Rotational Planes

Hello Community,

Attached is definition that has a sphere travel along a path in the X direction.

“Capture 1.png” shows the orientation of the orbiting sphere and my hope for understanding.
Item 1 shows the orbit orientation in the XY plane while travelling along the X direction.

Item 2 shows my first preference of trying to orientate the orbit perpendicular to the direction of travel. I have tried to determine an axis by creating a line (from center outward) but it seems the orbit gets shifted and not based on the origin of the (blue) sphere.

Item 3. Is it possible the rotational axis can be controlled to any direction within XYZ?

This definition uses Rhino 5/GH

Thank you for your help. (14.9 KB)

White group. Substitute any other plane instead of World YZ. (21.1 KB)

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Thank you kindly Joseph! Just what I was looking for.

The yellow group with ‘Azimuth’ and ‘Altitude’ sliders implements part two of your request: “any rotational angle in xyz”. In other words, you choose the plane in which the orbit (circle) is drawn. (26.3 KB)

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Another go at ‘Pan’ and ‘Tilt’ sliders affecting the circle’s (orbit’s) orientation. (22.4 KB)

The next question, of course, is how to have the cyan sphere (a planet) follow an ellipse while the “moon” (purple sphere) orbits the planet on an arbitrary plane? … :thinking:

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P.S. (Sorry @wim, the forum software gives me no other choice but “P.S.” here since I used up my three replies.)

This version scales the model to Earth, Moon and Sun dimensions. A yellow group “magnifies” size of earth and moon by a factor of ten to see them better. (29.8 KB)

‘scale_EO’ slider in cyan group reduces size of earth orbit, which is vast relative to moon orbit.

Distances are measured in thousands of miles:

  • earth radius: 3.963
  • moon radius: 1.0794
  • moon orbit: 239 (the one that can’t be scaled)
  • earth orbit:92960 (92.96 million miles, scaled to 0.02 as shown)

Happy Winter Solstice (yesterday)

P.P.S. December 26. Unable to post further in this thread due to forum restriction:


So… Added Starlink satellite constellation to previous (updated) Earth/Moon/Sun model: (35.8 KB)

24 orbital planes of 66 satellites each

source: Orbit of the Moon


Not surprised to find Joseph Oster here, brilliant as ever… I know this is resolved, but is there a definition to simulate the gravitational rotation as ellipsis rather than circular? ( via sine and range probably ?)

Gee, thanks. :blush:

A fully accurate model is way more complex than this, of course, but you could replace the circular orbits with ellipses and move their seams with the timer, like this: (gray group labeled “Inclined Ellipses”) (38.0 KB)

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