Planets on an elliptic curve

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The formulas for elliptic curves and elements moving along such a path can be found here:
Tutorial: Elliptic Motion

The challenge on this watch face was not the height and width of the elliptic curves - these are 1-to-1 from a drawing in CorelDraw. The speed of the planets relative to each other however is not straight forward. The planet with the fastest orbital velocity is Mercury and the slowest is the one furthest away: Neptune. In the elliptic path formulas, however, Mercury has the smallest factor.

Example:
Mecury:
X: (((sin((-(#DWFSS#+20)/20)*pi))*50)+160)
Y: (((cos((-(#DWFSS#+20)/20)*pi))*21)+92)

Earth:
X: (((sin((-(#DWFSS#+38.2)/38.2)*pi))*70)+160)
Y: (((cos((-(#DWFSS#+38.2)/38.2)*pi))*27)+92)

Watch facer (open for inspection):

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Great work, design, and explanation; nicely done my friend :+1:

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Wow!!! I really love this!!!

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Nice job Tom!

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Golly Gosh . Thank you Tom . Fantastic Tutorial and Gifts . This is what makes this Community the best anywhere :::)))

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That is really fantastic. Maybe an isometric version coming soon?

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Oh no, now you got me thinking what that could look like… :slight_smile: I only found you and another partner that have actually done isometric faces, so maybe I’ll join the club…

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Whatever you do, don’t make an isometric face for syncs…lol

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Awesome Tom! Masterclass! I love this one!

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Deos this one count as isometric? Ok I know it’s more of a parallax thing but hey ’ it’s sort of isometric! :upside_down_face:

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I had to give it a go … Each color is 5 secnds:

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Very clever. The ellipse itself is nicely mapped out, but the real trick is in the divisor: the smaller Mercury value makes the angle change faster. Tiny planet, tiny divisor, big hurry :ok_hand:

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Pretty

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Nice job Tom!

This is exactly the kind of project that reminds me how powerful formula-based watch face design can be. Most people see the planets moving, but the clever part is all the maths underneath making each orbit behave differently.

The more creators experiment with things like elliptical motion, physics, and procedural animation, the more they start pushing beyond what most watch face tools were originally designed for. Really impressive work.

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