Creating an orbit for a planet and place the planet on it

To create a planetary orbit and place a planet on it so that one can calculate precise position of the planet at a given time can be done by using Orbital Elements. You can read detailed information about them from this wikipedia page. In this guide, I will show detailed steps on how to do the calculation and implement it in Blender or Unity.

There are six parameters in orbital elements that are closely related to the 3-D positions and 3-D velocity of a planet.

In this diagram, the orbital plane (yellow) intersects a reference plane (gray). For Earth-orbiting satellites, the reference plane is usually the Earth's equatorial plane, and for satellites in solar orbits it is the ecliptic plane. The intersection is called the line of nodes, as it connects the center of mass with the ascending and descending nodes. The reference plane, together with the vernal point (♈︎), establishes a reference frame [from Wikipedia].
  • semi-major axis ($a$): determines the size of an orbit. For a given mass of the central object (e.g., Sun), $a$ is directly related to an orbital period ($P$) through Kepler's 3rd law.
  • eccentricity ($e$): shape of the ellipse. In an elliptical orbit, Sun is located at one of two foci.
  • inclination ($i$): the tilt angle of the orbital plane with respect to observer's line of sight.
  • longitude of the ascending node ($\Omega$): In an inclined orbit (i.e., non-zero $i$), there are two points where a planetary orbit crosses the plane of reference. We choose one of these points as $\Omega$ where a planet moves from below the reference planet to above the plane.
  • argument of periapsis ($\omega$): determines the orientation of the ellipse in the orbital plane. From the focus where the Sun is located at, the direction toward the periapsis can be anywhere on the plane. An angle measured from the ascending node to the periapsis can fix the orientation of the ellipse.
  • true anomaly ($\nu$): the position of the planet measured in angle from the periapsis for a given time (or epoch).
Simulation showing each orbital element (from pyorb site)


Check the Wikipedia for “Orbit Modeling” for useful information.

From a given set of orbital elements, let's see how we can calculate the planet's position at a given time $T$. At any arbitrary epoch (say $T=0$), orbital elements can be expressed as $(a_0,e_0,i_0,\Omega_0,\omega_0,\nu_0)$. Since the first five parameters do not change over time (without a perturbation like additional object), at a later time ($T+\delta T$), we only need to find the new $\nu$; i.e., at $T=T+\delta T \equiv new$, we have $(a_0,e_0,i_0,\Omega_0,\omega_0,\nu_{new})$ where $\nu_{new}=\nu_0 + \delta\nu$.

In this calculation, the reference plane is denoted as $(\hat{I},\hat J,\hat K)$ where $\hat I$ is the direction toward the vernal equinox and the orbital plane is denoted as $(\hat x,\hat y,\hat z)$ where $\hat x$ is toward the periapsis and $\hat z$ is toward the north pole. In the Solar System, we choose the ecliptic plane as the reference plane.

Then, the transformation between the reference plane and the orbital plane is defined by three Euler rotations.

where the new $xyz$ values are

There is a Python package called pyorb that can calculate Keplerian (i.e., $xyz$) from reference ($IJK$) or vice versa.

A good introduction on the whole calculation step (and the visualization of the orbital elements) is available from this YouTube video.

Check this YouTube video for Keplerian orbital elements and Euler Angles:

Tutorials for Beginngers

This introduction to blender documentation prepared by Michael Cai will be useful for students new to 3D programming.

Use this link to convert the Google Doc tutorial shown above to a DW content. offers many Blender tutorials. </panel>

Useful tips for creating objects in the Blender night sky

A preliminary version of the celestial sphere simulation by using NASA HDRI maps as the Blender World Background Texture was created and the tutorial on how to create such “Night Sky World” is shown in Simulating Celestial Sphere in Blender.

  • You need to download relevant NASA star maps and link them in the node editor to see the starry background.
  • In Blender rendering, because we are rendering only the changes of the background pixelated images (and no 3-D object), we can turn off ray tracing (Render → Light Paths → max bounce = 1) and set the cycles render's sampling to be 1 (Sampling → Render → Max Samples = 1). Then, it should take less than 10 sec per scene (~20 min rendering for 240 frame animation).

See these examples for creating a virtual, realistic, night sky in Blender:

  • Check this 3D Star Map Add-on in Blender which uses a dataset of real nearby ~3,000 stars. This also shows how to simulate a night sky (i.e., celestial sphere). A free demo version has 299 stars without constellation markings. ⇒ This shows a good tip on how to display texts on the scene (text fixed with respect to a camera)
  • NASA image as the HDRI background with constellation lines: Blender-Night-Sky ⇒ This demo also provides a Blender file that shows tips on how to use dynamic camera control (i.e., dynamically changing camera position, origin [i.e., camera field-of-view], etc.)
  • Blender 3.? and later versions provide a Geometry Node which can be used in simulating a planet in a orbit around its central star. Check this tutorial: Using orbital elements from JPL (, one can do a decent planetary orbit simulation.
  • Check this GitHub page showing a Blender package for simulating Solar System from orbital elements.
    • This package can simulate an orbit of a planet around a central star with all user-configurable physical parameters (mass, rotation rate, rotation axis tilt angle, orbital elements, etc.).
    • This package also display animated orbital elements annotations in the 3D render.

Simulate/Visualize Orbital Motions

Blender Add-ons for Space Scene

Python in Blender

Good tutorials from YouTube on Python in Blender

2024/04/20 13:31 · song

Check SimpleKeplerOrbits

There is a free asset called, SimplerKeplerOrbits, in the Unity asset store. It has three sample scenes and we can use this package to create a nice Solar System simulation. Especially, check Example 3 in the included scenes which allows users' tilting and zooming actions in the rendered window (i.e. in the GamePlay mode), and it also allows to set the observing date (set to “now” automatically). There is a UI slider that can speed up and go backward in time as well. Nice! We can recycle most of these in our 3-D model.

We can create a realistic Solar System model with three free Unity assets (Simple Kepler Orbits, Planets of the Solar System, and MilkyWay). Follow the sequence of operations below to create one.

  1. Start a new 3D Unity project
  2. Set project setting (Edit → Project Settings; pay attention to Graphics [Rendering], Quality etc.)
  3. Import necessary assets (Package Manager: Install assets from My Assets)
  4. In the main camera setting, choose the right Renderer and select “Post Processing”. Choose the MilkyWay skybox (drag one on the main camera).
  5. Create three objects (two spheres and one object). You can drag and drop Sun and Earth from “Planets of the Solar System”. One sphere is an attractor (i.e., the central star), the other sphere is an orbiting object (e.g., Earth), and the 3rd object is a velocity indicator.
    1. Drag and drop “KeplerOrbitMover” script on the orbiting object. Drop “KeplerOrbitLineDisplay” on the orbiting object as well if orbits need to be displayed with curves.
    2. Then, select the central object as the attractor and set the right mass value.
    3. Set velocity handle, length scale, and time scale.
  6. Render and you can see an animation.
  1. For faster script load, check “Fast Script Reload” asset.

Procedural (Script-based) Sun-Earth-Moon Model Creation

Click here to see detailed step-by-step procedure to create a Sun-Earth-Moon model

2024/04/25 14:16 · song

Sample WebGL model of the Sun-Earth-Moon System

This embedded WebGL rendering of the Sun-Earth-Moon system created with Unity can be played in any modern web browser. The right mouse button can tilt/rotate the scene, the middle mouse button scroll adjusts a zoom level. Click the image below to access the model.


Setup VR with a Quest Headset


  1. Create a Meta account
  2. Enable Developer mode
  3. Enable Quest Link
  4. Meta Quest Developer Hub (MQDH)

MicroSoft also has this tutorial: MS + Quest

Creating AR

This video describes the steps to create an AR video using Unity. Blender files can be imported to Unity.
This video demonstrates an example AR model.

Render 2+ camera views

Create cameras as you need. Then, change the “Viewport Rect” (Width and Height and X & Y) to set the desired location and size you need. In the render view then, you will have more than one camera views.

Display UI info and tools

You can add many UI components in three different ways in Unity by changing the “Render Mode”: (1) screen overlay (always displayed on screen), (2) camera space (displayed over camera view), and (3) world space (as if they are regular objects).

2024/04/20 13:31 · song

Space scene in Unreal Engine 5.x

Check these tutorials for UE5

2024/04/20 13:32 · song