations conform to astronomical principles.

Manual Reset Steps (purely manual alignment):

1. Rotate Earth's main revolution arm to the Vernal Equinox mark on the base.
2. Adjust the Earth's axial precession axis so that the Earth's axis direction aligns with the "North Pole Direction Mark" on the base (if no mark, set the Earth's axial tilt to be perpendicular to the Sun-Earth line, with the North Pole pointing away from the Sun - this is the standard orientation for the vernal equinox).
3. Lock the Earth's axial precession axis, and do not rotate it in subsequent demonstrations.
4. Rotate the Moon's revolution arm to the baseline position of the New Moon (between Sun and Earth).
5. Visually check that there is no offset in the inclination of the ecliptic plane and lunar orbital plane, then complete the reset.

Core Principle: Except for precession demonstrations or initial calibration, once the Earth's axis direction is set, it must remain fixed throughout the entire revolution demonstration. Phenomena such as the four seasons and polar day/night are entirely generated automatically by Earth's revolution, without the need to manually change the Earth's axial orientation

5. Basic Celestial Motion Demonstrations

5.1 Day and Night Alternation and the Terminator

Turn on the light source and uniformly rotate the Earth's rotation axis (from west to east).

• The side facing the light source is the day hemisphere, the side facing away is the night hemisphere, and the dividing line between light and darkness is the terminator circle.
• Following the direction of rotation, the line from night to day is the morning terminator, and from day to night is the evening terminator.
• Observe: The terminator is always perpendicular to the sun's rays, and the equator has equal day and night throughout the year. Fixing Earth's rotation angle can show the global day/night distribution at a given moment.

5.2 Annual Movement of the Sun's Direct Rays

Keep the Earth's axis direction fixed (axial precession axis locked), and slowly rotate the Earth's main revolution arm.

• During revolution, due to the fixed axial tilt, the sun's direct rays move between the Tropics of Cancer and Capricorn:
  • Summer Solstice (when revolving to the Summer Solstice mark) direct rays hit the Tropic of Cancer
  • Winter Solstice direct rays hit the Tropic of Capricorn
  • Vernal/Autumnal Equinox direct rays hit the Equator

5.3 Demonstration of Seasonal Changes (Correct Method)

Prerequisite: Earth's axis direction is locked and no longer adjusted.
Revolve sequentially to the four solar term marks and observe the illumination conditions:

Note: During demonstrations, do not rotate the Earth's axial precession adjustment knob, otherwise it will incorrectly suggest that seasons require manual adjustment of the Earth's axis direction.

5.4 Global Differences in Day and Night Length

Observe the length of day and night at different latitudes at various orbital positions:

• Summer Solstice: Northern Hemisphere has long days and short nights, polar day in the Arctic Circle; Southern Hemisphere is the opposite.
• Winter Solstice: Northern Hemisphere has short days and long nights, polar night in the Arctic Circle; Southern Hemisphere is the opposite.
• Vernal/Autumnal Equinox: Equal day and night globally.

5.5 Division of Earth's Five Zones

Demonstrate the division into tropical (between the Tropics of Cancer and Capricorn), temperate (between the tropics and polar circles), and frigid (within the polar circles) zones by observing the range of illumination and the movement of the sun's direct rays.

6. Advanced Professional Astronomical Phenomena Demonstrations (Polar Day/Night)

Prerequisite for Correct Demonstration: The Earth's axis direction is fixed (axial precession axis locked), and only Earth's revolution changes its position in orbit.

6.1 Polar Day in the Arctic and Polar Night in the Antarctic on the Summer Solstice

1. Turn on the light source, and rotate the main revolution arm to the Summer Solstice mark.
2. Keep the Earth's axis direction unchanged (the direction set during the vernal equinox); at this point, the North Pole of the Earth's axis naturally tilts towards the Sun.
3. Observe the terminator tangent to the Arctic Circle, with the entire area inside the Arctic Circle experiencing daylight (polar day), and the entire area inside the Antarctic Circle experiencing darkness (polar night).
4. Rotate the Earth's rotation axis; the polar day/night regions will not change.

6.2 Polar Day in the Antarctic and Polar Night in the Arctic on the Winter Solstice

1. Rotate the main revolution arm to the Winter Solstice mark.
2. The Earth's axis direction remains at the initial setting; at this point, the South Pole of the Earth's axis tilts towards the Sun.
3. The terminator is tangent to the Antarctic Circle, with the Antarctic Circle experiencing polar day, and the Arctic Circle experiencing polar night.

6.3 No Polar Day or Night on Vernal and Autumnal Equinoxes

When revolving to the Vernal or Autumnal Equinox marks, the sun's direct rays hit the equator, the terminator passes through both poles, global day and night are equal in length, and there is no polar day or night.

6.4 Gradual Change Demonstration of Polar Day/Night Extent

Slowly and continuously rotate the main revolution arm, observing the dynamic process where the polar day/night extent gradually expands from the poles to the polar circles, and then gradually shrinks, fully reproducing the annual changes.

7. Lunar Phases, Solar, and Lunar Eclipses (incorporating the inclination of the lunar orbit)

7.1 Lunar Phase Cycle Demonstration

Turn on the light source and manually rotate the Moon's revolution axis; the Moon revolves along the lunar orbital plane. Observe the changing shape of the illuminated part of the Moon:
New Moon (conjunction) → Crescent Moon → First Quarter Moon → Gibbous Moon → Full Moon (opposition) → Waning Gibbous Moon → Last Quarter Moon → Waning Crescent Moon → New Moon.
(Due to tidal locking, the same side of the Moon always faces Earth, but the illuminated area changes with its orbital position.)

7.2 Solar Eclipse Demonstration (New Moon Specific)

Rotate the Moon to be between the Sun and Earth (new moon point), and finely adjust the Moon's orbital angle to compensate for the inclination of the lunar orbit, making the Sun, Moon, and Earth approximately collinear. At this point, the Moon's shadow falls on Earth, demonstrating total/partial solar eclipse effects.
Explanation: Due to the inclination of the lunar orbit, most new moon days are not collinear, which is why solar eclipses are rare.

7.3 Lunar Eclipse Demonstration (Full Moon Specific)

Rotate the Moon to the Sun-Earth extension line (full moon point), finely adjust the angle to make the Sun, Earth, and Moon collinear, and the Earth's shadow covers the Moon, demonstrating a lunar eclipse. Similarly, it does not occur on every full moon day.

8. Standard Operating Precautions

1. The four-axis structure is precise; rotate gently and smoothly, violent operation is prohibited.
2. The Earth's axial precession axis should remain locked during regular demonstrations; it should only be adjusted when demonstrating precession or during initial calibration.
3. When demonstrating the terminator, polar day/night, and solar/lunar eclipses, it is recommended to do so in a dark environment.
4. Light source brightness and power supply methods can be adapted as needed.
5. The device is a precision model; dropping, impacting, or submerging it is prohibited; children should be accompanied by an adult when operating.
6. Do not disassemble the axes without authorization, as this may compromise the precision of the four-axis coupling.

9. Common Faults and Principle Q&A

Q1: Why doesn't the Moon rotate on its axis? Is this a defect?
A: No, it's not a defect. The real Moon is tidally locked, with its rotation and revolution periods being the same, always presenting the same face towards Earth. This device scientifically reproduces this characteristic.

Q2: Why is it unnecessary to rotate the Earth's axial precession adjustment knob when demonstrating the four seasons?
A: During Earth's actual revolution, the spatial orientation of its axis remains constant (pointing towards Polaris). Seasonal changes are entirely caused by the change in the position of the sun's direct rays due to Earth's revolution. Manually rotating the Earth's axis during revolution would result in an incorrect principle. This device's Earth's axial precession axis is only for initial calibration or demonstrating precession.

Q3: Why is the sun model smaller than the Earth model?
A: This is an engineering scale-down for the feasibility of desktop teaching. True proportions cannot be achieved in a desktop model. This device sacrifices size proportion but retains all angles, illumination geometry, and relative motion relationships, without affecting the teaching of any astronomical phenomena.

Q4: How is the 5°09′ inclination of the lunar orbit achieved? Does the absence of a lunar rotation axis affect it?
A: The inclination of the lunar orbit is the angle between the Moon's orbital plane (lunar orbital plane) and Earth's orbital plane (ecliptic plane), mechanically achieved through the inclined auxiliary arm for lunar revolution, and is unrelated to whether the Moon rotates. This device correctly preserves this angle for demonstrating the conditions for solar and lunar eclipses.

Q5: Why can't solar and lunar eclipses be demonstrated on every new moon and full moon day?
A: The device accurately reproduces the 5°09′ inclination of the lunar orbit; on most new moon and full moon days, the three celestial bodies are not collinear, which is consistent with reality and not a malfunction.

Q6: What if the polar day/night and terminator demonstration effects are not obvious?
A: Check if the revolution position accurately corresponds to the solar term marks, and confirm that the Earth's axis direction is locked and its tilt is correct (the precession knob has not been accidentally touched). Reset according to Chapter 4.

Q7: Why doesn't the terminator completely coincide with the meridians?
A: The terminator coincides with the meridians only on the two days of the vernal and autumnal equinoxes when the sun's direct rays hit the equator; at other times, due to the Earth's axial tilt, there is an angle between the terminator and the meridians, and this device can fully present this change.