I have a need to train a model on various trajectory data of flying objects (for clustering purpose).

I found trajectory data of air planes online. But since trajectory data for missiles, satellites and other objects like fighter jets are not made public, I will need to make some dummy data.

Does anyone know how I can generate dummy trajectory data.

Trajectory data needed is (Longitude, Latitude, Altitude and Time)

This is a dataset for Aircraft I found, but here I am asking about spacecraft.

Note: I only need (Longitude, Latitude, Altitude and Time), other data in above airplane dataset is not required


I think it might be possible to create different trajectories based on feeding random value to variable of some equation, and if I change some constants, I get slightly different dataset for same type of object. And if I change some powers I will get trajectories for some different objects.

Are there any equations that are used to define trajectory of any flying objects?

  • $\begingroup$ If you are asking for the RCS of various aircraft, then most certainly that will be classified for most military items. You might find info in Jane's series of military data. But since you asked for position vs. time, I'm confused: that has nothing whatsoever to do with an aircraft's radar signature. $\endgroup$ Mar 31, 2020 at 14:23
  • $\begingroup$ @CarlWitthoft As I said I want to use position vs time data to cluster the objects. Every object follows unique pattern based on trajectory. And I think that such position (Alt, lat, long) data is obtained from radar. Problem is I dont know how to simulate such data. $\endgroup$ Apr 1, 2020 at 4:34
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    $\begingroup$ I think this question is not really on topic here, but in any case: there's not much to it. A rotating radar observes a target once every rotation. If it rotates once every 10 seconds (6 RPM), then you have an observation once every 10 seconds, with every observation being a range and angle relative to the radar (plus possibly radial velocity if it is a Doppler radar). So generate a trajectory and create corresponding observations every 10 seconds. Add some noise and you have yourself a simulated radar. $\endgroup$
    – Ludo
    Apr 1, 2020 at 7:16
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    $\begingroup$ @Ludo I will simulate data at certain time interval as you said. But I need help finding some equations in which I change certain constants and get different trajectory data for similar object. And if I change the power of variable I can get somewhat different trajectory which will belong to some different object. $\endgroup$ Jul 5, 2020 at 5:30
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    $\begingroup$ @uhoh Thanks for the bounty. I have faith in community. $\endgroup$ Jul 6, 2020 at 10:56

1 Answer 1


It seems like you want to generate some Monte Carlo trajectories. I would recommend a tool which is designed for Monte Carlo analyzes: such a tool would allow you to write a script which quickly changes the inputs and run the scenario without any human intervention.

nyx: a mission design, orbit determination and Monte-Carlo tool

Important disclaimer: I am the author of nyx.

Specifically, I would recommend using nyx, whose API documentation is here and source code here. I wrote it because I was unsatisfied with the tools I used at work. Nyx is used on an upcoming mission to the Moon, and for numerous trade studies. It's extremely fast compared to other tools out there.

It has been validated against NASA GMAT for the most part, JPL Monte for some other parts, and the algorithms come from books by Vallado or Schaub. One of advantages of nyx is that you can execute a scenario simply by providing a TOML configuration file. The disadvantage is that, for the time being, you still need to compile the code yourself (but fear not, this should only require a few steps!).


  1. Install the Rust programming language: https://www.rust-lang.org/learn/get-started
  2. Download the source code from gitlab (either via git clone or by downloading a ZIP file).
  3. Build nyx by typing the following in a command line: cargo run --release -- -h . This step will take a few minutes to build all of the dependencies.

Setting up a scenario

Scenarios in nyx are defined in a TOML file. You can define the initial state in Cartesian, the spacecraft mass, the dynamics it is subjected to, the output file, and the data stored in the output file.

As nyx is in heavy development, I have not had time to produce quality documentation yet. Apologies for that.

A list of valid output headers form the API documentation is found here and the valid date time formats are here.

ISS TOML example

In this example, the headers are set to latitude (degrees), longitude (degree), altitude (meters) and time in Gregorian UTC.

sequence = ["iss"]

x = 8.59072560e2
y = -4.13720368e3
z = 5.29556871e3
vx = 7.37289205
vy = 2.08223573
vz = 4.39999794e-1
frame = "EME2000"
epoch = "2013-03-18T12:00:00.0 UTC"
unit_position = "km"  # Default value if unspecified
unit_velocity = "km/s"  # Default value if unspecified

integration_frame = "EME2000"
initial_state = "iss_init"
point_masses = ["Earth"]
accel_models = ["my_models"]

dry_mass = 100.0
fuel_mass = 20.0
orbital_dynamics = "iss"

dynamics = "iss"
stop_cond = "1.0 days"
output = "my_csv"

frame = "EME2000"
degree = 70
order = 70
file = "data/JGM3.cof.gz"

filename = "./data/iss.csv"
headers = ["geodetic_latitude", "geodetic_longitude", "geodetic_height", "epoch:GregorianUtc"]


Executing the scenario above outputted this for me:

cargo run --release -- data/iss-example.toml
    Finished release [optimized] target(s) in 0.06s
     Running `target/release/nyx data/iss-example.toml`
 INFO  nyx > Loaded scenario `data/iss-example.toml`
 INFO  nyx_space::celestia::cosm > Loaded 14 ephemerides in 0 seconds.
 INFO  nyx_space::celestia::cosm > Loaded frame iau moon
 INFO  nyx_space::celestia::cosm > Loaded frame iau neptune
 INFO  nyx_space::celestia::cosm > Loaded frame iau sun
 INFO  nyx_space::celestia::cosm > Loaded frame iau jupiter
 INFO  nyx_space::celestia::cosm > Loaded frame iau mars
 INFO  nyx_space::celestia::cosm > Loaded frame iau saturn
 INFO  nyx_space::celestia::cosm > Loaded frame iau earth
 INFO  nyx_space::celestia::cosm > Loaded frame iau uranus
 INFO  nyx_space::celestia::cosm > Loaded frame iau venus
 INFO  nyx_space::io::gravity    > data/JGM3.cof.gz loaded with (degree, order) = (70, 70)
 INFO  nyx                       > Executing sequence `iss`
 INFO  nyx_space::md::ui         > Saving output to ./data/iss.csv
 INFO  nyx_space::md::ui         > Propagating for 86400 seconds (~ 1.000 days)
 INFO  nyx_space::md::ui         > Done in 1.060 seconds

Output data

The first few lines of the CSV output file are the following:

5.1743091733434703e1,2.8555208350652231e2,4.1005867561649302e2,2013-03-18T12:00:36.738469123 UTC
5.1773299102335201e1,2.8928957847423612e2,4.1036548039617810e2,2013-03-18T12:01:12.527183055 UTC
5.1684646521754630e1,2.9302878309228544e2,4.1065234870355107e2,2013-03-18T12:01:48.381568908 UTC

How to generate your data set

That's up to you ;-) From what I understand, you need lots of data. So I would write a simple script (in Python for example) to modify the X, Y and Z coordinates of the TOML above using a random normal variable with a 1-sigma of 20 km. If you modify by more than that, the velocity components could be quite wrong, and you might not have a truly representative orbit. I would then code another script which would launch several subprocesses to run cargo run --release ... for each of the TOML files you generated.

  • $\begingroup$ Running you example file, I am getting output with very different magnitude than waht you said. See this $\endgroup$ Jul 16, 2020 at 5:17
  • $\begingroup$ @thisisjaymehta it seems like the configuration file you used is not using the correct output headers. Can you post a link to your configuration file? We can also converse using the service desk whose email can be found on this pastebin . $\endgroup$
    – ChrisR
    Jul 17, 2020 at 6:09
  • $\begingroup$ Heres the configuration TOML file $\endgroup$ Jul 17, 2020 at 10:04
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    $\begingroup$ @thisisjaymehta The last line of the TOML configuration you posted specifies the headers in the output file. You want those to be headers = ["geodetic_latitude", "geodetic_longitude", "geodetic_height", "epoch:GregorianUtc"] instead of the ones you currently have. $\endgroup$
    – ChrisR
    Jul 17, 2020 at 19:40

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