Ephemeris Explorer aims to be a multi-purpose interactive simulation of gravitationally bound systems, be it stellar systems, planetary systems or satellite systems. It uses concepts from various research, notably Numerical Representation of Planetary Ephemerides to generate accurate1 trajectories of celestial bodies and presents them in an interactive manner using the Bevy Engine and egui.
Simulations are achieved by separating objects into two categories: massive objects (celestial bodies) that affect other objects and massless objects (spacecrafts) that do not. This separation allows for the prediction of the trajectory of massless objects to be decoupled from the actual simulation of a system and other massless objects. The trajectory of massives objects is computed first for a given time span, which allows for the evaluation of the position of all objects at any time in that span. The trajectory of massless objects can then be computed in that time span quickly and accurately.
Epemeris Explorer is still in early development. The scope of the project is simply to provide a tool for experimenting with gravitationally bound systems with no significant scientific intent, at least not in the current state. As such, the project is open-source and contributions are welcome.
The camera can be moved using the WASD keys, Q and E for roll, as well as Space and Left Control to move up and down. The up and down arrow keys allow to change the FOV. The mouse can be used for pitch and yaw when the left mouse button is held down.
You can also use orbit controls around the followed body by holding the right mouse button.
The left panel provides a hierarchical view of the celestial bodies within the current system. Clicking the ⌖ allows setting the reference frame of the camera. You can toggle trajectory plotting using the ○ button.
Clicking a body's name or a body in the viewport selects it and allows you to read information about the body and configure plotting.
Spacecrafts are dynamically moved in the hierarchy depending on which body's sphere of influence they are in.
When a body is selected, information about the current state of the body is displayed. You can also configure the plotting of the body's trajectory. Changing the Reference of the body changes some of the displayed information and changes the reference frame of the body's trajectory.
If the body is a ship, you can also export it and its flight plan to a file and delete it from the current system.
Allows to add manoeuvres to ships. Manoeuvres are defined by a start epoch, a duration and an acceleration in a reference frame. Using the same window that displays body information, you can add, remove and edit manoeuvres. When a manoeuvre is changed, the trajectory of the ship is recomputed asynchronously. If the flight plan is shorter than the current prediction bounds, the ship will freeze at the end of its trajectory.
Allows to extend the ephemerides forward or backward in time independently and asynchronously by selecting start and end epochs. You can pause and cancel ongoing predictions. By default, predictions will auto-extend when the current time approaches the prediction bounds.
You can hover over or click on the trajectories to display information about the body at that point in time as well as adding manoeuvres for ships. Multiple points might be selected when picking a trajectory if the points are close together and belong to the same body.
Allows to change the speed of the simulation, pause it or set the epoch.
Allows to spawn ships in the system. Ships are defined by a name as well as a position and velocity within a reference frame. You can also import a ship and its flight plan from a file.
Allows to export the current state of the system to a file, selecting which bodies are included.
Allows loading a system from a directory. The directory should contain four files: ephemeris.json for the ephemerides configuration, hierarchy.json, state.json for the initial state of the system, and a skybox.png. The initial state file should be a JSON containing the state of the system. See export-solar-system for a python program that generates such files using NASA's development ephemerides and skyfield. It should be formatted as follows:
{
"epoch": "2000-01-01 00:00:00 TAI",
"bodies": [
{
"name": "Name",
"mu": 100.0,
"position": [1.0, -2.0, 2.0],
"velocity": [3.0, -2.0, 1.0]
}
]
}Displays information about each trajectory such as their bounds or their size. Useful when creating a system.
Generating accurate ephemerides for a given system requires the configuration of the following parameters:
- A starting epoch, for which the state vectors of the bodies in the system are provided, as well as their gravitational parameters. This data is loaded with the
state.jsonfile. - A time step or delta time
dtand for each body the sample countcountand the degreedegof the piecewise polynomial interpolation. This data is loaded with theephemeris.jsonfile. For now, the parameters need to be hand-tuned for each system to ensure the accuracy of the ephemerides. You can compute an estimate of the error from the interpolation in theEphemerides Debuginterface.
The initial state is used as the starting point for the generation of the ephemerides, whilst the other parameters define the accuracy of the ephemerides. More specifically, each polynomial of degree deg is interpolated using 9 samples from the numerical integration. The sample count count and the delta dt define the distance between each of these samples. For example, with dt = 1 min, the resulting trajectory of a body with count = 10 will be made of polynomials that have been interpolated with 9 samples at t = 0 min, t = 10 min, ..., t = 80 min. As such, each polynomial will be valid for 8 * count * dt and the delta between each sample will be count * dt.
Currently, the interpolation is done using a least squares polynomial fit using the poly_it crate.
This implementation was custom made for this project and is not validated in any way. It is also better suited to stable trajectories and incorrect configuration of a system will result non-continuous polynomials within the trajectories.
Footnotes
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The accuracy of the current implementation is limited by the fact that the acceleration computation does not take into account general relativity and all bodies are considered to be spheres with an homogeneous mass distribution. ↩
