Utilizing orbital mechanics for a celestial system visualization in Three.js with coordinates (x,y,z) for planetary bodies

Question

Utilizing orbital mechanics for a celestial system visualization in Three.js with coordinates (x,y,z) for planetary bodies

Currently, I am developing a Solar System visualization in Three.js. While my planets currently have basic circular orbits, my goal is to create a realistic model. Despite researching information on wiki and other articles, the content is quite advanced for me.

I am not concerned with tracking the orbits over thousands or millions of years. Instead, I aim to achieve a model that closely resembles reality, showcasing:

Accurate elliptical orbits
Inclination
Dynamically changing speed (faster at perihelion)

I am curious if there is a sufficiently complex method to calculate x,y,z coordinates for my planets at any given time t, with this time dynamically changing, possibly utilizing orbital elements.

I hope I have effectively communicated my concept. Thank you.

javascript math three.js visualization orbital-mechanics

Answer 1

Answer №1

Consider exploring a two-dimensional projection of the orbital paths. By doing so, you can simplify by parameterizing the ellipse as a vector function denoted as ɣ(x(t), y(t)).

For a more physical approach, envision two centers of mass: the sun M and a specific planet μ. The force acting on the planet F can be calculated using F=GμM/|ɣ|², leading to acceleration determined by Newton's second law, a=GM/|ɣ|², always directed towards the larger mass, M.

To define the curve ɣ accurately, reference equations provided at http://en.wikipedia.org/wiki/Ellipse#Equations

Answer 2

Consider exploring a two-dimensional projection of the orbital paths. By doing so, you can simplify by parameterizing the ellipse as a vector function denoted as ɣ(x(t), y(t)).

For a more physical approach, envision two centers of mass: the sun M and a specific planet μ. The force acting on the planet F can be calculated using F=GμM/|ɣ|², leading to acceleration determined by Newton's second law, a=GM/|ɣ|², always directed towards the larger mass, M.

To define the curve ɣ accurately, reference equations provided at http://en.wikipedia.org/wiki/Ellipse#Equations

Answer 3

Answer №2

If you are satisfied with a rough estimate to highlight key components, consider creating a lookup table for all planets over several years. For example, calculating the orbital period of Neptune which is 164 years can allow you to determine the positions of each planet every month within that timeframe to compile a manageable table size. To visualize the changes in orbital speed more accurately, finer resolution is necessary. Once the calculations are complete, constructing an animation to showcase the planetary positions is the next step.

The computations involved in this process are complex and detailed. Rather than going through each calculation here due to its length, you can find a comprehensive explanation here, along with a sample program coded in QBasic.

The fundamental steps include:

1. Determining the position of the planet in its orbit 2. Calculating the number of days since the elements' date 3. Finding the mean anomaly based on the Mean Longitude and daily motion 4. Obtaining the true anomaly using the Equation of Centre 5. Establishing the radius vector of the planet

After referencing this position to the Ecliptic, ascertain the heliocentric ecliptic coordinates of the planet.

Once you have the heliocentric coordinates, convert them to your specific frame of reference. The provided page demonstrates this transformation for geocentric coordinates, but you will need to adapt it accordingly for your needs. Incorporate these transformed coordinates into your table.

You may opt to run the calculations in real-time, offering more flexibility but potentially impacting the frame rate. It might be beneficial to conduct some trial and error experiments in this regard.

A special thanks to Keith Burnett (the author of the linked page) for providing the detailed information summarized above.

Answer 4

If you are satisfied with a rough estimate to highlight key components, consider creating a lookup table for all planets over several years. For example, calculating the orbital period of Neptune which is 164 years can allow you to determine the positions of each planet every month within that timeframe to compile a manageable table size. To visualize the changes in orbital speed more accurately, finer resolution is necessary. Once the calculations are complete, constructing an animation to showcase the planetary positions is the next step.

The computations involved in this process are complex and detailed. Rather than going through each calculation here due to its length, you can find a comprehensive explanation here, along with a sample program coded in QBasic.

The fundamental steps include:

1. Determining the position of the planet in its orbit 2. Calculating the number of days since the elements' date 3. Finding the mean anomaly based on the Mean Longitude and daily motion 4. Obtaining the true anomaly using the Equation of Centre 5. Establishing the radius vector of the planet

After referencing this position to the Ecliptic, ascertain the heliocentric ecliptic coordinates of the planet.

Once you have the heliocentric coordinates, convert them to your specific frame of reference. The provided page demonstrates this transformation for geocentric coordinates, but you will need to adapt it accordingly for your needs. Incorporate these transformed coordinates into your table.

You may opt to run the calculations in real-time, offering more flexibility but potentially impacting the frame rate. It might be beneficial to conduct some trial and error experiments in this regard.

A special thanks to Keith Burnett (the author of the linked page) for providing the detailed information summarized above.

Answer 5

Answer №3

Check out this C++ code snippet for accomplishing a specific task. Although it doesn't involve taking a date as a parameter, you can achieve the desired outcome by replacing the i value appropriately. I personally used this code to illustrate the orbital path around the sun.

double x = distanceFromSun * orbitScaleFactor;
double y = sin(inclination) * distanceFromSun * orbitScaleFactor;
double z = semiMinorAxis * orbitScaleFactor;

for (double i = 0; i < 2.0 * PI; i += PI / 32.0) {
    x = cos(i) * x;
    y = cos(i + lonOfAscendingNode) * y;
    z = sin(i) * z;
}

P.S. Despite your query being related to JavaScript, I didn't hesitate to provide C++ code as I believe the formula is what truly matters in this case.

You can view the complete code on my GitHub repository: https://github.com/SyntaxRules/SolarSystemSimulation/blob/master/src/Planet.cpp

All variable information can also be found there. Enjoy! :)

Answer 6

Check out this C++ code snippet for accomplishing a specific task. Although it doesn't involve taking a date as a parameter, you can achieve the desired outcome by replacing the i value appropriately. I personally used this code to illustrate the orbital path around the sun.

double x = distanceFromSun * orbitScaleFactor;
double y = sin(inclination) * distanceFromSun * orbitScaleFactor;
double z = semiMinorAxis * orbitScaleFactor;

for (double i = 0; i < 2.0 * PI; i += PI / 32.0) {
    x = cos(i) * x;
    y = cos(i + lonOfAscendingNode) * y;
    z = sin(i) * z;
}

P.S. Despite your query being related to JavaScript, I didn't hesitate to provide C++ code as I believe the formula is what truly matters in this case.

You can view the complete code on my GitHub repository: https://github.com/SyntaxRules/SolarSystemSimulation/blob/master/src/Planet.cpp

All variable information can also be found there. Enjoy! :)

Utilizing orbital mechanics for a celestial system visualization in Three.js with coordinates (x,y,z) for planetary bodies

Answer №1

Answer №2

Answer №3

Similar questions

Instructions on extracting a random element from an array and continue removing elements from the array until it is completely empty

Tips for keeping your button fixed in place

How can the Angular.js Service Factory module be configured to yield the inner code as a function?

Create an array populated with unclosed HTML tags that need to be rendered

Creating a new dynamic page can be achieved by clicking on a dynamically generated link. Would you like to learn how to do that?

Enhance precision with autofocus feature while utilizing Quasar's Q-Field validation

Is there a method available to identify browser compatibility problems within my JavaScript code?

Update the VueJS application by loading and replacing the existing JSON data with new information

Creating internal utility functions in Angular without exporting them as part of the module can be achieved by following a

Exploring History Navigation with AngularJS: Leveraging $routeParams and $location

What is the best approach for writing an asynchronous function while utilizing $rootScope.broadcast within a continuous loop?

Cursor-hugging tooltip

Leveraging ajax and jQuery for the implementation of PHP functionalities

Navigating with nodeJS

Tips on viewing class object values within the `useEffect` hook

Fresh Regular Expression created from a readable string

What could be causing the lack of updates to my component in this todo list?

Should we designate the array index as the unique identifier for React components?

dc.js bar graph bars blending together

Can you explain the distinction between the controls and get methods used with the FormGroup object?