Length Scales in the Solar System

A dynamically simplified solar system is constructed from online data to explore the real solar system on many different scales.
The realistically scaled solar system is surprising because nothing is visible due to the presence of many different scales. That is why it is usually rescaled in animations or illustrations. This is nice but gives us a wrong sense of distances and sizes. This Demonstration is intended to show the solar system's different scales in their full glory.
Since it is hardly possible to see anything when the real scales are used, controls have been added to modify the sizes of the celestial bodies.


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The formulas used are:
where is the orbital period in years and is the apoapsis.
Orbital inclinations are taken into account with a rotation matrix in the plane: all orbits are rotated around the same axis, which is probably wrong.
Time depends on the zoom, so you see every planet moving, whatever the scale of observation chosen. You can see that the years go much faster when you look from Neptune than from Mercury.
This model is dynamically wrong: the angle depends linearly on time, hence the angular velocity is constant and the angular momentum is not conserved.
To be correct, should be used, but that would imply solving differential equations, which would slow the simulation.
With the simplified approach taken here, instant velocities are not accurate and only averaged velocities (over a complete revolution) have meaning, which is sufficient for this model (the ratios of orbital periods are accurate, so Jupiter is still ~12 times slower than Earth).
The idea for this toy scale explorer solar system came from Laurent Nottale's Scale Relativity.
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