# How accurate is the model 42179 Planet Earth and Moon in Orbit?

The set 42179: Planet Earth and Moon in Orbit is described as a learning aid: "kids aged 10+ will love learning more about our solar system". For this purpose, the question arises: just how accurate a model of the real Solar system this model is?

The real Solar System is of course immensely complicated, so capturing all the details in a model would result in an impractical model in terms of size, complexity, and cost. The actual model's designer(s) needed to make compromises to end up with a model that could actually be manufactured, sold, built, and played with. Accordingly, we shall expect only the most important attributes to be translated into LEGO form.

Since I have received this set as part of the 2024 Q1 Activity Support, I could measure the properties of the model and compare them to the attributes of the real bodies and orbits (which I sadly couldn't measure, so had to look them up from mostly Wikipedia).

Metric Real Model
Radius of Sun (equatorial) 696 300 km 43.6 mm
Radius of Sun (polar) 696 265.185 km 43.75 mm
Obliquity of Sun 0.00005 -0.00344
Radius of Earth (equatorial) 6378.137 km 20.2 mm
Radius of Earth (polar) 6356.752 km 20.35mm
Obliquity of Earth 0.00335 -0.00742
Radius of Moon (equatorial) 1738.1 km 5.1 mm
Radius of Moon (polar) 1736.0 km 4.4 mm
Obliquity of Moon 0.0012 0.13725
Orbit radius of Earth (Semi-major axis) 149 598 023 km 197 mm
Orbit radius of Moon (Semi-major axis) 384 399 km 55 mm
Orbit eccentricity of Earth 0.0167 0
Orbit eccentricitity of Moon 0.0549 0
Inclination of the orbital plane of Earth 7.155°
Inclination of the orbital plane of Moon 5.145°
Rotation period of Sun (/day, equatorial) 1/24.47 1/27
Rotation period of Sun (/day, polar) 1/34 1/27
Rotation period of Earth (/day) 1 1
Rotation period of Moon (/day) 1/29.5305 0
Axial tilt of Sun 7.25°
Axial tilt of Earth 23.4° 22.5°
Axial tilt of Moon 6.68°
Orbit period of Earth (sidereal revolutions / orbit) 365.25 365.5
Orbit period of Earth (solar revolutions / orbit) 364.25 364.5
Orbit period of Moon (revolutions / orbit) 29.53059 27
Composition of Sun 73.46% H, 24.85% He, 0.77% O, 0.29% C, 0.16% Fe, 0.12% Ne 100% ABS
Composition of Earth 32.1% Fe, 30.1% O, 15.1% Si, 13.9% Mg, 2.9% S, 1.8% Ni, 1.5% Ca, 1.4% Al 100% ABS
Composition of Moon 43% O, 20% Si, 19% Mg, 10% Fe, 3% Ca, 3% Al 100% ABS
Mass of Sun 1.9885×1030 kg 42.3g
Mass of Earth 5.972168×1024 kg 7.62g
Mass of Moon 7.342×1022 kg 0.42g
Gears included Estimated to be in the low trillions 30
Gears involved in the motion of the celestial bodies 0 30

## Conclusion

As seen in the table, the important metrics related to motion (rotation and orbit periods) have been translated quite accurately into the model, especially considering the cost and complexity required to increase the accuracy. The absence of orbital plane inclinations also does not introduce jarring inaccuracies.

One surprising decision was the design of the new pieces for the bodies - the axle connectors have a barely measurable height from the spherical surface, which increases the polar radius above the equatorial, leading to a negative obliquity. When scaled up to match the equatorial radius of the real Earth, the model would have a 47.2 km tall plateau at both poles, reaching up to the stratopause, about 1.3 times higher than the record altitude reached by a non-rocket airplane.

## Size ratios and fun thought experiments

The other notable inconsistency affects the relative sizes and distances, but those were required to keep the model's size practical. If we were to make the model's size and distance relations accurate to reality while keeping the Sun the same size as in the model, the Earth would need to be an 0.4 mm radius ball 9.3 meters from the Sun, and the Moon a 0.1 mm radius dot orbiting the Earth at 2.4 cm distance.

Or if we kept the Earth's size, and updated all other measurements, we'd need a Sun over 4 meters in diameter placed 473 meters away. The Moon's size would barely change, but it would also need to be moved further from the Earth, into an orbit with a radius of 1.2 meters.

Finally, we could also keep the model's size (i.e. the Earth's orbit radius) constant. This would result in a Sun 1.8 mm in diameter, but we'd have a hard time finding the Earth, as it would have a diameter of 0.016 mm: smaller than a grain of flour.

## Edit

IvanSanchez asked about the model vs. reality size ratios, i.e. the scale of the model, which, as seen above, varies wildly (~2000 times difference between the smallest and largest scale ratios) with the actual metric chosen as the base for the comparison.

Model scale based on Scale